1 School of Mechanical and Electrical Engineering China University of Mining and Technology Xuzhou 221116 China2 Xuyi Mine Equipment and Materials RampD Center China University of Mining and Technology Huairsquoan 211700 China
Correspondence should be addressed to Xiao-hu Chen cxiaohu503163com and Zhong-bin Wang zhongbin wangsinacom
Received 19 January 2014 Revised 28 May 2014 Accepted 16 June 2014 Published 6 July 2014
Academic Editor Chia-Feng Juang
Copyright copy 2014 Xin-hua Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
In order to improve the performance of robot dexterous hand a controller based on GA-fuzzy-immune PID was designed Thecontrol systemof a robot dexterous hand andmathematicalmodel of an index fingerwere presentedMoreover immunemechanismwas applied to the controller design and an improved approach through integration of GA and fuzzy inference was proposed torealize parametersrsquo optimization Finally a simulation example was provided and the designed controller was proved ideal
1 Introduction
In the past few years massive research is committed to studythe anthropomorphic robot hands with dexterous manip-ulation abilities As an important tool to improve the intel-ligence and manipulation levels of robots multi-DOF andmultisensory robot dexterous hand has become one of themost promising researches in robot field [1 2]The robot dex-terous hand could distinguish objects with different materialsand shapes and snatch them successfully through the controlsystem Therefore the robustness and control accuracy of acontrol systemwould play an important role in evaluating theperformance of a robot dexterous hand [3]
Nowadays robot dexterous hands have been used inmany fields such as industry field agriculture field servicefield andmedical rehabilitation field However most of themhave some common disadvantages such as slow responsepoor flexibility weak anti-interference ability and poor con-trollability [4 5] To the best of our knowledge the problemofrobust and intelligent control for a robot dexterous hand hasalmost not been dealt with Based on our past researches onrobot dexterous hands and control methods this paper triesto tackle this problem
Bearing the above observation in mind a GA-fuzzy-immune PID (genetic algorithm-fuzzy- immune proportion-integration-differentiation) controller with incomplete deri-vation for robot dexterous hand is developed and the rest of
this paper is organized as follows In Section 2 some relatedworks are outlined based on the literatures The controlsystem of a robot dexterous hand and mathematical modelof an index finger are presented in Section 3 In Section 4the GA-fuzzy-immune PID controller is designed and someimprovements are proposed Section 5 provides a simulationexample to verify the feasibility and efficiency of proposedcontroller Our conclusions and futureworks are summarizedin Section 6
2 Literature Review
Recent publications relevant to this paper are mainly con-cerned with three research streams robot dexterous handcontrol methods PID control methods and fuzzy-immunityfeedback control methods In this section we try to summa-rize the relevant literatures
21 Robot Dexterous Hand Control Methods For the robotdexterous hand control methods many researchers hadworked on the problem and proposed different solutionssince the last decades As early as in 1962 a robot dexteroushand named after Belgrade was designed by Tomovic andBoni based on the most advanced control theory which wasconsidered to be the real significance dexterous hand [6]Nowadays with the development of computer technology
Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 564137 10 pageshttpdxdoiorg1011552014564137
2 The Scientific World Journal
microelectronics technology and advanced control theoryrobot dexterous hand has entered a new period Jafarovet al [7] took both sliding and stability issues into accountto present an augmented sliding surface design for robothand In [8] a new variable structure PID controller designapproach was considered for the tracking stabilization ofrobot motion Atia [9] designed a new nonlinear PID slidingmode controller for set-point control of robot hand whichensured that the error tended to zero asymptotically if therewas no disturbance applied to the robot dynamics Chenet al [10] presented two types of adaptive control programcombining conventional computed-torque control and dif-ferent fuzzy compensators for the robust tracking controlof robotic manipulators with structured and unstructureduncertainties In [11] a model-free recurrent fuzzy neuralnetwork (RFNN) control system for robot handwas proposedto approximate the ideal backstepping control law whichwas further proved stable by the Lyapunov stability anal-ysis By combining feedback linearization with Lyapunovrsquossecond method and genetic algorithm Hassanzadeh et al[12] designed a robust controller with performance tuningfor robot hand and the stability and robust performance ofproposed controller were verified through a four-bar linkagerobot simulation In [13] two fault-tolerant control strategiesfor robot hand were implemented based on output-feedback119867infin
controller and experimental results illustrated that theimprovements were feasible and efficient
22 PID Control Methods As one of the earliest controlstrategies PID control has been developed to deal withmore complex control problems due to the advantages ofsimple description high dependability strong robustnessand so forth Han [14] proposed a nonlinear PID controllerwith the capability of auto-disturbance-rejection control andcombination of differentiator and extended state observerand transition process overcame the disturbance effectivelyand improved the control performance Besides Su et al[15] applied the method of Han proposed for controlling ofmanipulator successfully Gundes and Ozguler [16] inves-tigated the problem of closed-loop stabilization using PIDcontroller for MIMO plants to show the existence of stabi-lizing PID controllers for MIMO plants Alvarez-Ramirez etal [17] addressed the position regulation problem of robotmanipulators under control input constraints and experimentresults showed that the saturated linear PID control wassemiglobally asymptotically stable Oliveira et al [18] usedHermite-Biehler theorem to establish results on the designof PID controllers for a class of time delay systems Zieglerand Nichols [19] proposed the most well-known Zieglerand Nichols tuning formula for PID parameter tuningChen and Huang [20] presented a method for regulatingPID parameters on line automatically with neural net algo-rithm Neurofuzzy controller and genetic-fuzzy controllerfor second-order control systems were presented to improvethe performance of conventional PID and fuzzy controller[21ndash23] Genetic-fuzzy controller was applied in the drumboiler simulated dynamics to improve the control speedand precision [24] Moreover further improvements for
neurofuzzy controller and genetic-fuzzy controller were car-ried out by genetic-neurofuzzy arithmetic [25ndash27] Kim et al[28] achieved automatic tuning of PID parameters throughintegration of taking 119867
infinas performance index and particle
swarm optimization algorithm Juang and Lu [29] proposedpower-system load-frequency control by fuzzy-PI controllerand simulations on a multiarea interconnected power systemwith different kinds of perturbationswere performed to verifythe performance of the proposed approach Lu et al [30]proposed an evolutionary fuzzy lead-lag control approachfor coordinated control of flexible AC transmission systemdevices in a multimachine power system Tang et al [31] putforward a newmethod integrated with genetic algorithm andfuzzy distance to tune parameters Zheng et al [32] appliedlinear matrix inequalities (LMIs) in PID controller and anumerical example validated the stability of the closed-loopsystems119867
2or119867infinperformance specifications or maximum
output control requirement respectively
23 Fuzzy Immunity FeedbackControlMethods Back to 1986Farmer et al [33] suggested a dynamic model of an immunesystem based on immune network theory firstly and dis-cussed the links between an immune system and other arti-ficial intelligence methods Xin et al [34] designed a fuzzy-immune-PD-type control algorithm for trajectory trackingbased on dynamics nonlinearities of robot manipulator andexperimental results showed that the control scheme hadbetter tracking precision stronger robustness and superiorcontrol performance to conventional PD controller Lei andRen-hou [35] proposed a fuzzy immune algorithm to designa classification system and the results of comparison withother classification schemes demonstrated the effectiveness ofthe proposed immune algorithm Wang et al [36] designeda fuzzy-immune-PID control system based on a mutativescale chaos optimization method to avoid a mass of tuningparameters work in the progress of design An immune-fuzzysliding mode controller (FISMC) was presented not onlyeliminating the synchronous reluctance motor system uncer-tainty but also overcoming the drawback of sign functionand sat function [37] Chang et al [38] presented an effectiveprocedure based on fuzzy logic and immune algorithm for theplacement and sizing of shunt capacitor banks in a distortedpower network Kuo et al [39] proposed an artificial immunesystem (AIS) based on fuzzy neural network (FNN) to avoidfalling into the local optimum and improve the learningcapability
24 Discussion However although many approaches forrobot dexterous hand have been proposed in above litera-tures they have some common disadvantages summarized asfollows Firstly some proposed controllers for self-adaptionrobot dexterous hand need to calculate the inverse of Jacobianmatrix but it is difficult to obtain and would consume muchtime Secondly due to the frictional disturbances at joints andexternal disturbance of payload it is difficult to design a fasterresponse less overshoot and satisfactory robust stabilitycontrol systemThirdly the performance of some methods isactually related to specificweights which is difficult to obtain
The Scientific World Journal 3
Index finger Motor driver
interfaceDC power
Development board based on DSP and CPLD
RS232
Figure 1 The control circuit board of robot dexterous hand and the index finger
Finally because of inherent deficiencies of some methods itis easy to produce premature convergence
In order to solve the above problems a PID positioncontroller based on immunity feedback control theory fuzzyinference and improved genetic algorithm is designed Asimulation example is provided and experiment results showthat the proposed controller can achieve shorter adjusttime better rapidity and higher steady-state precision thantraditional PID position controller
3 Robot Dexterous Hand
31 Robot Dexterous Hand Control System A dexterous hand(named after ABS-I) has been developed in our laboratorywhich is made by the reinforced acrylonitrile butadienestyrene copolymers (ABS) in a 3D printer It is composed ofDC servo motors cup-type planetary gear reducers sensorsIE2-400 encoders complicated programmable logic device(CPLD) and digital signal processor (DSP) unit Figure 1shows the control circuit board of robot dexterous hand andthe index finger
The hierarchical control strategy adopted by the dexter-ous hand control system takes perfect purpose in practiceFeedback data glove or personal computer as the upper mi-crocomputer communicateswith bottom-level block throughserial communication interface (SCI) The top-level block isresponsible for the signal processing of upper microcom-puter and the communicating with bottom-level block Thebottom-level block consists of DSP-CPLD servo controllerSCI circuit motor driver and so forth and it is responsiblefor the signal processing of torque sensors position sensorsand magnetoelectric encoders Moreover it is responsible forcontrolling the pulses and directing signals to drive servomotors The dexterous hand control system can be shown asin Figure 2
32 Mathematical Model for the Index Finger Taking thesingle multijoint finger as an example the equation of DCservo drive motor on armature loop [40] can be introducedas follows
In the single multijoint finger system the Faulhaber1319006SR DC servo motor has some important parametersthat is 119861
119898= 222 times 10
minus4mNmrpm 119870119879
= 419mNmA119877119886
= 826Ω 119871119886
= 130 120583H and 119869119898
= 040 gcm2 Thespeed control system consists of a gearbox and one-gradebevel gear and the gearbox ratio is 415 1 and the bevelgears ratio is 2 1 Moreover by using coupling four-barlinkage mechanism the three phalanxesrsquo transmission ratiois kept exactly 1 1 1 over the whole movement range Thehand material is ABS 119869
119871is set to 1 gcm2 and 119861
119871is set to
4 The Scientific World Journal
CPLD
DSP
DSP
Motor driver 1
Motor n
Motor driver n
Motor 1
Positionsensors
DCpowersource
RAM RS232
CAN bus
sensors Encoder n
Encoder 1
Torque middot middot middot
Figure 2 The robot dexterous hand control system
0002mNmrpmAccording to the parameters we can obtainthe transfer function as follows
119866 (119904) =120579 (119904)
119880119886(119904)
=1
1033 times 10minus61199043 + 6565 times 10minus21199042 + 0731119904
(5)
4 GA-Fuzzy-Immune PID Controller
41 Immune-Based PID Controller Design As a general rulein the discrete-time domain traditional increment PID con-troller can be expressed as follows
119906 (119896) = 119870119901
[
[
119890 (119896) +119879
119879119894
119896
sum
119895=0
119890 (119895) +119879119889
119879Δ119890 (119896)]
]
= 119906 (119896 minus 1) + 119870119901Δ119890 (119896) + 119870
119894119890 (119896)
+ 119870119889(Δ119890 (119896) minus Δ119890 (119896 minus 1))
(6)
whereΔ119890(119896) = 119890(119896)minus119890(119896minus1)119870119901is the proportional gain119879
119894is
the integral time constant 119879119889is the derivative time constant
119870119894= 119870119901119879119879119894 119870119889= 119870119901119879119889119879 119890(119896) is the systematic deviation
between reference input and system output119879 is the samplingperiod and 119906(119896) is the control signal
In general differential signal can be used to improvethe system dynamic characteristics which is likely to causethe problem of high frequency interference to the controlsystem Using low pass filter in control algorithm can bringsignificant improvements in system performance and itstransfer function is 119866
119891(119904) = 1(1 + 119879
119891119904) where 119879
119891is
a filter coefficient The transfer function of PID controllerwith incomplete derivation can be expressed as follows
119880 (119904) = 119870119901(1 +
1
119879119894119904+
119879119889119904
1 + 119879119891119904)119864 (119904)
= 119880119901+ 119880119894+ 119880119889
(7)
In the discrete-time domain differential equation ofPID controller with incomplete derivation can be written asfollows
119890 (119895) + 119870119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(11)
The Scientific World Journal 5
Lymphocyte
T lymphocyte Freeantigen
HelperT cell T cell(TH)
+
minus
minus
AntibodyB lymphocyte
TS(k)TH(k)
Suppressor(TS)
Foreignantigen
+
minus
Figure 3 The immunity feedback control mechanism
As a kind of control system biological immune systemhas very strong robustness and self-adapted ability evenwhenencountering strong disturbances and uncertain conditionsFor invasion by a foreign antigen it can produce correspond-ing antibodies to resist the antigen A series of biologicalreactions could be carried out after combining antigens withantibodies and it eliminates antigen under the function ofphagocyte or special enzymes The immune system consistsof lymphocyte and antibody The lymphocyte consists ofB cell produced from marrow and T cell produced fromthymus T cell includes assistant T cell 119879
119867and restrained T
cell 119879119878 When cell obtains signal from the antigen it would
transmit the information to 119879119867
and 119879119878 and then B cell
produces corresponding antibodies to resist the antigen withthe stimulation by119879
119867and119879119878The immunity feedback control
mechanism is shown in Figure 3According to immunity feedback control mechanism all
of the received simulations of B cell can be obtained
= 1198961(1 minus 120578119891 (119878 (119896) Δ119878 (119896))) 120576 (119896)
(14)
where 119879119867(119896) is the 119896th generation output of 119879
119867cell which
receives antigen presenting cell activation 119879119878(119896) is the 119896th
generation restrain action on B cell by 119879119878cell 120576(119896) is the 119896th
generation antigen amount 1198961is enhancing factor of 119879
119867cell
1198962is inhibitory factor of 119879
119878cell and 120578 = 119896
21198961 119891(lowast) is a
nonlinear function which describes the immunity result thatB-cell antibody and antigen act on each other and relate withthe amount of B cell
In this paper we try to apply bodyrsquos immune mechanismto the ABS-I position controller to overcome the weaknessof traditional PID controller For a PID controller we assumethat position error 119890(119896) on the 119896th sampling period represents120576(119896) the position controller output 119906(119896) on the 119896th samplingperiod represents 119878(119896) Therefore Δ119906(119896) = Δ119878(119896)
In the synthesis the immune PID controller with incom-plete derivation can be obtained
119906 (119896) = 1198701015840
119901119890 (119896) + 119870
1015840
119894
119896
sum
119895=1
119890 (119895)
+ 1198701015840
119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(15)
1198701015840
119901= 1198701(1 minus 120578
1119891 (119906 (119896) Δ119906 (119896))) (16)
1198701015840
119894= 1198702(1 minus 120578
2119891 (119906 (119896) Δ119906 (119896))) (17)
1198701015840
119889= 1198703(1 minus 120578
3119891 (119906 (119896) Δ119906 (119896))) (18)
where 119870119895(119895 = 1 2 3) is used to improve the response time
and 120578119895(119895 = 1 2 3) can enhance the stability of control system
Therefore the method for setting the parameters reasonablyplays an important role in the improved PID controller withhigher precision faster response and better robustness
42 Parameters Optimization through Fuzzy Theory andGenetic Algorithm The performance of improved PID con-troller largely depends on 119870
119895(119895 = 1 2 3) 120578
119895(119895 = 1 2 3) and
119891(lowast) As can be seen from the above formulas namely (15)(16) (17) and (18) because of the nonlinear characteristics offunction119891(lowast) a fuzzy inference algorithm is used to optimizethe function 119891(lowast) Because of the difficulty to obtain 119870
119895
(119895 = 1 2 3) and 120578119895(119895 = 1 2 3) based on analysis method
an improved genetic algorithm is proposed to solve thisproblemThe framework of GA-fuzzy-immune PID positioncontroller with incomplete derivation can be built up asshown in Figure 4
According to the immune feedbackmechanism of biolog-ical systems [42] four stages in the autoimmune reaction canbe summarized as follows
In the initial stage the antigen amount is higher andthe antibody amount is expected to increase quickly so the119879119904cell should be suppressed to produce After a period
of immunization the restrained action on 119879119904cell would
decrease in other words the antibody should not increasecontinually When most of antigens have been eliminated 119879
119904
should increase quickly to restrain B cell and the productionof antibody Finally when all of the antigens have been
6 The Scientific World Journal
Fuzzy inference
GA tuning
Control PID controller withincomplete derivation
Immunocorrection
ylowast
+minus
y(t)u(t)
K3K2K1
120578312057821205781
f(lowast)
e(t)
Kp Ki Kd
object
dudt
Figure 4 The framework of GA-fuzzy-immune PID position con-troller with incomplete derivation
eliminated both of antigen and antibody amount should keepstable till the immunization end
In the controller two inputs of 119906(119896) and Δ119906(119896) fuzzy sub-sets are all selected as NBNSPSPB and the output of119891(lowast)
fuzzy subset is all selected as NBNMNSZOPSPMPBwhere NB stands for negative big NM stands for negativemiddle NS stands for negative small ZO stands for zero PSstands for positive small PM stands for positive middle andPB stands for positive big According to the above immuno-logic processes 16 fuzzy rules are proposed to compute thenonlinear function 119891(lowast) as shown in Table 1 The fuzzy dis-course domain of 119906 is defined as minus10 minus3 +3 +10 the fuzzydiscourse domain of Δ119906 is defined as minus1 minus03 +03 +1and the fuzzy discourse domain of 119891(lowast) is defined asminus2 minus12 minus06 0 +06 +12 +2
As a frequently used membership function Gaussianmembership function has the feature of good smoothness andcan express the concept of fuzzy language more exactly thusit is applied for the proposed controller Figure 5 shows themembership functions for 119906 Figure 6 shows themembershipfunctions for Δ119906 and Figure 7 shows the membership func-tions for 119891(lowast)
The immune PID parameters 119870119895(119895 = 1 2 3) and 120578
119895
(119895 = 1 2 3) are tuned and optimized by an improved geneticalgorithm Traditional genetic algorithm in solving the prob-lem especially the complex problems is easily trapped inthe local optimum and appeared premature convergence Tosettle this question some improvements of traditional geneticalgorithm are presentedThe overall process can be describedas follows
Step 1 (coding) As a general coding method for GA binarycoding is used widely due to the simple processes of codingand decoding and easy operation of crossover and mutationHowever for amultivariable optimization problem the stringof binary gene is too long to result in lower search efficiencyIn order to solve this problem float-point genes are used inthe optimization model With this strategy the number ofvariables is not limited coding and decoding are not neededFurthermore the precision and efficiency can be increasedand the calculation speed is high A mixed coding programis presented in the improved GA During the initial stagebinary coding is adopted to quickly search for the area with
NB NS PS PB
08
06
04
02
1
0
0minus10 minus5 105
Deg
ree o
f mem
bers
hip
u(k)
Figure 5 Membership functions for u
Deg
ree o
f mem
bers
hip
NB NS PS PB
08
06
04
02
1
0
minus05 050 1minus1
Δu(k)
Figure 6 Membership functions for Δu
Table 1 The fuzzy control rule for nonlinear function 119891(lowast)
119906Δ119906
NB NS PS PBNB PB PM PS ZONS PM PS ZO NSPS PS ZO NS NMPB ZO NS NM NB
excellent properties In the later stage float-point coding isused to improve the precision
Step 2 (generating initial population) According to experi-ence six empirical coefficients (119870
1 1198702 1198703 1205781 1205782and 1205783) are
determined and initial population can be generated aroundthe coefficients By this generating method the searchingspace is reduced and the operating rate is increased
Step 3 (selecting fitness function) In an evolution searchprocess an appropriate fitness function plays an importantrole in parameter optimization In order to obtain satisfactory
The Scientific World Journal 7D
egre
e of m
embe
rshi
p
NB NM NS ZO PS PM PB
08
06
04
02
1
0
f(lowast)
minus2 minus15 minus1 minus05 0 05 1 15 2
Figure 7 Membership functions for 119891(lowast)
dynamic characteristics of the transition process the integralof time multiplied absolute value of error (ITAE) is also pro-vided as a comprehensive performance index and the squareof control input is introduced to prevent the control energyfrom growing too bigThe comprehensive performance indexfunction [43] can be calculated as follows
119869 =
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905)) 119889119905
+1205963119905119903
119890 (119905) ge 0
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905) + 1205964|119890 (119905)|) 119889119905
+1205963119905119903
119890 (119905) lt 0
(19)
where 1205961 1205962 1205963 and 120596
4are weights and 120596
4≫ 1205961 119890(119905) is
the system error 119906(119905) is the output of controller and 119905119903is the
rising time To avoid overshoot the introduction of punitivefunction is essential in the function
Then the fitness function 119865 can be defined as follows
119865 =119862
(119869 + 120576) (20)
where 119862 is a constant and can be set equal to 1 in this paper 120576is a small positive number to prevent 119869 from becoming equalto zero and 120576 = 10
minus10
Step 4 (selection) Selection is a very important step in thecriteria of ldquosurvival of the fittestrdquo that means selecting thesuperior individual and eliminating the inferior one from apopulation For genetic algorithm an individual is selectedas a parent according to its fitness In rank-based selectionalgorithm all individuals of every generation are ranked inorder of increasing fitness value The survival probability ofthe 119894th individual is prob(119894) = 119902(1 minus 119902)
119894minus1 where 119902 isin (0 1) isevolutionary pressure
Step 5 (crossover and mutation) Because of its strong globalsearch capability crossover operator of GA can be regarded
as the main operator and due to its local search capabilitymutation operator can be regarded as an auxiliary operatorSelf-adaptive crossover and mutation operators are proposedin this paper in other words crossover probabilities 119875
119888
and mutation probabilities 119875119898
are automatically adjustedwith the addition of evolutionary generations In the initialstage a larger 119875
119888and a smaller 119875
119898can effectively accelerate
convergence velocity of iteration however in the later stage asmaller119875
119888and a larger119875
119898would avoid local optimal solution
The formulas of 119875119888and 119875
119898are given as follows
119875119888(119896 + 1) = 119875
119888(119896) minus
[119875119888(1) minus 05]
119866119898
(21)
119875119898
(119896 + 1) = 119875119898
(119896) minus[119875119898
(1) minus 01]
119866119898
(22)
where 119896 is the generation number of heredity 119896 = 1 sim 119866119898
119866119898is themaximumgeneration number119875
119888(1) is the crossover
probability of first generation and 119875119898(1) is the mutation
probability of first generationAccording to these operators the 119875
119888and 119875
119898of best
individuals are not equal to zero where 119875119888isin (05 119875
119888(1)) and
119875119898
isin (119875119898(1) 01) so the performance of excellent individual
would not be in a circle due to the 119875119888and 119875
119898being too
small or equal to zero To protect excellent individuals ofeach generation the elitist strategy was applied in GA toimprove the convergence and optimization results thus thebest individual would be copied directly into next generation
5 A Simulation Example
In order to verify the performance of proposed GA-fuzzy-immune PID controller a simulation example is provided inthis section and the parameters are illustrated as follows
1205961
= 004 1205962
= 0001 1205963
= 2 and 1205964
= 500 Thepopulation size is set to 50 119866
119898is set to 100 119875
119888(1) is set to
09 119875119898(1) is set to 001 119879
119891is set to 9 and sampling time 119879 is
set to 1msIn order to indicate the comparison with other con-
trollers fuzzy PID immune PID fuzzy-immune PID andreal-coded GA PID simulations are carried out The configu-rations of simulation environment for these controllers wereuniform In immune PID and fuzzy-immune PID 119870
1= 10
1198702
= 002 1198703
= 10 1205781
= 002 1205782
= 006 and 1205783
= 10and119891(lowast) = 001 in immune PID In fuzzy PID and real-codedGA PID 119870
119901isin (0 80) 119870
119894isin (0 2) and 119870
119889isin (0 2) Other
parameters are the same as GA-fuzzy-immune PIDThe input of robot dexterous hand system is a unit step
signal and the simulation time is 1 s The unit step responsesof this system are shown in Figure 8 The first curve isresponse obtained with fuzzy inference the second curve isresponse obtained with immune algorithm the third curveis response obtained with fuzzy-immune inference (F-I) thefourth curve is response obtained with real-coded GA andthe fifth curve is response obtained through integration ofimproved genetic algorithm and fuzzy-immune inference(GA-F-I)
8 The Scientific World Journal
Table 2 PID parameters and performance indexes of five control methods
Control methods Fuzzy Immune F-I Real-coded GA GA-F-I119870119901
The PID parameters and performance indexes of the fivecontrol methods are shown in Table 2The proposed control-ler parameters can be calculated by improved GA and fuzzyinference
1198701= 1114655 119870
2= 001737 119870
3= 081208
1205781= 002121 120578
2= 006604 120578
3= 094233
119891 (lowast) = 0000544
(23)
Compared with other four methods the overshoot120590 based on GA-F-I PID controller with incomplete deriva-tion is decreased from 3630 to 0 The settling time 119905
119904is
reduced from 0592 s to 0362 s The rising time 119905119903is reduced
from 0393 s to 0226 s Although the rising time 119905119903is not
the best the nonovershoot and shortest settling time can beachieved by the proposed PID controller
6 Conclusions and Future Works
In this paper a GA-fuzzy-immune PID controller wasdesigned to improve the performance of robot dexteroushand The control system of a robot dexterous hand andmathematical model of an index finger were presented Inorder to improve the characteristics of proposed controllerimmune mechanism genetic algorithm and fuzzy inference
were applied Finally a simulation experimentwas carried outand the results showed that the designed controller was ideal
In future studies the authors plan to investigate mul-tifinger coordination control system Furthermore moreintelligent control algorithms for multifinger coordinationcontrol system are worth further study for the authors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of Fundamental Research Funds for the CentralUniversities (no 2014QNA38) and the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions in carrying out this research are gratefully acknowl-edged
References
[1] A Bicchi and V Kumar ldquoRobotic grasping and contact areviewrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo00) pp 348ndash353 San Francis-co Calif USA April 2000
[2] H Liu P Meusel N Seitz et al ldquoThe modular multisensoryDLR-HIT-handrdquo Mechanism and Machine Theory vol 42 no5 pp 612ndash625 2007
[3] M Controzzi C Cipriani B Jehenne M Donati and M CCarrozza ldquoBio-inspired mechanical design of a tendon-drivendexterous prosthetic handrdquo in Proceedings of the 32nd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society (EMBC rsquo10) pp 499ndash502 Buenos AiresArgentina September 2010
[4] R M Murray and S S Sastry A Mathematical Introduction toRobotic Manipulation CRC Press 1994
[5] T Yoshikawa ldquoMultifingered robot hands Control for graspingandmanipulationrdquoAnnual Reviews in Control vol 34 no 2 pp199ndash208 2010
[6] R Tomovic and G Boni ldquoAn adaptive artificial handrdquo Transac-tions on Automatic Control IRE vol 7 no 3 pp 3ndash10 1962
[7] E M Jafarov Y Istefanopulos and M N A Parlakci ldquoAnew variable structure PID-controller for robot manipulatorswith parameter perturbations an augmented sliding surfaceapproachrdquo Sign vol 2 article 1 2002
The Scientific World Journal 9
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
microelectronics technology and advanced control theoryrobot dexterous hand has entered a new period Jafarovet al [7] took both sliding and stability issues into accountto present an augmented sliding surface design for robothand In [8] a new variable structure PID controller designapproach was considered for the tracking stabilization ofrobot motion Atia [9] designed a new nonlinear PID slidingmode controller for set-point control of robot hand whichensured that the error tended to zero asymptotically if therewas no disturbance applied to the robot dynamics Chenet al [10] presented two types of adaptive control programcombining conventional computed-torque control and dif-ferent fuzzy compensators for the robust tracking controlof robotic manipulators with structured and unstructureduncertainties In [11] a model-free recurrent fuzzy neuralnetwork (RFNN) control system for robot handwas proposedto approximate the ideal backstepping control law whichwas further proved stable by the Lyapunov stability anal-ysis By combining feedback linearization with Lyapunovrsquossecond method and genetic algorithm Hassanzadeh et al[12] designed a robust controller with performance tuningfor robot hand and the stability and robust performance ofproposed controller were verified through a four-bar linkagerobot simulation In [13] two fault-tolerant control strategiesfor robot hand were implemented based on output-feedback119867infin
controller and experimental results illustrated that theimprovements were feasible and efficient
22 PID Control Methods As one of the earliest controlstrategies PID control has been developed to deal withmore complex control problems due to the advantages ofsimple description high dependability strong robustnessand so forth Han [14] proposed a nonlinear PID controllerwith the capability of auto-disturbance-rejection control andcombination of differentiator and extended state observerand transition process overcame the disturbance effectivelyand improved the control performance Besides Su et al[15] applied the method of Han proposed for controlling ofmanipulator successfully Gundes and Ozguler [16] inves-tigated the problem of closed-loop stabilization using PIDcontroller for MIMO plants to show the existence of stabi-lizing PID controllers for MIMO plants Alvarez-Ramirez etal [17] addressed the position regulation problem of robotmanipulators under control input constraints and experimentresults showed that the saturated linear PID control wassemiglobally asymptotically stable Oliveira et al [18] usedHermite-Biehler theorem to establish results on the designof PID controllers for a class of time delay systems Zieglerand Nichols [19] proposed the most well-known Zieglerand Nichols tuning formula for PID parameter tuningChen and Huang [20] presented a method for regulatingPID parameters on line automatically with neural net algo-rithm Neurofuzzy controller and genetic-fuzzy controllerfor second-order control systems were presented to improvethe performance of conventional PID and fuzzy controller[21ndash23] Genetic-fuzzy controller was applied in the drumboiler simulated dynamics to improve the control speedand precision [24] Moreover further improvements for
neurofuzzy controller and genetic-fuzzy controller were car-ried out by genetic-neurofuzzy arithmetic [25ndash27] Kim et al[28] achieved automatic tuning of PID parameters throughintegration of taking 119867
infinas performance index and particle
swarm optimization algorithm Juang and Lu [29] proposedpower-system load-frequency control by fuzzy-PI controllerand simulations on a multiarea interconnected power systemwith different kinds of perturbationswere performed to verifythe performance of the proposed approach Lu et al [30]proposed an evolutionary fuzzy lead-lag control approachfor coordinated control of flexible AC transmission systemdevices in a multimachine power system Tang et al [31] putforward a newmethod integrated with genetic algorithm andfuzzy distance to tune parameters Zheng et al [32] appliedlinear matrix inequalities (LMIs) in PID controller and anumerical example validated the stability of the closed-loopsystems119867
2or119867infinperformance specifications or maximum
output control requirement respectively
23 Fuzzy Immunity FeedbackControlMethods Back to 1986Farmer et al [33] suggested a dynamic model of an immunesystem based on immune network theory firstly and dis-cussed the links between an immune system and other arti-ficial intelligence methods Xin et al [34] designed a fuzzy-immune-PD-type control algorithm for trajectory trackingbased on dynamics nonlinearities of robot manipulator andexperimental results showed that the control scheme hadbetter tracking precision stronger robustness and superiorcontrol performance to conventional PD controller Lei andRen-hou [35] proposed a fuzzy immune algorithm to designa classification system and the results of comparison withother classification schemes demonstrated the effectiveness ofthe proposed immune algorithm Wang et al [36] designeda fuzzy-immune-PID control system based on a mutativescale chaos optimization method to avoid a mass of tuningparameters work in the progress of design An immune-fuzzysliding mode controller (FISMC) was presented not onlyeliminating the synchronous reluctance motor system uncer-tainty but also overcoming the drawback of sign functionand sat function [37] Chang et al [38] presented an effectiveprocedure based on fuzzy logic and immune algorithm for theplacement and sizing of shunt capacitor banks in a distortedpower network Kuo et al [39] proposed an artificial immunesystem (AIS) based on fuzzy neural network (FNN) to avoidfalling into the local optimum and improve the learningcapability
24 Discussion However although many approaches forrobot dexterous hand have been proposed in above litera-tures they have some common disadvantages summarized asfollows Firstly some proposed controllers for self-adaptionrobot dexterous hand need to calculate the inverse of Jacobianmatrix but it is difficult to obtain and would consume muchtime Secondly due to the frictional disturbances at joints andexternal disturbance of payload it is difficult to design a fasterresponse less overshoot and satisfactory robust stabilitycontrol systemThirdly the performance of some methods isactually related to specificweights which is difficult to obtain
The Scientific World Journal 3
Index finger Motor driver
interfaceDC power
Development board based on DSP and CPLD
RS232
Figure 1 The control circuit board of robot dexterous hand and the index finger
Finally because of inherent deficiencies of some methods itis easy to produce premature convergence
In order to solve the above problems a PID positioncontroller based on immunity feedback control theory fuzzyinference and improved genetic algorithm is designed Asimulation example is provided and experiment results showthat the proposed controller can achieve shorter adjusttime better rapidity and higher steady-state precision thantraditional PID position controller
3 Robot Dexterous Hand
31 Robot Dexterous Hand Control System A dexterous hand(named after ABS-I) has been developed in our laboratorywhich is made by the reinforced acrylonitrile butadienestyrene copolymers (ABS) in a 3D printer It is composed ofDC servo motors cup-type planetary gear reducers sensorsIE2-400 encoders complicated programmable logic device(CPLD) and digital signal processor (DSP) unit Figure 1shows the control circuit board of robot dexterous hand andthe index finger
The hierarchical control strategy adopted by the dexter-ous hand control system takes perfect purpose in practiceFeedback data glove or personal computer as the upper mi-crocomputer communicateswith bottom-level block throughserial communication interface (SCI) The top-level block isresponsible for the signal processing of upper microcom-puter and the communicating with bottom-level block Thebottom-level block consists of DSP-CPLD servo controllerSCI circuit motor driver and so forth and it is responsiblefor the signal processing of torque sensors position sensorsand magnetoelectric encoders Moreover it is responsible forcontrolling the pulses and directing signals to drive servomotors The dexterous hand control system can be shown asin Figure 2
32 Mathematical Model for the Index Finger Taking thesingle multijoint finger as an example the equation of DCservo drive motor on armature loop [40] can be introducedas follows
In the single multijoint finger system the Faulhaber1319006SR DC servo motor has some important parametersthat is 119861
119898= 222 times 10
minus4mNmrpm 119870119879
= 419mNmA119877119886
= 826Ω 119871119886
= 130 120583H and 119869119898
= 040 gcm2 Thespeed control system consists of a gearbox and one-gradebevel gear and the gearbox ratio is 415 1 and the bevelgears ratio is 2 1 Moreover by using coupling four-barlinkage mechanism the three phalanxesrsquo transmission ratiois kept exactly 1 1 1 over the whole movement range Thehand material is ABS 119869
119871is set to 1 gcm2 and 119861
119871is set to
4 The Scientific World Journal
CPLD
DSP
DSP
Motor driver 1
Motor n
Motor driver n
Motor 1
Positionsensors
DCpowersource
RAM RS232
CAN bus
sensors Encoder n
Encoder 1
Torque middot middot middot
Figure 2 The robot dexterous hand control system
0002mNmrpmAccording to the parameters we can obtainthe transfer function as follows
119866 (119904) =120579 (119904)
119880119886(119904)
=1
1033 times 10minus61199043 + 6565 times 10minus21199042 + 0731119904
(5)
4 GA-Fuzzy-Immune PID Controller
41 Immune-Based PID Controller Design As a general rulein the discrete-time domain traditional increment PID con-troller can be expressed as follows
119906 (119896) = 119870119901
[
[
119890 (119896) +119879
119879119894
119896
sum
119895=0
119890 (119895) +119879119889
119879Δ119890 (119896)]
]
= 119906 (119896 minus 1) + 119870119901Δ119890 (119896) + 119870
119894119890 (119896)
+ 119870119889(Δ119890 (119896) minus Δ119890 (119896 minus 1))
(6)
whereΔ119890(119896) = 119890(119896)minus119890(119896minus1)119870119901is the proportional gain119879
119894is
the integral time constant 119879119889is the derivative time constant
119870119894= 119870119901119879119879119894 119870119889= 119870119901119879119889119879 119890(119896) is the systematic deviation
between reference input and system output119879 is the samplingperiod and 119906(119896) is the control signal
In general differential signal can be used to improvethe system dynamic characteristics which is likely to causethe problem of high frequency interference to the controlsystem Using low pass filter in control algorithm can bringsignificant improvements in system performance and itstransfer function is 119866
119891(119904) = 1(1 + 119879
119891119904) where 119879
119891is
a filter coefficient The transfer function of PID controllerwith incomplete derivation can be expressed as follows
119880 (119904) = 119870119901(1 +
1
119879119894119904+
119879119889119904
1 + 119879119891119904)119864 (119904)
= 119880119901+ 119880119894+ 119880119889
(7)
In the discrete-time domain differential equation ofPID controller with incomplete derivation can be written asfollows
119890 (119895) + 119870119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(11)
The Scientific World Journal 5
Lymphocyte
T lymphocyte Freeantigen
HelperT cell T cell(TH)
+
minus
minus
AntibodyB lymphocyte
TS(k)TH(k)
Suppressor(TS)
Foreignantigen
+
minus
Figure 3 The immunity feedback control mechanism
As a kind of control system biological immune systemhas very strong robustness and self-adapted ability evenwhenencountering strong disturbances and uncertain conditionsFor invasion by a foreign antigen it can produce correspond-ing antibodies to resist the antigen A series of biologicalreactions could be carried out after combining antigens withantibodies and it eliminates antigen under the function ofphagocyte or special enzymes The immune system consistsof lymphocyte and antibody The lymphocyte consists ofB cell produced from marrow and T cell produced fromthymus T cell includes assistant T cell 119879
119867and restrained T
cell 119879119878 When cell obtains signal from the antigen it would
transmit the information to 119879119867
and 119879119878 and then B cell
produces corresponding antibodies to resist the antigen withthe stimulation by119879
119867and119879119878The immunity feedback control
mechanism is shown in Figure 3According to immunity feedback control mechanism all
of the received simulations of B cell can be obtained
= 1198961(1 minus 120578119891 (119878 (119896) Δ119878 (119896))) 120576 (119896)
(14)
where 119879119867(119896) is the 119896th generation output of 119879
119867cell which
receives antigen presenting cell activation 119879119878(119896) is the 119896th
generation restrain action on B cell by 119879119878cell 120576(119896) is the 119896th
generation antigen amount 1198961is enhancing factor of 119879
119867cell
1198962is inhibitory factor of 119879
119878cell and 120578 = 119896
21198961 119891(lowast) is a
nonlinear function which describes the immunity result thatB-cell antibody and antigen act on each other and relate withthe amount of B cell
In this paper we try to apply bodyrsquos immune mechanismto the ABS-I position controller to overcome the weaknessof traditional PID controller For a PID controller we assumethat position error 119890(119896) on the 119896th sampling period represents120576(119896) the position controller output 119906(119896) on the 119896th samplingperiod represents 119878(119896) Therefore Δ119906(119896) = Δ119878(119896)
In the synthesis the immune PID controller with incom-plete derivation can be obtained
119906 (119896) = 1198701015840
119901119890 (119896) + 119870
1015840
119894
119896
sum
119895=1
119890 (119895)
+ 1198701015840
119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(15)
1198701015840
119901= 1198701(1 minus 120578
1119891 (119906 (119896) Δ119906 (119896))) (16)
1198701015840
119894= 1198702(1 minus 120578
2119891 (119906 (119896) Δ119906 (119896))) (17)
1198701015840
119889= 1198703(1 minus 120578
3119891 (119906 (119896) Δ119906 (119896))) (18)
where 119870119895(119895 = 1 2 3) is used to improve the response time
and 120578119895(119895 = 1 2 3) can enhance the stability of control system
Therefore the method for setting the parameters reasonablyplays an important role in the improved PID controller withhigher precision faster response and better robustness
42 Parameters Optimization through Fuzzy Theory andGenetic Algorithm The performance of improved PID con-troller largely depends on 119870
119895(119895 = 1 2 3) 120578
119895(119895 = 1 2 3) and
119891(lowast) As can be seen from the above formulas namely (15)(16) (17) and (18) because of the nonlinear characteristics offunction119891(lowast) a fuzzy inference algorithm is used to optimizethe function 119891(lowast) Because of the difficulty to obtain 119870
119895
(119895 = 1 2 3) and 120578119895(119895 = 1 2 3) based on analysis method
an improved genetic algorithm is proposed to solve thisproblemThe framework of GA-fuzzy-immune PID positioncontroller with incomplete derivation can be built up asshown in Figure 4
According to the immune feedbackmechanism of biolog-ical systems [42] four stages in the autoimmune reaction canbe summarized as follows
In the initial stage the antigen amount is higher andthe antibody amount is expected to increase quickly so the119879119904cell should be suppressed to produce After a period
of immunization the restrained action on 119879119904cell would
decrease in other words the antibody should not increasecontinually When most of antigens have been eliminated 119879
119904
should increase quickly to restrain B cell and the productionof antibody Finally when all of the antigens have been
6 The Scientific World Journal
Fuzzy inference
GA tuning
Control PID controller withincomplete derivation
Immunocorrection
ylowast
+minus
y(t)u(t)
K3K2K1
120578312057821205781
f(lowast)
e(t)
Kp Ki Kd
object
dudt
Figure 4 The framework of GA-fuzzy-immune PID position con-troller with incomplete derivation
eliminated both of antigen and antibody amount should keepstable till the immunization end
In the controller two inputs of 119906(119896) and Δ119906(119896) fuzzy sub-sets are all selected as NBNSPSPB and the output of119891(lowast)
fuzzy subset is all selected as NBNMNSZOPSPMPBwhere NB stands for negative big NM stands for negativemiddle NS stands for negative small ZO stands for zero PSstands for positive small PM stands for positive middle andPB stands for positive big According to the above immuno-logic processes 16 fuzzy rules are proposed to compute thenonlinear function 119891(lowast) as shown in Table 1 The fuzzy dis-course domain of 119906 is defined as minus10 minus3 +3 +10 the fuzzydiscourse domain of Δ119906 is defined as minus1 minus03 +03 +1and the fuzzy discourse domain of 119891(lowast) is defined asminus2 minus12 minus06 0 +06 +12 +2
As a frequently used membership function Gaussianmembership function has the feature of good smoothness andcan express the concept of fuzzy language more exactly thusit is applied for the proposed controller Figure 5 shows themembership functions for 119906 Figure 6 shows themembershipfunctions for Δ119906 and Figure 7 shows the membership func-tions for 119891(lowast)
The immune PID parameters 119870119895(119895 = 1 2 3) and 120578
119895
(119895 = 1 2 3) are tuned and optimized by an improved geneticalgorithm Traditional genetic algorithm in solving the prob-lem especially the complex problems is easily trapped inthe local optimum and appeared premature convergence Tosettle this question some improvements of traditional geneticalgorithm are presentedThe overall process can be describedas follows
Step 1 (coding) As a general coding method for GA binarycoding is used widely due to the simple processes of codingand decoding and easy operation of crossover and mutationHowever for amultivariable optimization problem the stringof binary gene is too long to result in lower search efficiencyIn order to solve this problem float-point genes are used inthe optimization model With this strategy the number ofvariables is not limited coding and decoding are not neededFurthermore the precision and efficiency can be increasedand the calculation speed is high A mixed coding programis presented in the improved GA During the initial stagebinary coding is adopted to quickly search for the area with
NB NS PS PB
08
06
04
02
1
0
0minus10 minus5 105
Deg
ree o
f mem
bers
hip
u(k)
Figure 5 Membership functions for u
Deg
ree o
f mem
bers
hip
NB NS PS PB
08
06
04
02
1
0
minus05 050 1minus1
Δu(k)
Figure 6 Membership functions for Δu
Table 1 The fuzzy control rule for nonlinear function 119891(lowast)
119906Δ119906
NB NS PS PBNB PB PM PS ZONS PM PS ZO NSPS PS ZO NS NMPB ZO NS NM NB
excellent properties In the later stage float-point coding isused to improve the precision
Step 2 (generating initial population) According to experi-ence six empirical coefficients (119870
1 1198702 1198703 1205781 1205782and 1205783) are
determined and initial population can be generated aroundthe coefficients By this generating method the searchingspace is reduced and the operating rate is increased
Step 3 (selecting fitness function) In an evolution searchprocess an appropriate fitness function plays an importantrole in parameter optimization In order to obtain satisfactory
The Scientific World Journal 7D
egre
e of m
embe
rshi
p
NB NM NS ZO PS PM PB
08
06
04
02
1
0
f(lowast)
minus2 minus15 minus1 minus05 0 05 1 15 2
Figure 7 Membership functions for 119891(lowast)
dynamic characteristics of the transition process the integralof time multiplied absolute value of error (ITAE) is also pro-vided as a comprehensive performance index and the squareof control input is introduced to prevent the control energyfrom growing too bigThe comprehensive performance indexfunction [43] can be calculated as follows
119869 =
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905)) 119889119905
+1205963119905119903
119890 (119905) ge 0
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905) + 1205964|119890 (119905)|) 119889119905
+1205963119905119903
119890 (119905) lt 0
(19)
where 1205961 1205962 1205963 and 120596
4are weights and 120596
4≫ 1205961 119890(119905) is
the system error 119906(119905) is the output of controller and 119905119903is the
rising time To avoid overshoot the introduction of punitivefunction is essential in the function
Then the fitness function 119865 can be defined as follows
119865 =119862
(119869 + 120576) (20)
where 119862 is a constant and can be set equal to 1 in this paper 120576is a small positive number to prevent 119869 from becoming equalto zero and 120576 = 10
minus10
Step 4 (selection) Selection is a very important step in thecriteria of ldquosurvival of the fittestrdquo that means selecting thesuperior individual and eliminating the inferior one from apopulation For genetic algorithm an individual is selectedas a parent according to its fitness In rank-based selectionalgorithm all individuals of every generation are ranked inorder of increasing fitness value The survival probability ofthe 119894th individual is prob(119894) = 119902(1 minus 119902)
119894minus1 where 119902 isin (0 1) isevolutionary pressure
Step 5 (crossover and mutation) Because of its strong globalsearch capability crossover operator of GA can be regarded
as the main operator and due to its local search capabilitymutation operator can be regarded as an auxiliary operatorSelf-adaptive crossover and mutation operators are proposedin this paper in other words crossover probabilities 119875
119888
and mutation probabilities 119875119898
are automatically adjustedwith the addition of evolutionary generations In the initialstage a larger 119875
119888and a smaller 119875
119898can effectively accelerate
convergence velocity of iteration however in the later stage asmaller119875
119888and a larger119875
119898would avoid local optimal solution
The formulas of 119875119888and 119875
119898are given as follows
119875119888(119896 + 1) = 119875
119888(119896) minus
[119875119888(1) minus 05]
119866119898
(21)
119875119898
(119896 + 1) = 119875119898
(119896) minus[119875119898
(1) minus 01]
119866119898
(22)
where 119896 is the generation number of heredity 119896 = 1 sim 119866119898
119866119898is themaximumgeneration number119875
119888(1) is the crossover
probability of first generation and 119875119898(1) is the mutation
probability of first generationAccording to these operators the 119875
119888and 119875
119898of best
individuals are not equal to zero where 119875119888isin (05 119875
119888(1)) and
119875119898
isin (119875119898(1) 01) so the performance of excellent individual
would not be in a circle due to the 119875119888and 119875
119898being too
small or equal to zero To protect excellent individuals ofeach generation the elitist strategy was applied in GA toimprove the convergence and optimization results thus thebest individual would be copied directly into next generation
5 A Simulation Example
In order to verify the performance of proposed GA-fuzzy-immune PID controller a simulation example is provided inthis section and the parameters are illustrated as follows
1205961
= 004 1205962
= 0001 1205963
= 2 and 1205964
= 500 Thepopulation size is set to 50 119866
119898is set to 100 119875
119888(1) is set to
09 119875119898(1) is set to 001 119879
119891is set to 9 and sampling time 119879 is
set to 1msIn order to indicate the comparison with other con-
trollers fuzzy PID immune PID fuzzy-immune PID andreal-coded GA PID simulations are carried out The configu-rations of simulation environment for these controllers wereuniform In immune PID and fuzzy-immune PID 119870
1= 10
1198702
= 002 1198703
= 10 1205781
= 002 1205782
= 006 and 1205783
= 10and119891(lowast) = 001 in immune PID In fuzzy PID and real-codedGA PID 119870
119901isin (0 80) 119870
119894isin (0 2) and 119870
119889isin (0 2) Other
parameters are the same as GA-fuzzy-immune PIDThe input of robot dexterous hand system is a unit step
signal and the simulation time is 1 s The unit step responsesof this system are shown in Figure 8 The first curve isresponse obtained with fuzzy inference the second curve isresponse obtained with immune algorithm the third curveis response obtained with fuzzy-immune inference (F-I) thefourth curve is response obtained with real-coded GA andthe fifth curve is response obtained through integration ofimproved genetic algorithm and fuzzy-immune inference(GA-F-I)
8 The Scientific World Journal
Table 2 PID parameters and performance indexes of five control methods
Control methods Fuzzy Immune F-I Real-coded GA GA-F-I119870119901
The PID parameters and performance indexes of the fivecontrol methods are shown in Table 2The proposed control-ler parameters can be calculated by improved GA and fuzzyinference
1198701= 1114655 119870
2= 001737 119870
3= 081208
1205781= 002121 120578
2= 006604 120578
3= 094233
119891 (lowast) = 0000544
(23)
Compared with other four methods the overshoot120590 based on GA-F-I PID controller with incomplete deriva-tion is decreased from 3630 to 0 The settling time 119905
119904is
reduced from 0592 s to 0362 s The rising time 119905119903is reduced
from 0393 s to 0226 s Although the rising time 119905119903is not
the best the nonovershoot and shortest settling time can beachieved by the proposed PID controller
6 Conclusions and Future Works
In this paper a GA-fuzzy-immune PID controller wasdesigned to improve the performance of robot dexteroushand The control system of a robot dexterous hand andmathematical model of an index finger were presented Inorder to improve the characteristics of proposed controllerimmune mechanism genetic algorithm and fuzzy inference
were applied Finally a simulation experimentwas carried outand the results showed that the designed controller was ideal
In future studies the authors plan to investigate mul-tifinger coordination control system Furthermore moreintelligent control algorithms for multifinger coordinationcontrol system are worth further study for the authors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of Fundamental Research Funds for the CentralUniversities (no 2014QNA38) and the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions in carrying out this research are gratefully acknowl-edged
References
[1] A Bicchi and V Kumar ldquoRobotic grasping and contact areviewrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo00) pp 348ndash353 San Francis-co Calif USA April 2000
[2] H Liu P Meusel N Seitz et al ldquoThe modular multisensoryDLR-HIT-handrdquo Mechanism and Machine Theory vol 42 no5 pp 612ndash625 2007
[3] M Controzzi C Cipriani B Jehenne M Donati and M CCarrozza ldquoBio-inspired mechanical design of a tendon-drivendexterous prosthetic handrdquo in Proceedings of the 32nd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society (EMBC rsquo10) pp 499ndash502 Buenos AiresArgentina September 2010
[4] R M Murray and S S Sastry A Mathematical Introduction toRobotic Manipulation CRC Press 1994
[5] T Yoshikawa ldquoMultifingered robot hands Control for graspingandmanipulationrdquoAnnual Reviews in Control vol 34 no 2 pp199ndash208 2010
[6] R Tomovic and G Boni ldquoAn adaptive artificial handrdquo Transac-tions on Automatic Control IRE vol 7 no 3 pp 3ndash10 1962
[7] E M Jafarov Y Istefanopulos and M N A Parlakci ldquoAnew variable structure PID-controller for robot manipulatorswith parameter perturbations an augmented sliding surfaceapproachrdquo Sign vol 2 article 1 2002
The Scientific World Journal 9
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
Figure 1 The control circuit board of robot dexterous hand and the index finger
Finally because of inherent deficiencies of some methods itis easy to produce premature convergence
In order to solve the above problems a PID positioncontroller based on immunity feedback control theory fuzzyinference and improved genetic algorithm is designed Asimulation example is provided and experiment results showthat the proposed controller can achieve shorter adjusttime better rapidity and higher steady-state precision thantraditional PID position controller
3 Robot Dexterous Hand
31 Robot Dexterous Hand Control System A dexterous hand(named after ABS-I) has been developed in our laboratorywhich is made by the reinforced acrylonitrile butadienestyrene copolymers (ABS) in a 3D printer It is composed ofDC servo motors cup-type planetary gear reducers sensorsIE2-400 encoders complicated programmable logic device(CPLD) and digital signal processor (DSP) unit Figure 1shows the control circuit board of robot dexterous hand andthe index finger
The hierarchical control strategy adopted by the dexter-ous hand control system takes perfect purpose in practiceFeedback data glove or personal computer as the upper mi-crocomputer communicateswith bottom-level block throughserial communication interface (SCI) The top-level block isresponsible for the signal processing of upper microcom-puter and the communicating with bottom-level block Thebottom-level block consists of DSP-CPLD servo controllerSCI circuit motor driver and so forth and it is responsiblefor the signal processing of torque sensors position sensorsand magnetoelectric encoders Moreover it is responsible forcontrolling the pulses and directing signals to drive servomotors The dexterous hand control system can be shown asin Figure 2
32 Mathematical Model for the Index Finger Taking thesingle multijoint finger as an example the equation of DCservo drive motor on armature loop [40] can be introducedas follows
In the single multijoint finger system the Faulhaber1319006SR DC servo motor has some important parametersthat is 119861
119898= 222 times 10
minus4mNmrpm 119870119879
= 419mNmA119877119886
= 826Ω 119871119886
= 130 120583H and 119869119898
= 040 gcm2 Thespeed control system consists of a gearbox and one-gradebevel gear and the gearbox ratio is 415 1 and the bevelgears ratio is 2 1 Moreover by using coupling four-barlinkage mechanism the three phalanxesrsquo transmission ratiois kept exactly 1 1 1 over the whole movement range Thehand material is ABS 119869
119871is set to 1 gcm2 and 119861
119871is set to
4 The Scientific World Journal
CPLD
DSP
DSP
Motor driver 1
Motor n
Motor driver n
Motor 1
Positionsensors
DCpowersource
RAM RS232
CAN bus
sensors Encoder n
Encoder 1
Torque middot middot middot
Figure 2 The robot dexterous hand control system
0002mNmrpmAccording to the parameters we can obtainthe transfer function as follows
119866 (119904) =120579 (119904)
119880119886(119904)
=1
1033 times 10minus61199043 + 6565 times 10minus21199042 + 0731119904
(5)
4 GA-Fuzzy-Immune PID Controller
41 Immune-Based PID Controller Design As a general rulein the discrete-time domain traditional increment PID con-troller can be expressed as follows
119906 (119896) = 119870119901
[
[
119890 (119896) +119879
119879119894
119896
sum
119895=0
119890 (119895) +119879119889
119879Δ119890 (119896)]
]
= 119906 (119896 minus 1) + 119870119901Δ119890 (119896) + 119870
119894119890 (119896)
+ 119870119889(Δ119890 (119896) minus Δ119890 (119896 minus 1))
(6)
whereΔ119890(119896) = 119890(119896)minus119890(119896minus1)119870119901is the proportional gain119879
119894is
the integral time constant 119879119889is the derivative time constant
119870119894= 119870119901119879119879119894 119870119889= 119870119901119879119889119879 119890(119896) is the systematic deviation
between reference input and system output119879 is the samplingperiod and 119906(119896) is the control signal
In general differential signal can be used to improvethe system dynamic characteristics which is likely to causethe problem of high frequency interference to the controlsystem Using low pass filter in control algorithm can bringsignificant improvements in system performance and itstransfer function is 119866
119891(119904) = 1(1 + 119879
119891119904) where 119879
119891is
a filter coefficient The transfer function of PID controllerwith incomplete derivation can be expressed as follows
119880 (119904) = 119870119901(1 +
1
119879119894119904+
119879119889119904
1 + 119879119891119904)119864 (119904)
= 119880119901+ 119880119894+ 119880119889
(7)
In the discrete-time domain differential equation ofPID controller with incomplete derivation can be written asfollows
119890 (119895) + 119870119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(11)
The Scientific World Journal 5
Lymphocyte
T lymphocyte Freeantigen
HelperT cell T cell(TH)
+
minus
minus
AntibodyB lymphocyte
TS(k)TH(k)
Suppressor(TS)
Foreignantigen
+
minus
Figure 3 The immunity feedback control mechanism
As a kind of control system biological immune systemhas very strong robustness and self-adapted ability evenwhenencountering strong disturbances and uncertain conditionsFor invasion by a foreign antigen it can produce correspond-ing antibodies to resist the antigen A series of biologicalreactions could be carried out after combining antigens withantibodies and it eliminates antigen under the function ofphagocyte or special enzymes The immune system consistsof lymphocyte and antibody The lymphocyte consists ofB cell produced from marrow and T cell produced fromthymus T cell includes assistant T cell 119879
119867and restrained T
cell 119879119878 When cell obtains signal from the antigen it would
transmit the information to 119879119867
and 119879119878 and then B cell
produces corresponding antibodies to resist the antigen withthe stimulation by119879
119867and119879119878The immunity feedback control
mechanism is shown in Figure 3According to immunity feedback control mechanism all
of the received simulations of B cell can be obtained
= 1198961(1 minus 120578119891 (119878 (119896) Δ119878 (119896))) 120576 (119896)
(14)
where 119879119867(119896) is the 119896th generation output of 119879
119867cell which
receives antigen presenting cell activation 119879119878(119896) is the 119896th
generation restrain action on B cell by 119879119878cell 120576(119896) is the 119896th
generation antigen amount 1198961is enhancing factor of 119879
119867cell
1198962is inhibitory factor of 119879
119878cell and 120578 = 119896
21198961 119891(lowast) is a
nonlinear function which describes the immunity result thatB-cell antibody and antigen act on each other and relate withthe amount of B cell
In this paper we try to apply bodyrsquos immune mechanismto the ABS-I position controller to overcome the weaknessof traditional PID controller For a PID controller we assumethat position error 119890(119896) on the 119896th sampling period represents120576(119896) the position controller output 119906(119896) on the 119896th samplingperiod represents 119878(119896) Therefore Δ119906(119896) = Δ119878(119896)
In the synthesis the immune PID controller with incom-plete derivation can be obtained
119906 (119896) = 1198701015840
119901119890 (119896) + 119870
1015840
119894
119896
sum
119895=1
119890 (119895)
+ 1198701015840
119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(15)
1198701015840
119901= 1198701(1 minus 120578
1119891 (119906 (119896) Δ119906 (119896))) (16)
1198701015840
119894= 1198702(1 minus 120578
2119891 (119906 (119896) Δ119906 (119896))) (17)
1198701015840
119889= 1198703(1 minus 120578
3119891 (119906 (119896) Δ119906 (119896))) (18)
where 119870119895(119895 = 1 2 3) is used to improve the response time
and 120578119895(119895 = 1 2 3) can enhance the stability of control system
Therefore the method for setting the parameters reasonablyplays an important role in the improved PID controller withhigher precision faster response and better robustness
42 Parameters Optimization through Fuzzy Theory andGenetic Algorithm The performance of improved PID con-troller largely depends on 119870
119895(119895 = 1 2 3) 120578
119895(119895 = 1 2 3) and
119891(lowast) As can be seen from the above formulas namely (15)(16) (17) and (18) because of the nonlinear characteristics offunction119891(lowast) a fuzzy inference algorithm is used to optimizethe function 119891(lowast) Because of the difficulty to obtain 119870
119895
(119895 = 1 2 3) and 120578119895(119895 = 1 2 3) based on analysis method
an improved genetic algorithm is proposed to solve thisproblemThe framework of GA-fuzzy-immune PID positioncontroller with incomplete derivation can be built up asshown in Figure 4
According to the immune feedbackmechanism of biolog-ical systems [42] four stages in the autoimmune reaction canbe summarized as follows
In the initial stage the antigen amount is higher andthe antibody amount is expected to increase quickly so the119879119904cell should be suppressed to produce After a period
of immunization the restrained action on 119879119904cell would
decrease in other words the antibody should not increasecontinually When most of antigens have been eliminated 119879
119904
should increase quickly to restrain B cell and the productionof antibody Finally when all of the antigens have been
6 The Scientific World Journal
Fuzzy inference
GA tuning
Control PID controller withincomplete derivation
Immunocorrection
ylowast
+minus
y(t)u(t)
K3K2K1
120578312057821205781
f(lowast)
e(t)
Kp Ki Kd
object
dudt
Figure 4 The framework of GA-fuzzy-immune PID position con-troller with incomplete derivation
eliminated both of antigen and antibody amount should keepstable till the immunization end
In the controller two inputs of 119906(119896) and Δ119906(119896) fuzzy sub-sets are all selected as NBNSPSPB and the output of119891(lowast)
fuzzy subset is all selected as NBNMNSZOPSPMPBwhere NB stands for negative big NM stands for negativemiddle NS stands for negative small ZO stands for zero PSstands for positive small PM stands for positive middle andPB stands for positive big According to the above immuno-logic processes 16 fuzzy rules are proposed to compute thenonlinear function 119891(lowast) as shown in Table 1 The fuzzy dis-course domain of 119906 is defined as minus10 minus3 +3 +10 the fuzzydiscourse domain of Δ119906 is defined as minus1 minus03 +03 +1and the fuzzy discourse domain of 119891(lowast) is defined asminus2 minus12 minus06 0 +06 +12 +2
As a frequently used membership function Gaussianmembership function has the feature of good smoothness andcan express the concept of fuzzy language more exactly thusit is applied for the proposed controller Figure 5 shows themembership functions for 119906 Figure 6 shows themembershipfunctions for Δ119906 and Figure 7 shows the membership func-tions for 119891(lowast)
The immune PID parameters 119870119895(119895 = 1 2 3) and 120578
119895
(119895 = 1 2 3) are tuned and optimized by an improved geneticalgorithm Traditional genetic algorithm in solving the prob-lem especially the complex problems is easily trapped inthe local optimum and appeared premature convergence Tosettle this question some improvements of traditional geneticalgorithm are presentedThe overall process can be describedas follows
Step 1 (coding) As a general coding method for GA binarycoding is used widely due to the simple processes of codingand decoding and easy operation of crossover and mutationHowever for amultivariable optimization problem the stringof binary gene is too long to result in lower search efficiencyIn order to solve this problem float-point genes are used inthe optimization model With this strategy the number ofvariables is not limited coding and decoding are not neededFurthermore the precision and efficiency can be increasedand the calculation speed is high A mixed coding programis presented in the improved GA During the initial stagebinary coding is adopted to quickly search for the area with
NB NS PS PB
08
06
04
02
1
0
0minus10 minus5 105
Deg
ree o
f mem
bers
hip
u(k)
Figure 5 Membership functions for u
Deg
ree o
f mem
bers
hip
NB NS PS PB
08
06
04
02
1
0
minus05 050 1minus1
Δu(k)
Figure 6 Membership functions for Δu
Table 1 The fuzzy control rule for nonlinear function 119891(lowast)
119906Δ119906
NB NS PS PBNB PB PM PS ZONS PM PS ZO NSPS PS ZO NS NMPB ZO NS NM NB
excellent properties In the later stage float-point coding isused to improve the precision
Step 2 (generating initial population) According to experi-ence six empirical coefficients (119870
1 1198702 1198703 1205781 1205782and 1205783) are
determined and initial population can be generated aroundthe coefficients By this generating method the searchingspace is reduced and the operating rate is increased
Step 3 (selecting fitness function) In an evolution searchprocess an appropriate fitness function plays an importantrole in parameter optimization In order to obtain satisfactory
The Scientific World Journal 7D
egre
e of m
embe
rshi
p
NB NM NS ZO PS PM PB
08
06
04
02
1
0
f(lowast)
minus2 minus15 minus1 minus05 0 05 1 15 2
Figure 7 Membership functions for 119891(lowast)
dynamic characteristics of the transition process the integralof time multiplied absolute value of error (ITAE) is also pro-vided as a comprehensive performance index and the squareof control input is introduced to prevent the control energyfrom growing too bigThe comprehensive performance indexfunction [43] can be calculated as follows
119869 =
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905)) 119889119905
+1205963119905119903
119890 (119905) ge 0
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905) + 1205964|119890 (119905)|) 119889119905
+1205963119905119903
119890 (119905) lt 0
(19)
where 1205961 1205962 1205963 and 120596
4are weights and 120596
4≫ 1205961 119890(119905) is
the system error 119906(119905) is the output of controller and 119905119903is the
rising time To avoid overshoot the introduction of punitivefunction is essential in the function
Then the fitness function 119865 can be defined as follows
119865 =119862
(119869 + 120576) (20)
where 119862 is a constant and can be set equal to 1 in this paper 120576is a small positive number to prevent 119869 from becoming equalto zero and 120576 = 10
minus10
Step 4 (selection) Selection is a very important step in thecriteria of ldquosurvival of the fittestrdquo that means selecting thesuperior individual and eliminating the inferior one from apopulation For genetic algorithm an individual is selectedas a parent according to its fitness In rank-based selectionalgorithm all individuals of every generation are ranked inorder of increasing fitness value The survival probability ofthe 119894th individual is prob(119894) = 119902(1 minus 119902)
119894minus1 where 119902 isin (0 1) isevolutionary pressure
Step 5 (crossover and mutation) Because of its strong globalsearch capability crossover operator of GA can be regarded
as the main operator and due to its local search capabilitymutation operator can be regarded as an auxiliary operatorSelf-adaptive crossover and mutation operators are proposedin this paper in other words crossover probabilities 119875
119888
and mutation probabilities 119875119898
are automatically adjustedwith the addition of evolutionary generations In the initialstage a larger 119875
119888and a smaller 119875
119898can effectively accelerate
convergence velocity of iteration however in the later stage asmaller119875
119888and a larger119875
119898would avoid local optimal solution
The formulas of 119875119888and 119875
119898are given as follows
119875119888(119896 + 1) = 119875
119888(119896) minus
[119875119888(1) minus 05]
119866119898
(21)
119875119898
(119896 + 1) = 119875119898
(119896) minus[119875119898
(1) minus 01]
119866119898
(22)
where 119896 is the generation number of heredity 119896 = 1 sim 119866119898
119866119898is themaximumgeneration number119875
119888(1) is the crossover
probability of first generation and 119875119898(1) is the mutation
probability of first generationAccording to these operators the 119875
119888and 119875
119898of best
individuals are not equal to zero where 119875119888isin (05 119875
119888(1)) and
119875119898
isin (119875119898(1) 01) so the performance of excellent individual
would not be in a circle due to the 119875119888and 119875
119898being too
small or equal to zero To protect excellent individuals ofeach generation the elitist strategy was applied in GA toimprove the convergence and optimization results thus thebest individual would be copied directly into next generation
5 A Simulation Example
In order to verify the performance of proposed GA-fuzzy-immune PID controller a simulation example is provided inthis section and the parameters are illustrated as follows
1205961
= 004 1205962
= 0001 1205963
= 2 and 1205964
= 500 Thepopulation size is set to 50 119866
119898is set to 100 119875
119888(1) is set to
09 119875119898(1) is set to 001 119879
119891is set to 9 and sampling time 119879 is
set to 1msIn order to indicate the comparison with other con-
trollers fuzzy PID immune PID fuzzy-immune PID andreal-coded GA PID simulations are carried out The configu-rations of simulation environment for these controllers wereuniform In immune PID and fuzzy-immune PID 119870
1= 10
1198702
= 002 1198703
= 10 1205781
= 002 1205782
= 006 and 1205783
= 10and119891(lowast) = 001 in immune PID In fuzzy PID and real-codedGA PID 119870
119901isin (0 80) 119870
119894isin (0 2) and 119870
119889isin (0 2) Other
parameters are the same as GA-fuzzy-immune PIDThe input of robot dexterous hand system is a unit step
signal and the simulation time is 1 s The unit step responsesof this system are shown in Figure 8 The first curve isresponse obtained with fuzzy inference the second curve isresponse obtained with immune algorithm the third curveis response obtained with fuzzy-immune inference (F-I) thefourth curve is response obtained with real-coded GA andthe fifth curve is response obtained through integration ofimproved genetic algorithm and fuzzy-immune inference(GA-F-I)
8 The Scientific World Journal
Table 2 PID parameters and performance indexes of five control methods
Control methods Fuzzy Immune F-I Real-coded GA GA-F-I119870119901
The PID parameters and performance indexes of the fivecontrol methods are shown in Table 2The proposed control-ler parameters can be calculated by improved GA and fuzzyinference
1198701= 1114655 119870
2= 001737 119870
3= 081208
1205781= 002121 120578
2= 006604 120578
3= 094233
119891 (lowast) = 0000544
(23)
Compared with other four methods the overshoot120590 based on GA-F-I PID controller with incomplete deriva-tion is decreased from 3630 to 0 The settling time 119905
119904is
reduced from 0592 s to 0362 s The rising time 119905119903is reduced
from 0393 s to 0226 s Although the rising time 119905119903is not
the best the nonovershoot and shortest settling time can beachieved by the proposed PID controller
6 Conclusions and Future Works
In this paper a GA-fuzzy-immune PID controller wasdesigned to improve the performance of robot dexteroushand The control system of a robot dexterous hand andmathematical model of an index finger were presented Inorder to improve the characteristics of proposed controllerimmune mechanism genetic algorithm and fuzzy inference
were applied Finally a simulation experimentwas carried outand the results showed that the designed controller was ideal
In future studies the authors plan to investigate mul-tifinger coordination control system Furthermore moreintelligent control algorithms for multifinger coordinationcontrol system are worth further study for the authors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of Fundamental Research Funds for the CentralUniversities (no 2014QNA38) and the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions in carrying out this research are gratefully acknowl-edged
References
[1] A Bicchi and V Kumar ldquoRobotic grasping and contact areviewrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo00) pp 348ndash353 San Francis-co Calif USA April 2000
[2] H Liu P Meusel N Seitz et al ldquoThe modular multisensoryDLR-HIT-handrdquo Mechanism and Machine Theory vol 42 no5 pp 612ndash625 2007
[3] M Controzzi C Cipriani B Jehenne M Donati and M CCarrozza ldquoBio-inspired mechanical design of a tendon-drivendexterous prosthetic handrdquo in Proceedings of the 32nd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society (EMBC rsquo10) pp 499ndash502 Buenos AiresArgentina September 2010
[4] R M Murray and S S Sastry A Mathematical Introduction toRobotic Manipulation CRC Press 1994
[5] T Yoshikawa ldquoMultifingered robot hands Control for graspingandmanipulationrdquoAnnual Reviews in Control vol 34 no 2 pp199ndash208 2010
[6] R Tomovic and G Boni ldquoAn adaptive artificial handrdquo Transac-tions on Automatic Control IRE vol 7 no 3 pp 3ndash10 1962
[7] E M Jafarov Y Istefanopulos and M N A Parlakci ldquoAnew variable structure PID-controller for robot manipulatorswith parameter perturbations an augmented sliding surfaceapproachrdquo Sign vol 2 article 1 2002
The Scientific World Journal 9
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
0002mNmrpmAccording to the parameters we can obtainthe transfer function as follows
119866 (119904) =120579 (119904)
119880119886(119904)
=1
1033 times 10minus61199043 + 6565 times 10minus21199042 + 0731119904
(5)
4 GA-Fuzzy-Immune PID Controller
41 Immune-Based PID Controller Design As a general rulein the discrete-time domain traditional increment PID con-troller can be expressed as follows
119906 (119896) = 119870119901
[
[
119890 (119896) +119879
119879119894
119896
sum
119895=0
119890 (119895) +119879119889
119879Δ119890 (119896)]
]
= 119906 (119896 minus 1) + 119870119901Δ119890 (119896) + 119870
119894119890 (119896)
+ 119870119889(Δ119890 (119896) minus Δ119890 (119896 minus 1))
(6)
whereΔ119890(119896) = 119890(119896)minus119890(119896minus1)119870119901is the proportional gain119879
119894is
the integral time constant 119879119889is the derivative time constant
119870119894= 119870119901119879119879119894 119870119889= 119870119901119879119889119879 119890(119896) is the systematic deviation
between reference input and system output119879 is the samplingperiod and 119906(119896) is the control signal
In general differential signal can be used to improvethe system dynamic characteristics which is likely to causethe problem of high frequency interference to the controlsystem Using low pass filter in control algorithm can bringsignificant improvements in system performance and itstransfer function is 119866
119891(119904) = 1(1 + 119879
119891119904) where 119879
119891is
a filter coefficient The transfer function of PID controllerwith incomplete derivation can be expressed as follows
119880 (119904) = 119870119901(1 +
1
119879119894119904+
119879119889119904
1 + 119879119891119904)119864 (119904)
= 119880119901+ 119880119894+ 119880119889
(7)
In the discrete-time domain differential equation ofPID controller with incomplete derivation can be written asfollows
119890 (119895) + 119870119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(11)
The Scientific World Journal 5
Lymphocyte
T lymphocyte Freeantigen
HelperT cell T cell(TH)
+
minus
minus
AntibodyB lymphocyte
TS(k)TH(k)
Suppressor(TS)
Foreignantigen
+
minus
Figure 3 The immunity feedback control mechanism
As a kind of control system biological immune systemhas very strong robustness and self-adapted ability evenwhenencountering strong disturbances and uncertain conditionsFor invasion by a foreign antigen it can produce correspond-ing antibodies to resist the antigen A series of biologicalreactions could be carried out after combining antigens withantibodies and it eliminates antigen under the function ofphagocyte or special enzymes The immune system consistsof lymphocyte and antibody The lymphocyte consists ofB cell produced from marrow and T cell produced fromthymus T cell includes assistant T cell 119879
119867and restrained T
cell 119879119878 When cell obtains signal from the antigen it would
transmit the information to 119879119867
and 119879119878 and then B cell
produces corresponding antibodies to resist the antigen withthe stimulation by119879
119867and119879119878The immunity feedback control
mechanism is shown in Figure 3According to immunity feedback control mechanism all
of the received simulations of B cell can be obtained
= 1198961(1 minus 120578119891 (119878 (119896) Δ119878 (119896))) 120576 (119896)
(14)
where 119879119867(119896) is the 119896th generation output of 119879
119867cell which
receives antigen presenting cell activation 119879119878(119896) is the 119896th
generation restrain action on B cell by 119879119878cell 120576(119896) is the 119896th
generation antigen amount 1198961is enhancing factor of 119879
119867cell
1198962is inhibitory factor of 119879
119878cell and 120578 = 119896
21198961 119891(lowast) is a
nonlinear function which describes the immunity result thatB-cell antibody and antigen act on each other and relate withthe amount of B cell
In this paper we try to apply bodyrsquos immune mechanismto the ABS-I position controller to overcome the weaknessof traditional PID controller For a PID controller we assumethat position error 119890(119896) on the 119896th sampling period represents120576(119896) the position controller output 119906(119896) on the 119896th samplingperiod represents 119878(119896) Therefore Δ119906(119896) = Δ119878(119896)
In the synthesis the immune PID controller with incom-plete derivation can be obtained
119906 (119896) = 1198701015840
119901119890 (119896) + 119870
1015840
119894
119896
sum
119895=1
119890 (119895)
+ 1198701015840
119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(15)
1198701015840
119901= 1198701(1 minus 120578
1119891 (119906 (119896) Δ119906 (119896))) (16)
1198701015840
119894= 1198702(1 minus 120578
2119891 (119906 (119896) Δ119906 (119896))) (17)
1198701015840
119889= 1198703(1 minus 120578
3119891 (119906 (119896) Δ119906 (119896))) (18)
where 119870119895(119895 = 1 2 3) is used to improve the response time
and 120578119895(119895 = 1 2 3) can enhance the stability of control system
Therefore the method for setting the parameters reasonablyplays an important role in the improved PID controller withhigher precision faster response and better robustness
42 Parameters Optimization through Fuzzy Theory andGenetic Algorithm The performance of improved PID con-troller largely depends on 119870
119895(119895 = 1 2 3) 120578
119895(119895 = 1 2 3) and
119891(lowast) As can be seen from the above formulas namely (15)(16) (17) and (18) because of the nonlinear characteristics offunction119891(lowast) a fuzzy inference algorithm is used to optimizethe function 119891(lowast) Because of the difficulty to obtain 119870
119895
(119895 = 1 2 3) and 120578119895(119895 = 1 2 3) based on analysis method
an improved genetic algorithm is proposed to solve thisproblemThe framework of GA-fuzzy-immune PID positioncontroller with incomplete derivation can be built up asshown in Figure 4
According to the immune feedbackmechanism of biolog-ical systems [42] four stages in the autoimmune reaction canbe summarized as follows
In the initial stage the antigen amount is higher andthe antibody amount is expected to increase quickly so the119879119904cell should be suppressed to produce After a period
of immunization the restrained action on 119879119904cell would
decrease in other words the antibody should not increasecontinually When most of antigens have been eliminated 119879
119904
should increase quickly to restrain B cell and the productionof antibody Finally when all of the antigens have been
6 The Scientific World Journal
Fuzzy inference
GA tuning
Control PID controller withincomplete derivation
Immunocorrection
ylowast
+minus
y(t)u(t)
K3K2K1
120578312057821205781
f(lowast)
e(t)
Kp Ki Kd
object
dudt
Figure 4 The framework of GA-fuzzy-immune PID position con-troller with incomplete derivation
eliminated both of antigen and antibody amount should keepstable till the immunization end
In the controller two inputs of 119906(119896) and Δ119906(119896) fuzzy sub-sets are all selected as NBNSPSPB and the output of119891(lowast)
fuzzy subset is all selected as NBNMNSZOPSPMPBwhere NB stands for negative big NM stands for negativemiddle NS stands for negative small ZO stands for zero PSstands for positive small PM stands for positive middle andPB stands for positive big According to the above immuno-logic processes 16 fuzzy rules are proposed to compute thenonlinear function 119891(lowast) as shown in Table 1 The fuzzy dis-course domain of 119906 is defined as minus10 minus3 +3 +10 the fuzzydiscourse domain of Δ119906 is defined as minus1 minus03 +03 +1and the fuzzy discourse domain of 119891(lowast) is defined asminus2 minus12 minus06 0 +06 +12 +2
As a frequently used membership function Gaussianmembership function has the feature of good smoothness andcan express the concept of fuzzy language more exactly thusit is applied for the proposed controller Figure 5 shows themembership functions for 119906 Figure 6 shows themembershipfunctions for Δ119906 and Figure 7 shows the membership func-tions for 119891(lowast)
The immune PID parameters 119870119895(119895 = 1 2 3) and 120578
119895
(119895 = 1 2 3) are tuned and optimized by an improved geneticalgorithm Traditional genetic algorithm in solving the prob-lem especially the complex problems is easily trapped inthe local optimum and appeared premature convergence Tosettle this question some improvements of traditional geneticalgorithm are presentedThe overall process can be describedas follows
Step 1 (coding) As a general coding method for GA binarycoding is used widely due to the simple processes of codingand decoding and easy operation of crossover and mutationHowever for amultivariable optimization problem the stringof binary gene is too long to result in lower search efficiencyIn order to solve this problem float-point genes are used inthe optimization model With this strategy the number ofvariables is not limited coding and decoding are not neededFurthermore the precision and efficiency can be increasedand the calculation speed is high A mixed coding programis presented in the improved GA During the initial stagebinary coding is adopted to quickly search for the area with
NB NS PS PB
08
06
04
02
1
0
0minus10 minus5 105
Deg
ree o
f mem
bers
hip
u(k)
Figure 5 Membership functions for u
Deg
ree o
f mem
bers
hip
NB NS PS PB
08
06
04
02
1
0
minus05 050 1minus1
Δu(k)
Figure 6 Membership functions for Δu
Table 1 The fuzzy control rule for nonlinear function 119891(lowast)
119906Δ119906
NB NS PS PBNB PB PM PS ZONS PM PS ZO NSPS PS ZO NS NMPB ZO NS NM NB
excellent properties In the later stage float-point coding isused to improve the precision
Step 2 (generating initial population) According to experi-ence six empirical coefficients (119870
1 1198702 1198703 1205781 1205782and 1205783) are
determined and initial population can be generated aroundthe coefficients By this generating method the searchingspace is reduced and the operating rate is increased
Step 3 (selecting fitness function) In an evolution searchprocess an appropriate fitness function plays an importantrole in parameter optimization In order to obtain satisfactory
The Scientific World Journal 7D
egre
e of m
embe
rshi
p
NB NM NS ZO PS PM PB
08
06
04
02
1
0
f(lowast)
minus2 minus15 minus1 minus05 0 05 1 15 2
Figure 7 Membership functions for 119891(lowast)
dynamic characteristics of the transition process the integralof time multiplied absolute value of error (ITAE) is also pro-vided as a comprehensive performance index and the squareof control input is introduced to prevent the control energyfrom growing too bigThe comprehensive performance indexfunction [43] can be calculated as follows
119869 =
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905)) 119889119905
+1205963119905119903
119890 (119905) ge 0
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905) + 1205964|119890 (119905)|) 119889119905
+1205963119905119903
119890 (119905) lt 0
(19)
where 1205961 1205962 1205963 and 120596
4are weights and 120596
4≫ 1205961 119890(119905) is
the system error 119906(119905) is the output of controller and 119905119903is the
rising time To avoid overshoot the introduction of punitivefunction is essential in the function
Then the fitness function 119865 can be defined as follows
119865 =119862
(119869 + 120576) (20)
where 119862 is a constant and can be set equal to 1 in this paper 120576is a small positive number to prevent 119869 from becoming equalto zero and 120576 = 10
minus10
Step 4 (selection) Selection is a very important step in thecriteria of ldquosurvival of the fittestrdquo that means selecting thesuperior individual and eliminating the inferior one from apopulation For genetic algorithm an individual is selectedas a parent according to its fitness In rank-based selectionalgorithm all individuals of every generation are ranked inorder of increasing fitness value The survival probability ofthe 119894th individual is prob(119894) = 119902(1 minus 119902)
119894minus1 where 119902 isin (0 1) isevolutionary pressure
Step 5 (crossover and mutation) Because of its strong globalsearch capability crossover operator of GA can be regarded
as the main operator and due to its local search capabilitymutation operator can be regarded as an auxiliary operatorSelf-adaptive crossover and mutation operators are proposedin this paper in other words crossover probabilities 119875
119888
and mutation probabilities 119875119898
are automatically adjustedwith the addition of evolutionary generations In the initialstage a larger 119875
119888and a smaller 119875
119898can effectively accelerate
convergence velocity of iteration however in the later stage asmaller119875
119888and a larger119875
119898would avoid local optimal solution
The formulas of 119875119888and 119875
119898are given as follows
119875119888(119896 + 1) = 119875
119888(119896) minus
[119875119888(1) minus 05]
119866119898
(21)
119875119898
(119896 + 1) = 119875119898
(119896) minus[119875119898
(1) minus 01]
119866119898
(22)
where 119896 is the generation number of heredity 119896 = 1 sim 119866119898
119866119898is themaximumgeneration number119875
119888(1) is the crossover
probability of first generation and 119875119898(1) is the mutation
probability of first generationAccording to these operators the 119875
119888and 119875
119898of best
individuals are not equal to zero where 119875119888isin (05 119875
119888(1)) and
119875119898
isin (119875119898(1) 01) so the performance of excellent individual
would not be in a circle due to the 119875119888and 119875
119898being too
small or equal to zero To protect excellent individuals ofeach generation the elitist strategy was applied in GA toimprove the convergence and optimization results thus thebest individual would be copied directly into next generation
5 A Simulation Example
In order to verify the performance of proposed GA-fuzzy-immune PID controller a simulation example is provided inthis section and the parameters are illustrated as follows
1205961
= 004 1205962
= 0001 1205963
= 2 and 1205964
= 500 Thepopulation size is set to 50 119866
119898is set to 100 119875
119888(1) is set to
09 119875119898(1) is set to 001 119879
119891is set to 9 and sampling time 119879 is
set to 1msIn order to indicate the comparison with other con-
trollers fuzzy PID immune PID fuzzy-immune PID andreal-coded GA PID simulations are carried out The configu-rations of simulation environment for these controllers wereuniform In immune PID and fuzzy-immune PID 119870
1= 10
1198702
= 002 1198703
= 10 1205781
= 002 1205782
= 006 and 1205783
= 10and119891(lowast) = 001 in immune PID In fuzzy PID and real-codedGA PID 119870
119901isin (0 80) 119870
119894isin (0 2) and 119870
119889isin (0 2) Other
parameters are the same as GA-fuzzy-immune PIDThe input of robot dexterous hand system is a unit step
signal and the simulation time is 1 s The unit step responsesof this system are shown in Figure 8 The first curve isresponse obtained with fuzzy inference the second curve isresponse obtained with immune algorithm the third curveis response obtained with fuzzy-immune inference (F-I) thefourth curve is response obtained with real-coded GA andthe fifth curve is response obtained through integration ofimproved genetic algorithm and fuzzy-immune inference(GA-F-I)
8 The Scientific World Journal
Table 2 PID parameters and performance indexes of five control methods
Control methods Fuzzy Immune F-I Real-coded GA GA-F-I119870119901
The PID parameters and performance indexes of the fivecontrol methods are shown in Table 2The proposed control-ler parameters can be calculated by improved GA and fuzzyinference
1198701= 1114655 119870
2= 001737 119870
3= 081208
1205781= 002121 120578
2= 006604 120578
3= 094233
119891 (lowast) = 0000544
(23)
Compared with other four methods the overshoot120590 based on GA-F-I PID controller with incomplete deriva-tion is decreased from 3630 to 0 The settling time 119905
119904is
reduced from 0592 s to 0362 s The rising time 119905119903is reduced
from 0393 s to 0226 s Although the rising time 119905119903is not
the best the nonovershoot and shortest settling time can beachieved by the proposed PID controller
6 Conclusions and Future Works
In this paper a GA-fuzzy-immune PID controller wasdesigned to improve the performance of robot dexteroushand The control system of a robot dexterous hand andmathematical model of an index finger were presented Inorder to improve the characteristics of proposed controllerimmune mechanism genetic algorithm and fuzzy inference
were applied Finally a simulation experimentwas carried outand the results showed that the designed controller was ideal
In future studies the authors plan to investigate mul-tifinger coordination control system Furthermore moreintelligent control algorithms for multifinger coordinationcontrol system are worth further study for the authors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of Fundamental Research Funds for the CentralUniversities (no 2014QNA38) and the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions in carrying out this research are gratefully acknowl-edged
References
[1] A Bicchi and V Kumar ldquoRobotic grasping and contact areviewrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo00) pp 348ndash353 San Francis-co Calif USA April 2000
[2] H Liu P Meusel N Seitz et al ldquoThe modular multisensoryDLR-HIT-handrdquo Mechanism and Machine Theory vol 42 no5 pp 612ndash625 2007
[3] M Controzzi C Cipriani B Jehenne M Donati and M CCarrozza ldquoBio-inspired mechanical design of a tendon-drivendexterous prosthetic handrdquo in Proceedings of the 32nd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society (EMBC rsquo10) pp 499ndash502 Buenos AiresArgentina September 2010
[4] R M Murray and S S Sastry A Mathematical Introduction toRobotic Manipulation CRC Press 1994
[5] T Yoshikawa ldquoMultifingered robot hands Control for graspingandmanipulationrdquoAnnual Reviews in Control vol 34 no 2 pp199ndash208 2010
[6] R Tomovic and G Boni ldquoAn adaptive artificial handrdquo Transac-tions on Automatic Control IRE vol 7 no 3 pp 3ndash10 1962
[7] E M Jafarov Y Istefanopulos and M N A Parlakci ldquoAnew variable structure PID-controller for robot manipulatorswith parameter perturbations an augmented sliding surfaceapproachrdquo Sign vol 2 article 1 2002
The Scientific World Journal 9
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
As a kind of control system biological immune systemhas very strong robustness and self-adapted ability evenwhenencountering strong disturbances and uncertain conditionsFor invasion by a foreign antigen it can produce correspond-ing antibodies to resist the antigen A series of biologicalreactions could be carried out after combining antigens withantibodies and it eliminates antigen under the function ofphagocyte or special enzymes The immune system consistsof lymphocyte and antibody The lymphocyte consists ofB cell produced from marrow and T cell produced fromthymus T cell includes assistant T cell 119879
119867and restrained T
cell 119879119878 When cell obtains signal from the antigen it would
transmit the information to 119879119867
and 119879119878 and then B cell
produces corresponding antibodies to resist the antigen withthe stimulation by119879
119867and119879119878The immunity feedback control
mechanism is shown in Figure 3According to immunity feedback control mechanism all
of the received simulations of B cell can be obtained
= 1198961(1 minus 120578119891 (119878 (119896) Δ119878 (119896))) 120576 (119896)
(14)
where 119879119867(119896) is the 119896th generation output of 119879
119867cell which
receives antigen presenting cell activation 119879119878(119896) is the 119896th
generation restrain action on B cell by 119879119878cell 120576(119896) is the 119896th
generation antigen amount 1198961is enhancing factor of 119879
119867cell
1198962is inhibitory factor of 119879
119878cell and 120578 = 119896
21198961 119891(lowast) is a
nonlinear function which describes the immunity result thatB-cell antibody and antigen act on each other and relate withthe amount of B cell
In this paper we try to apply bodyrsquos immune mechanismto the ABS-I position controller to overcome the weaknessof traditional PID controller For a PID controller we assumethat position error 119890(119896) on the 119896th sampling period represents120576(119896) the position controller output 119906(119896) on the 119896th samplingperiod represents 119878(119896) Therefore Δ119906(119896) = Δ119878(119896)
In the synthesis the immune PID controller with incom-plete derivation can be obtained
119906 (119896) = 1198701015840
119901119890 (119896) + 119870
1015840
119894
119896
sum
119895=1
119890 (119895)
+ 1198701015840
119889(1 minus 120572) [119890 (119896) minus 119890 (119896 minus 1)]
+ 120572119906119889(119896 minus 1)
(15)
1198701015840
119901= 1198701(1 minus 120578
1119891 (119906 (119896) Δ119906 (119896))) (16)
1198701015840
119894= 1198702(1 minus 120578
2119891 (119906 (119896) Δ119906 (119896))) (17)
1198701015840
119889= 1198703(1 minus 120578
3119891 (119906 (119896) Δ119906 (119896))) (18)
where 119870119895(119895 = 1 2 3) is used to improve the response time
and 120578119895(119895 = 1 2 3) can enhance the stability of control system
Therefore the method for setting the parameters reasonablyplays an important role in the improved PID controller withhigher precision faster response and better robustness
42 Parameters Optimization through Fuzzy Theory andGenetic Algorithm The performance of improved PID con-troller largely depends on 119870
119895(119895 = 1 2 3) 120578
119895(119895 = 1 2 3) and
119891(lowast) As can be seen from the above formulas namely (15)(16) (17) and (18) because of the nonlinear characteristics offunction119891(lowast) a fuzzy inference algorithm is used to optimizethe function 119891(lowast) Because of the difficulty to obtain 119870
119895
(119895 = 1 2 3) and 120578119895(119895 = 1 2 3) based on analysis method
an improved genetic algorithm is proposed to solve thisproblemThe framework of GA-fuzzy-immune PID positioncontroller with incomplete derivation can be built up asshown in Figure 4
According to the immune feedbackmechanism of biolog-ical systems [42] four stages in the autoimmune reaction canbe summarized as follows
In the initial stage the antigen amount is higher andthe antibody amount is expected to increase quickly so the119879119904cell should be suppressed to produce After a period
of immunization the restrained action on 119879119904cell would
decrease in other words the antibody should not increasecontinually When most of antigens have been eliminated 119879
119904
should increase quickly to restrain B cell and the productionof antibody Finally when all of the antigens have been
6 The Scientific World Journal
Fuzzy inference
GA tuning
Control PID controller withincomplete derivation
Immunocorrection
ylowast
+minus
y(t)u(t)
K3K2K1
120578312057821205781
f(lowast)
e(t)
Kp Ki Kd
object
dudt
Figure 4 The framework of GA-fuzzy-immune PID position con-troller with incomplete derivation
eliminated both of antigen and antibody amount should keepstable till the immunization end
In the controller two inputs of 119906(119896) and Δ119906(119896) fuzzy sub-sets are all selected as NBNSPSPB and the output of119891(lowast)
fuzzy subset is all selected as NBNMNSZOPSPMPBwhere NB stands for negative big NM stands for negativemiddle NS stands for negative small ZO stands for zero PSstands for positive small PM stands for positive middle andPB stands for positive big According to the above immuno-logic processes 16 fuzzy rules are proposed to compute thenonlinear function 119891(lowast) as shown in Table 1 The fuzzy dis-course domain of 119906 is defined as minus10 minus3 +3 +10 the fuzzydiscourse domain of Δ119906 is defined as minus1 minus03 +03 +1and the fuzzy discourse domain of 119891(lowast) is defined asminus2 minus12 minus06 0 +06 +12 +2
As a frequently used membership function Gaussianmembership function has the feature of good smoothness andcan express the concept of fuzzy language more exactly thusit is applied for the proposed controller Figure 5 shows themembership functions for 119906 Figure 6 shows themembershipfunctions for Δ119906 and Figure 7 shows the membership func-tions for 119891(lowast)
The immune PID parameters 119870119895(119895 = 1 2 3) and 120578
119895
(119895 = 1 2 3) are tuned and optimized by an improved geneticalgorithm Traditional genetic algorithm in solving the prob-lem especially the complex problems is easily trapped inthe local optimum and appeared premature convergence Tosettle this question some improvements of traditional geneticalgorithm are presentedThe overall process can be describedas follows
Step 1 (coding) As a general coding method for GA binarycoding is used widely due to the simple processes of codingand decoding and easy operation of crossover and mutationHowever for amultivariable optimization problem the stringof binary gene is too long to result in lower search efficiencyIn order to solve this problem float-point genes are used inthe optimization model With this strategy the number ofvariables is not limited coding and decoding are not neededFurthermore the precision and efficiency can be increasedand the calculation speed is high A mixed coding programis presented in the improved GA During the initial stagebinary coding is adopted to quickly search for the area with
NB NS PS PB
08
06
04
02
1
0
0minus10 minus5 105
Deg
ree o
f mem
bers
hip
u(k)
Figure 5 Membership functions for u
Deg
ree o
f mem
bers
hip
NB NS PS PB
08
06
04
02
1
0
minus05 050 1minus1
Δu(k)
Figure 6 Membership functions for Δu
Table 1 The fuzzy control rule for nonlinear function 119891(lowast)
119906Δ119906
NB NS PS PBNB PB PM PS ZONS PM PS ZO NSPS PS ZO NS NMPB ZO NS NM NB
excellent properties In the later stage float-point coding isused to improve the precision
Step 2 (generating initial population) According to experi-ence six empirical coefficients (119870
1 1198702 1198703 1205781 1205782and 1205783) are
determined and initial population can be generated aroundthe coefficients By this generating method the searchingspace is reduced and the operating rate is increased
Step 3 (selecting fitness function) In an evolution searchprocess an appropriate fitness function plays an importantrole in parameter optimization In order to obtain satisfactory
The Scientific World Journal 7D
egre
e of m
embe
rshi
p
NB NM NS ZO PS PM PB
08
06
04
02
1
0
f(lowast)
minus2 minus15 minus1 minus05 0 05 1 15 2
Figure 7 Membership functions for 119891(lowast)
dynamic characteristics of the transition process the integralof time multiplied absolute value of error (ITAE) is also pro-vided as a comprehensive performance index and the squareof control input is introduced to prevent the control energyfrom growing too bigThe comprehensive performance indexfunction [43] can be calculated as follows
119869 =
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905)) 119889119905
+1205963119905119903
119890 (119905) ge 0
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905) + 1205964|119890 (119905)|) 119889119905
+1205963119905119903
119890 (119905) lt 0
(19)
where 1205961 1205962 1205963 and 120596
4are weights and 120596
4≫ 1205961 119890(119905) is
the system error 119906(119905) is the output of controller and 119905119903is the
rising time To avoid overshoot the introduction of punitivefunction is essential in the function
Then the fitness function 119865 can be defined as follows
119865 =119862
(119869 + 120576) (20)
where 119862 is a constant and can be set equal to 1 in this paper 120576is a small positive number to prevent 119869 from becoming equalto zero and 120576 = 10
minus10
Step 4 (selection) Selection is a very important step in thecriteria of ldquosurvival of the fittestrdquo that means selecting thesuperior individual and eliminating the inferior one from apopulation For genetic algorithm an individual is selectedas a parent according to its fitness In rank-based selectionalgorithm all individuals of every generation are ranked inorder of increasing fitness value The survival probability ofthe 119894th individual is prob(119894) = 119902(1 minus 119902)
119894minus1 where 119902 isin (0 1) isevolutionary pressure
Step 5 (crossover and mutation) Because of its strong globalsearch capability crossover operator of GA can be regarded
as the main operator and due to its local search capabilitymutation operator can be regarded as an auxiliary operatorSelf-adaptive crossover and mutation operators are proposedin this paper in other words crossover probabilities 119875
119888
and mutation probabilities 119875119898
are automatically adjustedwith the addition of evolutionary generations In the initialstage a larger 119875
119888and a smaller 119875
119898can effectively accelerate
convergence velocity of iteration however in the later stage asmaller119875
119888and a larger119875
119898would avoid local optimal solution
The formulas of 119875119888and 119875
119898are given as follows
119875119888(119896 + 1) = 119875
119888(119896) minus
[119875119888(1) minus 05]
119866119898
(21)
119875119898
(119896 + 1) = 119875119898
(119896) minus[119875119898
(1) minus 01]
119866119898
(22)
where 119896 is the generation number of heredity 119896 = 1 sim 119866119898
119866119898is themaximumgeneration number119875
119888(1) is the crossover
probability of first generation and 119875119898(1) is the mutation
probability of first generationAccording to these operators the 119875
119888and 119875
119898of best
individuals are not equal to zero where 119875119888isin (05 119875
119888(1)) and
119875119898
isin (119875119898(1) 01) so the performance of excellent individual
would not be in a circle due to the 119875119888and 119875
119898being too
small or equal to zero To protect excellent individuals ofeach generation the elitist strategy was applied in GA toimprove the convergence and optimization results thus thebest individual would be copied directly into next generation
5 A Simulation Example
In order to verify the performance of proposed GA-fuzzy-immune PID controller a simulation example is provided inthis section and the parameters are illustrated as follows
1205961
= 004 1205962
= 0001 1205963
= 2 and 1205964
= 500 Thepopulation size is set to 50 119866
119898is set to 100 119875
119888(1) is set to
09 119875119898(1) is set to 001 119879
119891is set to 9 and sampling time 119879 is
set to 1msIn order to indicate the comparison with other con-
trollers fuzzy PID immune PID fuzzy-immune PID andreal-coded GA PID simulations are carried out The configu-rations of simulation environment for these controllers wereuniform In immune PID and fuzzy-immune PID 119870
1= 10
1198702
= 002 1198703
= 10 1205781
= 002 1205782
= 006 and 1205783
= 10and119891(lowast) = 001 in immune PID In fuzzy PID and real-codedGA PID 119870
119901isin (0 80) 119870
119894isin (0 2) and 119870
119889isin (0 2) Other
parameters are the same as GA-fuzzy-immune PIDThe input of robot dexterous hand system is a unit step
signal and the simulation time is 1 s The unit step responsesof this system are shown in Figure 8 The first curve isresponse obtained with fuzzy inference the second curve isresponse obtained with immune algorithm the third curveis response obtained with fuzzy-immune inference (F-I) thefourth curve is response obtained with real-coded GA andthe fifth curve is response obtained through integration ofimproved genetic algorithm and fuzzy-immune inference(GA-F-I)
8 The Scientific World Journal
Table 2 PID parameters and performance indexes of five control methods
Control methods Fuzzy Immune F-I Real-coded GA GA-F-I119870119901
The PID parameters and performance indexes of the fivecontrol methods are shown in Table 2The proposed control-ler parameters can be calculated by improved GA and fuzzyinference
1198701= 1114655 119870
2= 001737 119870
3= 081208
1205781= 002121 120578
2= 006604 120578
3= 094233
119891 (lowast) = 0000544
(23)
Compared with other four methods the overshoot120590 based on GA-F-I PID controller with incomplete deriva-tion is decreased from 3630 to 0 The settling time 119905
119904is
reduced from 0592 s to 0362 s The rising time 119905119903is reduced
from 0393 s to 0226 s Although the rising time 119905119903is not
the best the nonovershoot and shortest settling time can beachieved by the proposed PID controller
6 Conclusions and Future Works
In this paper a GA-fuzzy-immune PID controller wasdesigned to improve the performance of robot dexteroushand The control system of a robot dexterous hand andmathematical model of an index finger were presented Inorder to improve the characteristics of proposed controllerimmune mechanism genetic algorithm and fuzzy inference
were applied Finally a simulation experimentwas carried outand the results showed that the designed controller was ideal
In future studies the authors plan to investigate mul-tifinger coordination control system Furthermore moreintelligent control algorithms for multifinger coordinationcontrol system are worth further study for the authors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of Fundamental Research Funds for the CentralUniversities (no 2014QNA38) and the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions in carrying out this research are gratefully acknowl-edged
References
[1] A Bicchi and V Kumar ldquoRobotic grasping and contact areviewrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo00) pp 348ndash353 San Francis-co Calif USA April 2000
[2] H Liu P Meusel N Seitz et al ldquoThe modular multisensoryDLR-HIT-handrdquo Mechanism and Machine Theory vol 42 no5 pp 612ndash625 2007
[3] M Controzzi C Cipriani B Jehenne M Donati and M CCarrozza ldquoBio-inspired mechanical design of a tendon-drivendexterous prosthetic handrdquo in Proceedings of the 32nd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society (EMBC rsquo10) pp 499ndash502 Buenos AiresArgentina September 2010
[4] R M Murray and S S Sastry A Mathematical Introduction toRobotic Manipulation CRC Press 1994
[5] T Yoshikawa ldquoMultifingered robot hands Control for graspingandmanipulationrdquoAnnual Reviews in Control vol 34 no 2 pp199ndash208 2010
[6] R Tomovic and G Boni ldquoAn adaptive artificial handrdquo Transac-tions on Automatic Control IRE vol 7 no 3 pp 3ndash10 1962
[7] E M Jafarov Y Istefanopulos and M N A Parlakci ldquoAnew variable structure PID-controller for robot manipulatorswith parameter perturbations an augmented sliding surfaceapproachrdquo Sign vol 2 article 1 2002
The Scientific World Journal 9
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
Figure 4 The framework of GA-fuzzy-immune PID position con-troller with incomplete derivation
eliminated both of antigen and antibody amount should keepstable till the immunization end
In the controller two inputs of 119906(119896) and Δ119906(119896) fuzzy sub-sets are all selected as NBNSPSPB and the output of119891(lowast)
fuzzy subset is all selected as NBNMNSZOPSPMPBwhere NB stands for negative big NM stands for negativemiddle NS stands for negative small ZO stands for zero PSstands for positive small PM stands for positive middle andPB stands for positive big According to the above immuno-logic processes 16 fuzzy rules are proposed to compute thenonlinear function 119891(lowast) as shown in Table 1 The fuzzy dis-course domain of 119906 is defined as minus10 minus3 +3 +10 the fuzzydiscourse domain of Δ119906 is defined as minus1 minus03 +03 +1and the fuzzy discourse domain of 119891(lowast) is defined asminus2 minus12 minus06 0 +06 +12 +2
As a frequently used membership function Gaussianmembership function has the feature of good smoothness andcan express the concept of fuzzy language more exactly thusit is applied for the proposed controller Figure 5 shows themembership functions for 119906 Figure 6 shows themembershipfunctions for Δ119906 and Figure 7 shows the membership func-tions for 119891(lowast)
The immune PID parameters 119870119895(119895 = 1 2 3) and 120578
119895
(119895 = 1 2 3) are tuned and optimized by an improved geneticalgorithm Traditional genetic algorithm in solving the prob-lem especially the complex problems is easily trapped inthe local optimum and appeared premature convergence Tosettle this question some improvements of traditional geneticalgorithm are presentedThe overall process can be describedas follows
Step 1 (coding) As a general coding method for GA binarycoding is used widely due to the simple processes of codingand decoding and easy operation of crossover and mutationHowever for amultivariable optimization problem the stringof binary gene is too long to result in lower search efficiencyIn order to solve this problem float-point genes are used inthe optimization model With this strategy the number ofvariables is not limited coding and decoding are not neededFurthermore the precision and efficiency can be increasedand the calculation speed is high A mixed coding programis presented in the improved GA During the initial stagebinary coding is adopted to quickly search for the area with
NB NS PS PB
08
06
04
02
1
0
0minus10 minus5 105
Deg
ree o
f mem
bers
hip
u(k)
Figure 5 Membership functions for u
Deg
ree o
f mem
bers
hip
NB NS PS PB
08
06
04
02
1
0
minus05 050 1minus1
Δu(k)
Figure 6 Membership functions for Δu
Table 1 The fuzzy control rule for nonlinear function 119891(lowast)
119906Δ119906
NB NS PS PBNB PB PM PS ZONS PM PS ZO NSPS PS ZO NS NMPB ZO NS NM NB
excellent properties In the later stage float-point coding isused to improve the precision
Step 2 (generating initial population) According to experi-ence six empirical coefficients (119870
1 1198702 1198703 1205781 1205782and 1205783) are
determined and initial population can be generated aroundthe coefficients By this generating method the searchingspace is reduced and the operating rate is increased
Step 3 (selecting fitness function) In an evolution searchprocess an appropriate fitness function plays an importantrole in parameter optimization In order to obtain satisfactory
The Scientific World Journal 7D
egre
e of m
embe
rshi
p
NB NM NS ZO PS PM PB
08
06
04
02
1
0
f(lowast)
minus2 minus15 minus1 minus05 0 05 1 15 2
Figure 7 Membership functions for 119891(lowast)
dynamic characteristics of the transition process the integralof time multiplied absolute value of error (ITAE) is also pro-vided as a comprehensive performance index and the squareof control input is introduced to prevent the control energyfrom growing too bigThe comprehensive performance indexfunction [43] can be calculated as follows
119869 =
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905)) 119889119905
+1205963119905119903
119890 (119905) ge 0
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905) + 1205964|119890 (119905)|) 119889119905
+1205963119905119903
119890 (119905) lt 0
(19)
where 1205961 1205962 1205963 and 120596
4are weights and 120596
4≫ 1205961 119890(119905) is
the system error 119906(119905) is the output of controller and 119905119903is the
rising time To avoid overshoot the introduction of punitivefunction is essential in the function
Then the fitness function 119865 can be defined as follows
119865 =119862
(119869 + 120576) (20)
where 119862 is a constant and can be set equal to 1 in this paper 120576is a small positive number to prevent 119869 from becoming equalto zero and 120576 = 10
minus10
Step 4 (selection) Selection is a very important step in thecriteria of ldquosurvival of the fittestrdquo that means selecting thesuperior individual and eliminating the inferior one from apopulation For genetic algorithm an individual is selectedas a parent according to its fitness In rank-based selectionalgorithm all individuals of every generation are ranked inorder of increasing fitness value The survival probability ofthe 119894th individual is prob(119894) = 119902(1 minus 119902)
119894minus1 where 119902 isin (0 1) isevolutionary pressure
Step 5 (crossover and mutation) Because of its strong globalsearch capability crossover operator of GA can be regarded
as the main operator and due to its local search capabilitymutation operator can be regarded as an auxiliary operatorSelf-adaptive crossover and mutation operators are proposedin this paper in other words crossover probabilities 119875
119888
and mutation probabilities 119875119898
are automatically adjustedwith the addition of evolutionary generations In the initialstage a larger 119875
119888and a smaller 119875
119898can effectively accelerate
convergence velocity of iteration however in the later stage asmaller119875
119888and a larger119875
119898would avoid local optimal solution
The formulas of 119875119888and 119875
119898are given as follows
119875119888(119896 + 1) = 119875
119888(119896) minus
[119875119888(1) minus 05]
119866119898
(21)
119875119898
(119896 + 1) = 119875119898
(119896) minus[119875119898
(1) minus 01]
119866119898
(22)
where 119896 is the generation number of heredity 119896 = 1 sim 119866119898
119866119898is themaximumgeneration number119875
119888(1) is the crossover
probability of first generation and 119875119898(1) is the mutation
probability of first generationAccording to these operators the 119875
119888and 119875
119898of best
individuals are not equal to zero where 119875119888isin (05 119875
119888(1)) and
119875119898
isin (119875119898(1) 01) so the performance of excellent individual
would not be in a circle due to the 119875119888and 119875
119898being too
small or equal to zero To protect excellent individuals ofeach generation the elitist strategy was applied in GA toimprove the convergence and optimization results thus thebest individual would be copied directly into next generation
5 A Simulation Example
In order to verify the performance of proposed GA-fuzzy-immune PID controller a simulation example is provided inthis section and the parameters are illustrated as follows
1205961
= 004 1205962
= 0001 1205963
= 2 and 1205964
= 500 Thepopulation size is set to 50 119866
119898is set to 100 119875
119888(1) is set to
09 119875119898(1) is set to 001 119879
119891is set to 9 and sampling time 119879 is
set to 1msIn order to indicate the comparison with other con-
trollers fuzzy PID immune PID fuzzy-immune PID andreal-coded GA PID simulations are carried out The configu-rations of simulation environment for these controllers wereuniform In immune PID and fuzzy-immune PID 119870
1= 10
1198702
= 002 1198703
= 10 1205781
= 002 1205782
= 006 and 1205783
= 10and119891(lowast) = 001 in immune PID In fuzzy PID and real-codedGA PID 119870
119901isin (0 80) 119870
119894isin (0 2) and 119870
119889isin (0 2) Other
parameters are the same as GA-fuzzy-immune PIDThe input of robot dexterous hand system is a unit step
signal and the simulation time is 1 s The unit step responsesof this system are shown in Figure 8 The first curve isresponse obtained with fuzzy inference the second curve isresponse obtained with immune algorithm the third curveis response obtained with fuzzy-immune inference (F-I) thefourth curve is response obtained with real-coded GA andthe fifth curve is response obtained through integration ofimproved genetic algorithm and fuzzy-immune inference(GA-F-I)
8 The Scientific World Journal
Table 2 PID parameters and performance indexes of five control methods
Control methods Fuzzy Immune F-I Real-coded GA GA-F-I119870119901
The PID parameters and performance indexes of the fivecontrol methods are shown in Table 2The proposed control-ler parameters can be calculated by improved GA and fuzzyinference
1198701= 1114655 119870
2= 001737 119870
3= 081208
1205781= 002121 120578
2= 006604 120578
3= 094233
119891 (lowast) = 0000544
(23)
Compared with other four methods the overshoot120590 based on GA-F-I PID controller with incomplete deriva-tion is decreased from 3630 to 0 The settling time 119905
119904is
reduced from 0592 s to 0362 s The rising time 119905119903is reduced
from 0393 s to 0226 s Although the rising time 119905119903is not
the best the nonovershoot and shortest settling time can beachieved by the proposed PID controller
6 Conclusions and Future Works
In this paper a GA-fuzzy-immune PID controller wasdesigned to improve the performance of robot dexteroushand The control system of a robot dexterous hand andmathematical model of an index finger were presented Inorder to improve the characteristics of proposed controllerimmune mechanism genetic algorithm and fuzzy inference
were applied Finally a simulation experimentwas carried outand the results showed that the designed controller was ideal
In future studies the authors plan to investigate mul-tifinger coordination control system Furthermore moreintelligent control algorithms for multifinger coordinationcontrol system are worth further study for the authors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of Fundamental Research Funds for the CentralUniversities (no 2014QNA38) and the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions in carrying out this research are gratefully acknowl-edged
References
[1] A Bicchi and V Kumar ldquoRobotic grasping and contact areviewrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo00) pp 348ndash353 San Francis-co Calif USA April 2000
[2] H Liu P Meusel N Seitz et al ldquoThe modular multisensoryDLR-HIT-handrdquo Mechanism and Machine Theory vol 42 no5 pp 612ndash625 2007
[3] M Controzzi C Cipriani B Jehenne M Donati and M CCarrozza ldquoBio-inspired mechanical design of a tendon-drivendexterous prosthetic handrdquo in Proceedings of the 32nd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society (EMBC rsquo10) pp 499ndash502 Buenos AiresArgentina September 2010
[4] R M Murray and S S Sastry A Mathematical Introduction toRobotic Manipulation CRC Press 1994
[5] T Yoshikawa ldquoMultifingered robot hands Control for graspingandmanipulationrdquoAnnual Reviews in Control vol 34 no 2 pp199ndash208 2010
[6] R Tomovic and G Boni ldquoAn adaptive artificial handrdquo Transac-tions on Automatic Control IRE vol 7 no 3 pp 3ndash10 1962
[7] E M Jafarov Y Istefanopulos and M N A Parlakci ldquoAnew variable structure PID-controller for robot manipulatorswith parameter perturbations an augmented sliding surfaceapproachrdquo Sign vol 2 article 1 2002
The Scientific World Journal 9
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
dynamic characteristics of the transition process the integralof time multiplied absolute value of error (ITAE) is also pro-vided as a comprehensive performance index and the squareof control input is introduced to prevent the control energyfrom growing too bigThe comprehensive performance indexfunction [43] can be calculated as follows
119869 =
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905)) 119889119905
+1205963119905119903
119890 (119905) ge 0
int
infin
0
(1205961|119890 (119905)| + 120596
21199062
(119905) + 1205964|119890 (119905)|) 119889119905
+1205963119905119903
119890 (119905) lt 0
(19)
where 1205961 1205962 1205963 and 120596
4are weights and 120596
4≫ 1205961 119890(119905) is
the system error 119906(119905) is the output of controller and 119905119903is the
rising time To avoid overshoot the introduction of punitivefunction is essential in the function
Then the fitness function 119865 can be defined as follows
119865 =119862
(119869 + 120576) (20)
where 119862 is a constant and can be set equal to 1 in this paper 120576is a small positive number to prevent 119869 from becoming equalto zero and 120576 = 10
minus10
Step 4 (selection) Selection is a very important step in thecriteria of ldquosurvival of the fittestrdquo that means selecting thesuperior individual and eliminating the inferior one from apopulation For genetic algorithm an individual is selectedas a parent according to its fitness In rank-based selectionalgorithm all individuals of every generation are ranked inorder of increasing fitness value The survival probability ofthe 119894th individual is prob(119894) = 119902(1 minus 119902)
119894minus1 where 119902 isin (0 1) isevolutionary pressure
Step 5 (crossover and mutation) Because of its strong globalsearch capability crossover operator of GA can be regarded
as the main operator and due to its local search capabilitymutation operator can be regarded as an auxiliary operatorSelf-adaptive crossover and mutation operators are proposedin this paper in other words crossover probabilities 119875
119888
and mutation probabilities 119875119898
are automatically adjustedwith the addition of evolutionary generations In the initialstage a larger 119875
119888and a smaller 119875
119898can effectively accelerate
convergence velocity of iteration however in the later stage asmaller119875
119888and a larger119875
119898would avoid local optimal solution
The formulas of 119875119888and 119875
119898are given as follows
119875119888(119896 + 1) = 119875
119888(119896) minus
[119875119888(1) minus 05]
119866119898
(21)
119875119898
(119896 + 1) = 119875119898
(119896) minus[119875119898
(1) minus 01]
119866119898
(22)
where 119896 is the generation number of heredity 119896 = 1 sim 119866119898
119866119898is themaximumgeneration number119875
119888(1) is the crossover
probability of first generation and 119875119898(1) is the mutation
probability of first generationAccording to these operators the 119875
119888and 119875
119898of best
individuals are not equal to zero where 119875119888isin (05 119875
119888(1)) and
119875119898
isin (119875119898(1) 01) so the performance of excellent individual
would not be in a circle due to the 119875119888and 119875
119898being too
small or equal to zero To protect excellent individuals ofeach generation the elitist strategy was applied in GA toimprove the convergence and optimization results thus thebest individual would be copied directly into next generation
5 A Simulation Example
In order to verify the performance of proposed GA-fuzzy-immune PID controller a simulation example is provided inthis section and the parameters are illustrated as follows
1205961
= 004 1205962
= 0001 1205963
= 2 and 1205964
= 500 Thepopulation size is set to 50 119866
119898is set to 100 119875
119888(1) is set to
09 119875119898(1) is set to 001 119879
119891is set to 9 and sampling time 119879 is
set to 1msIn order to indicate the comparison with other con-
trollers fuzzy PID immune PID fuzzy-immune PID andreal-coded GA PID simulations are carried out The configu-rations of simulation environment for these controllers wereuniform In immune PID and fuzzy-immune PID 119870
1= 10
1198702
= 002 1198703
= 10 1205781
= 002 1205782
= 006 and 1205783
= 10and119891(lowast) = 001 in immune PID In fuzzy PID and real-codedGA PID 119870
119901isin (0 80) 119870
119894isin (0 2) and 119870
119889isin (0 2) Other
parameters are the same as GA-fuzzy-immune PIDThe input of robot dexterous hand system is a unit step
signal and the simulation time is 1 s The unit step responsesof this system are shown in Figure 8 The first curve isresponse obtained with fuzzy inference the second curve isresponse obtained with immune algorithm the third curveis response obtained with fuzzy-immune inference (F-I) thefourth curve is response obtained with real-coded GA andthe fifth curve is response obtained through integration ofimproved genetic algorithm and fuzzy-immune inference(GA-F-I)
8 The Scientific World Journal
Table 2 PID parameters and performance indexes of five control methods
Control methods Fuzzy Immune F-I Real-coded GA GA-F-I119870119901
The PID parameters and performance indexes of the fivecontrol methods are shown in Table 2The proposed control-ler parameters can be calculated by improved GA and fuzzyinference
1198701= 1114655 119870
2= 001737 119870
3= 081208
1205781= 002121 120578
2= 006604 120578
3= 094233
119891 (lowast) = 0000544
(23)
Compared with other four methods the overshoot120590 based on GA-F-I PID controller with incomplete deriva-tion is decreased from 3630 to 0 The settling time 119905
119904is
reduced from 0592 s to 0362 s The rising time 119905119903is reduced
from 0393 s to 0226 s Although the rising time 119905119903is not
the best the nonovershoot and shortest settling time can beachieved by the proposed PID controller
6 Conclusions and Future Works
In this paper a GA-fuzzy-immune PID controller wasdesigned to improve the performance of robot dexteroushand The control system of a robot dexterous hand andmathematical model of an index finger were presented Inorder to improve the characteristics of proposed controllerimmune mechanism genetic algorithm and fuzzy inference
were applied Finally a simulation experimentwas carried outand the results showed that the designed controller was ideal
In future studies the authors plan to investigate mul-tifinger coordination control system Furthermore moreintelligent control algorithms for multifinger coordinationcontrol system are worth further study for the authors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of Fundamental Research Funds for the CentralUniversities (no 2014QNA38) and the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions in carrying out this research are gratefully acknowl-edged
References
[1] A Bicchi and V Kumar ldquoRobotic grasping and contact areviewrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo00) pp 348ndash353 San Francis-co Calif USA April 2000
[2] H Liu P Meusel N Seitz et al ldquoThe modular multisensoryDLR-HIT-handrdquo Mechanism and Machine Theory vol 42 no5 pp 612ndash625 2007
[3] M Controzzi C Cipriani B Jehenne M Donati and M CCarrozza ldquoBio-inspired mechanical design of a tendon-drivendexterous prosthetic handrdquo in Proceedings of the 32nd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society (EMBC rsquo10) pp 499ndash502 Buenos AiresArgentina September 2010
[4] R M Murray and S S Sastry A Mathematical Introduction toRobotic Manipulation CRC Press 1994
[5] T Yoshikawa ldquoMultifingered robot hands Control for graspingandmanipulationrdquoAnnual Reviews in Control vol 34 no 2 pp199ndash208 2010
[6] R Tomovic and G Boni ldquoAn adaptive artificial handrdquo Transac-tions on Automatic Control IRE vol 7 no 3 pp 3ndash10 1962
[7] E M Jafarov Y Istefanopulos and M N A Parlakci ldquoAnew variable structure PID-controller for robot manipulatorswith parameter perturbations an augmented sliding surfaceapproachrdquo Sign vol 2 article 1 2002
The Scientific World Journal 9
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
The PID parameters and performance indexes of the fivecontrol methods are shown in Table 2The proposed control-ler parameters can be calculated by improved GA and fuzzyinference
1198701= 1114655 119870
2= 001737 119870
3= 081208
1205781= 002121 120578
2= 006604 120578
3= 094233
119891 (lowast) = 0000544
(23)
Compared with other four methods the overshoot120590 based on GA-F-I PID controller with incomplete deriva-tion is decreased from 3630 to 0 The settling time 119905
119904is
reduced from 0592 s to 0362 s The rising time 119905119903is reduced
from 0393 s to 0226 s Although the rising time 119905119903is not
the best the nonovershoot and shortest settling time can beachieved by the proposed PID controller
6 Conclusions and Future Works
In this paper a GA-fuzzy-immune PID controller wasdesigned to improve the performance of robot dexteroushand The control system of a robot dexterous hand andmathematical model of an index finger were presented Inorder to improve the characteristics of proposed controllerimmune mechanism genetic algorithm and fuzzy inference
were applied Finally a simulation experimentwas carried outand the results showed that the designed controller was ideal
In future studies the authors plan to investigate mul-tifinger coordination control system Furthermore moreintelligent control algorithms for multifinger coordinationcontrol system are worth further study for the authors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
The support of Fundamental Research Funds for the CentralUniversities (no 2014QNA38) and the Priority AcademicProgram Development of Jiangsu Higher Education Institu-tions in carrying out this research are gratefully acknowl-edged
References
[1] A Bicchi and V Kumar ldquoRobotic grasping and contact areviewrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo00) pp 348ndash353 San Francis-co Calif USA April 2000
[2] H Liu P Meusel N Seitz et al ldquoThe modular multisensoryDLR-HIT-handrdquo Mechanism and Machine Theory vol 42 no5 pp 612ndash625 2007
[3] M Controzzi C Cipriani B Jehenne M Donati and M CCarrozza ldquoBio-inspired mechanical design of a tendon-drivendexterous prosthetic handrdquo in Proceedings of the 32nd AnnualInternational Conference of the IEEE Engineering in Medicineand Biology Society (EMBC rsquo10) pp 499ndash502 Buenos AiresArgentina September 2010
[4] R M Murray and S S Sastry A Mathematical Introduction toRobotic Manipulation CRC Press 1994
[5] T Yoshikawa ldquoMultifingered robot hands Control for graspingandmanipulationrdquoAnnual Reviews in Control vol 34 no 2 pp199ndash208 2010
[6] R Tomovic and G Boni ldquoAn adaptive artificial handrdquo Transac-tions on Automatic Control IRE vol 7 no 3 pp 3ndash10 1962
[7] E M Jafarov Y Istefanopulos and M N A Parlakci ldquoAnew variable structure PID-controller for robot manipulatorswith parameter perturbations an augmented sliding surfaceapproachrdquo Sign vol 2 article 1 2002
The Scientific World Journal 9
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
[8] E M Jafarov M N A Parlakci and Y Istefanopulos ldquoA newvariable structure PID-controller design for robot manipula-torsrdquo IEEE Transactions on Control Systems Technology vol 13no 1 pp 122ndash130 2005
[9] K R Atia ldquoA new variable structure controller for robotmanipulators with a nonlinear PID sliding surfacerdquo Roboticavol 31 no 4 pp 503ndash510 2013
[10] Y Chen G Ma S Lin and J Gao ldquoAdaptive fuzzy computed-torque control for robotmanipulator with uncertain dynamicsrdquoInternational Journal of Advanced Robotic Systems vol 9 pp201ndash209 2012
[11] S H Park and S I Han ldquoRobust-tracking control for robotmanipulator with deadzone and friction using backsteppingand RFNN controllerrdquo IET Control Theory amp Applications vol5 no 12 pp 1397ndash1417 2011
[12] I Hassanzadeh G Alizadeh F Hashemzadeh et al ldquoPerfor-mance tuning for robot manipulators using intelligent robustcontrollerrdquo Proceedings of the Institution of Mechanical Engi-neers Part I Journal of Systems and Control Engineering vol225 no 3 pp 385ndash392 2011
[13] A A G Siqueira M H Terra and C Buosi ldquoFault-tolerantrobot manipulators based on output-feedback H
infincontrollersrdquo
Robotics and Autonomous Systems vol 55 no 10 pp 785ndash7942007
[14] J Q Han ldquoFrom PID to active disturbance rejection controlrdquoIEEE Transactions on Industrial Electronics vol 56 no 3 pp900ndash906 2009
[15] Y X Su B Y Duan and C H Zheng ldquoNonlinear PID controlof a six-DOF parallel manipulatorrdquo IEE Proceedings ControlTheory and Applications vol 151 no 1 pp 95ndash102 2004
[16] A N Gundes and A B Ozguler ldquoPID stabilization of MIMOplantsrdquo IEEE Transactions on Automatic Control vol 52 no 8pp 1502ndash1508 2007
[17] J Alvarez-Ramirez R Kelly and I Cervantes ldquoSemiglobalstability of saturated linear PID control for robotmanipulatorsrdquoAutomatica vol 39 no 6 pp 989ndash995 2003
[18] V A Oliveira L V Cossi M C M Teixeira and A M F SilvaldquoSynthesis of PID controllers for a class of time delay systemsrdquoAutomatica vol 45 no 7 pp 1778ndash1782 2009
[19] J G Ziegler and N B Nichols ldquoOptimum setting for automaticcontrollersrdquo ASME Transactions vol 64 no 11 pp 759ndash7681942
[20] J Chen and T Huang ldquoApplying neural networks to on-lineupdated PID controllers for nonlinear process controlrdquo Journalof Process Control vol 14 no 2 pp 211ndash230 2004
[21] D Pelusi ldquoGenetic-neuro-fuzzy controllers for second ordercontrol systemsrdquo in Proceedings of the 5th UKSim EuropeanModelling Symposium on Computer Modelling and Simulation(EMS rsquo11) pp 12ndash17 Madrid Spain November 2011
[22] D Pelusi ldquoOn designing optimal control systems throughgenetic and neuro-fuzzy techniquesrdquo in Proceedings of the IEEEInternational Symposium on Signal Processing and InformationTechnology (ISSPIT 11) pp 134ndash139 Bilbao Spain December2011
[23] D Pelusi ldquoPID and intelligent controllers for optimal timingperformances of industrial actuatorsrdquo International Journal ofSimulation Systems Science and Technology vol 13 no 2 pp65ndash71 2012
[24] D Pelusi L Vazquez D Diaz et al ldquoFuzzy algorithm controleffectiveness on drum boiler simulated dynamicsrdquo in Proceed-ings of the 36th International Conference on Telecommunicationsand Signal Processing (TSP rsquo13) pp 272ndash276 IEEE 2013
[25] D Pelusi ldquoImproving settling and rise times of controllers viaintelligent algorithmsrdquo in Proceedings of the 14th InternationalConference on Modelling and Simulation (UKSim rsquo12) pp 187ndash192 Cambridge Mass USA March 2012
[26] D Pelusi ldquoDesigning neural networks to improve timingperformances of intelligent controllersrdquo Journal of DiscreteMathematical Sciences and Cryptography vol 16 no 2-3 pp187ndash193 2013
[27] D Pelusi and R Mascella ldquoOptimal control algorithms forsecond order systemsrdquo Journal of Computer Science vol 9 no2 pp 183ndash197 2013
[28] T Kim I Maruta and T Sugie ldquoRobust PID controllertuning based on the constrained particle swarm optimizationrdquoAutomatica vol 44 no 4 pp 1104ndash1110 2008
[29] C F Juang and C F Lu ldquoLoad-frequency control by hybridevolutionary fuzzy PI controllerrdquo IEE Proceedings GenerationTransmission amp Distribution vol 153 no 2 pp 196ndash204 2006
[30] C Lu C Hsu and C Juang ldquoCoordinated control of flexibleAC transmission system devices using an evolutionary fuzzylead-lag controller with advanced continuous ant colony opti-mizationrdquo IEEE Transactions on Power Systems vol 28 no 1pp 385ndash392 2013
[31] K S Tang K FMan G Chen and S Kwong ldquoAn optimal fuzzyPID controllerrdquo IEEE Transactions on Industrial Electronics vol48 no 4 pp 757ndash765 2001
[32] F Zheng Q Wang and T H Lee ldquoOn the design of multivari-able PID controllers via LMI approachrdquoAutomatica vol 38 no3 pp 517ndash526 2002
[33] J D Farmer N H Packard and A S Perelson ldquoThe immunesystem adaptation and machine learningrdquo Physica D Nonlin-ear Phenomena vol 22 no 1ndash3 pp 187ndash204 1986
[34] J Xin D Liu and Y Yang ldquoRobot trajectory tracking controlbased on fuzzy immune PD-type controllerrdquo in Proceedings ofthe 5th World Congress on Intelligent Control and Automation(WCICA rsquo04) vol 6 pp 4942ndash4945 June 2004
[35] Z Lei and L Ren-hou ldquoDesigning of classifiers based onimmune principles and fuzzy rulesrdquo Information Sciences vol178 no 7 pp 1836ndash1847 2008
[36] S XWang Y Jiang and H Yang ldquoChaos optimization strategyon fuzzy-immune-PID control of the turbine governing sys-temrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems (IROS rsquo06) pp 1594ndash1598 IEEEBeijing China October 2006
[37] W B Lin H K Chiang and Y L Chung ldquoThe speed controlof immune-fuzzy sliding mode controller for a synchronousreluctance motorrdquo Applied Mechanics and Materials vol 300-301 pp 1490ndash1493 2013
[38] G W Chang W Chang C Chuang and D Shih ldquoFuzzylogic and immune-based algorithm for placement and sizingof shunt capacitor banks in a distorted power networkrdquo IEEETransactions on Power Delivery vol 26 no 4 pp 2145ndash21532011
[39] R J Kuo W L Tseng F C Tien and T Warren LiaoldquoApplication of an artificial immune system-based fuzzy neuralnetwork to a RFID-based positioning systemrdquo Computers andIndustrial Engineering vol 63 no 4 pp 943ndash956 2012
[40] E Lianjie Automatic Control System Beijing University PressBeijing China 1994
[41] G Er and Y Dou Motion Control System Tsinghua UniversityPress Beijing China 2002
10 The Scientific World Journal
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
[42] J Deng X Y Li and W Wei ldquoOPC controller for turbo-generating set based on immune fuzzy algorithmrdquo Proceedingof the CSU-EPSA vol 23 no 3 pp 1ndash7 2011
[43] J K Liu Advanced PID Control based on MATLAB PublishingHouse of Electronics Industry Beijing China 2011
