Measurement 54 (2014) 40–50

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Measurement

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Application of response surface methodology on findinginfluencing parameters in servo pneumatic system

http://dx.doi.org/10.1016/j.measurement.2014.04.0170263-2241/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +91 9994872013.E-mail addresses: saravanapoy@gmail.com (D. Saravanakumar), mohan@

mitindia.edu (B. Mohan), muthu1060@gmail.com (T. Muthuramalingam).1 Tel.: +91 9791964510.2 Tel.: +91 9445774915.

D. Saravanakumar a,1, B. Mohan b,2, T. Muthuramalingam a,⇑a Department of Production Technology, MIT Campus, Chromepet, Anna University, Chennai, Tamil Nadu 600044, Indiab Department of Mechanical Engineering, CEG Campus, Guindy, Anna University, Chennai, Tamil Nadu 600025, India

a r t i c l e i n f o

Article history:Received 22 September 2013Received in revised form 7 February 2014Accepted 18 April 2014Available online 30 April 2014

Keywords:Servo pneumaticsParameter influencesResponse surface methodologyANOVAPositioning system

a b s t r a c t

Servo pneumatic positioning system is a mechatronics approach that enables to use pneu-matic cylinders as multi-position actuators. In the present study, an endeavor has beenmade to simulate the response of pneumatic cylinder parameters. Response surface meth-odology based analysis have been conducted to evaluate the influences of system param-eters such as external load, supply pressure and cross sectional area of cylinder on theresponse characteristics such as settling time, maximum overshoot, integral time absoluteerror and maximum force generated using fuzzy rule base models. From the experimentalresults, it has been inferred that supply pressure has mostly influent nature on determiningmaximum overshoot and integral of time absolute error (ITAE). It has been observed thatcross sectional area and external load has significantly affected the maximum generatedforce and settling time respectively.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Pneumatic actuators are widely used in the field ofautomation, robotics and manufacturing. The pneumatictechnology exhibits many advantages such as high speed,high force generation, better efficiency, less maintenanceand low operating costs. Traditionally pneumatic cylindersare used for motion between two hard stops. In order toexpand the capabilities of the pneumatic cylinders to beoperated as multi-position actuator, servo control tech-niques are being used. But the pneumatic actuators are dif-ficult to control due to nonlinear characteristics of thesystem [1,2]. The nonlinearities present in pneumatic actu-ators are very low stiffness (caused by air compressibility),mass flow rate variations and low damping of the actuator

systems, which make it difficult to achieve precise motioncontrol [1]. The main nonlinearities in pneumatic servosystems are the valve dead zone, air flow-pressure rela-tionship through valve orifice, the air compressibility andfriction effects between contact surfaces in actuator seals[2].

Over the past decade modelling and control of the servopneumatic actuators is an interesting topic that hasattracted the researchers around the world. Valdiero et al.[2] presented the model of the system with combinationof theoretical equations and system identification methods.Sorli et al. [3] analysed the dynamic characteristics of theservo pneumatic positioning system. Takosoglu et al. [4]presented overall theoretical model of the servo pneumaticsystem using proportional valve. Najafi et al. [5] modelledthe cushioning sections of the pneumatic cylinder. Manyauthors have presented different control approaches andalgorithms for accurate control of the pneumatic actuators.Aziz and Bone [6] presented the automatic tuning procedurefor the servo controllers for pneumatic systems. Rao andBone [7] presented novel MISO nonlinear position control

Fig. 1. Schematic diagram of pneumatic servo positioning system.

Fig. 2. Block diagram of the fuzzy controller for the pneumatic positioning system.

Fig. 3. Membership functions of variables of fuzzy PD controller.

D. Saravanakumar et al. / Measurement 54 (2014) 40–50 41

Table 1Rule base for fuzzy PD controller.

Rule base Change in position error De(k)

NE ZE PE

Position error e(k)NB NB NS NSNS NS NVS NVSZE NS Z PSPS PVS PVS PSPB PS PS PB

Table 3Values of system parameters of the servo pneumatic positioning system forvarious levels.

Parameter Notation Level 1 Level 2 Level 3

External load applied in kg m 3 5 10Supply pressure in MPa Ps 0.2 0.4 0.6Internal diameter of the

cylinder in md 0.006 0.025 0.05

42 D. Saravanakumar et al. / Measurement 54 (2014) 40–50

law designed using the back stepping method for the pneu-matic systems. Tsai and Huang [8] proposed an adaptivecontroller based on the function approximation technique(FAT) to estimate the time-varying uncertainties in theservo pneumatic positioning systems. Gulati and Barth [9]designed a Lyapunov-based pressure observer for a pneu-matic servo system. The design of the complex control sys-tems is quite difficult. It is relatively easier to make use offuzzy logic controller which makes use of knowledge baselike human operator. Gao and Feng [10] developed adaptivefuzzy PD controller for the pneumatic positioning system.Nagi and Perumal [11] optimized the fuzzy controller forminimal time response. Kaitwanidvilai and Olranthichachat

Fig. 4. Simulink block diagram model of servo pneuma

Table 2The system parameters used in the numerical simulations.

Parameter Repre

Internal mass of piston and slide MLength of the cylinder lAdiabatic exponent jLength of dead zone in the cylinder l0Specific gas constant RAir temperature TAir density q0

Sonic conductance consistent C14, CCritical pressure ratios b14,b4

Viscous coefficient of friction fl

Kinetic coefficient of friction Fk

Stribeck velocity vs

Break away force Fpr

Friction coefficients due to seals kp

[12] proposed robust loop shaping fuzzy controller method-ology for positioning control of the servo pneumatic system.

In process of designing any automated applicationbased on servo pneumatic drives, problem of using theoptimal size and pressure plays a vital role. The drive needsto be able to perform a predefined automation-task speci-fied by the desired force, speed, and accuracy [13]. In pneu-matic drives there will be a compromise between accuracyand speed. The settling time, overshoot and integral perfor-mance coefficients such as Integral absolute error (IAE) andIntegral time-weighed absolute error (ITAE) can be used asa measure of positioning accuracy and speed of the system[14]. The force and position controls are specificallydesigned based on the application. Mohd Faudzi et al.[15] developed an intelligent cylinder with a combinedforce and position control algorithm. In the current

tic positioning system using fuzzy PD controller.

sentation Values

0.5 kg0.2 kg1.40.02 m288 Nm/kg K298 K1.225 kg/m3

45, C23 and C12 1.462 � 10�8 m4 s/kg5,b23 and b12 0.28

250 Ns/m100 N0.1 m/s200 N3 N/Pa

Table 5ANOVA table for settling time.

Source DF SS MS F P %C

m 2 12.1086 6.6543 181.20 0.000 48.51Ps 2 11.7774 5.8887 176.24 0.000 47.19d 2 0.4053 0.2026 6.06 0.009 1.62Error 20 0.6682 0.0334 2.68Total 26 24.9595

R–Sq = 97.32%.

Table 4Design layout and pneumatic system parameters.

Trial Coded factors Actual factors Performance measures

A B C m (kg) Ps (MPa) d (m) Ts (s) OS (%) ITAE (ms) Fmax (N)

1. �1 �1 �1 3 0.2 0.006 2.12 1.98 0.452 4.822. �1 �1 0 3 0.2 0.025 2.05 2.38 0.448 91.623. �1 �1 +1 3 0.2 0.05 1.94 2.74 0.446 369.864. �1 0 �1 3 0.4 0.006 1.51 3.58 0.442 10.525. �1 0 0 3 0.4 0.025 1.34 3.92 0.442 182.946. �1 0 +1 3 0.4 0.05 1.15 4.24 0.441 737.347. �1 +1 �1 3 0.6 0.006 0.91 6.16 0.441 15.378. �1 +1 0 3 0.6 0.025 0.81 7.16 0.442 778.049. �1 +1 +1 3 0.6 0.05 0.69 8.58 0.444 1127.96

10. 0 �1 �1 5 0.2 0.006 3.07 1.18 0.468 4.911. 0 �1 0 5 0.2 0.025 2.94 1.36 0.463 92.1112. 0 �1 +1 5 0.2 0.05 2.81 1.62 0.457 373.1413. 0 0 �1 5 0.4 0.006 2.55 2.52 0.447 10.7814. 0 0 0 5 0.4 0.025 2.41 2.84 0.445 186.0715. 0 0 +1 5 0.4 0.05 2.2 3.42 0.442 743.2716. 0 +1 �1 5 0.6 0.006 1.65 4.28 0.441 15.6217. 0 +1 0 5 0.6 0.025 1.39 5.02 0.44 792.2718. 0 +1 +1 5 0.6 0.05 1.15 5.96 0.441 1142.6119. +1 �1 �1 10 0.2 0.006 4.17 0.36 0.564 4.9920. +1 �1 0 10 0.2 0.025 4.03 0.48 0.529 92.7821. +1 �1 +1 10 0.2 0.05 3.91 0.7 0.497 377.9422. +1 0 �1 10 0.4 0.006 3.21 1.16 0.469 10.8923. +1 0 0 10 0.4 0.025 3.1 1.48 0.46 188.9324. +1 0 +1 10 0.4 0.05 2.96 1.86 0.453 749.5725. +1 +1 �1 10 0.6 0.006 2.13 3.54 0.442 16.8226. +1 +1 0 10 0.6 0.025 1.96 3.82 0.441 797.1727. +1 +1 +1 10 0.6 0.05 1.81 4.84 0.439 1158.15

D. Saravanakumar et al. / Measurement 54 (2014) 40–50 43

research effect of size of the drive, supply pressure andexternal load on the positioning and force generationcapabilities of the servo pneumatic system has been stud-ied. A simulation model of the servo pneumatic systembased on the mathematical model of the system with fuzzyPD controller has been created in the Matlab-Simulinksoftware for studying the effect of the parameters.

Response surface methodology is a statistical methodused for analysis of relationships between several explan-atory variables and one or more response variables. Tzenget al. [16] and Natarajan et al. [17] discussed the procedure

Fig. 5. Simulation results of few trials.

Fig. 6. Surface plots between settling time and pneumatic system parameters.

44 D. Saravanakumar et al. / Measurement 54 (2014) 40–50

analyzing parameters using Response Surface Methodol-ogy. In the present study, the influence on system param-eters such as external load applied, diameter of the

cylinder and supply pressure on the speed, accuratepositioning and force generating capabilities of the pneu-matic system. The other factors which are not taken into

Fig. 7. Surface plots between maximum overshoot and pneumatic system parameters.

D. Saravanakumar et al. / Measurement 54 (2014) 40–50 45

account but will affect the system performance are lengthof the cylinder, ambient air temperature and pressure andother system design features such as valve conductanceand dead zone in valve and cylinders. The effect of theseparameters is very low compared to the parameters thosehave been taken into account.

2. Servo pneumatic positioning system

2.1. System overview

The schematic diagram of the pneumatic servo posi-tioning system is shown in Fig. 1. The main components

Table 7ANOVA table for integral time absolute error.

Source DF SS MS F P %C

m 2 12.3454 6.1727 9.36 0.010 34.68Ps 2 13.1912 6.5956 9.78 0.000 37.06d 2 0.9883 0.4941 0.75 0.486 2.78Error 20 9.0708 0.4535 25.50Total 26 35.5957

R–Sq = 95.42%.

Table 6ANOVA table for maximum overshoot.

Source DF SS MS F P %C

m 2 7.0621 3.5310 70.41 0.000 24.78Ps 2 19.2444 9.6222 191.86 0.000 67.52d 2 1.1906 0.5953 11.87 0.000 4.18Error 20 1.0030 0.0502 3.52Total 26 28.5001

R–Sq = 96.48%.

Table 8ANOVA table for maximum force generated.

Source DF SS MS F P %C

m 2 345 173 0.61 0.994 0.12Ps 2 1139516 569758 18.75 0.000 26.91d 2 2486934 1243467 40.93 0.000 58.73Error 20 607608 30380 14.35Total 26 4234404

R–Sq = 95.78%.

46 D. Saravanakumar et al. / Measurement 54 (2014) 40–50

in the system are rodless pneumatic cylinder, proportionaldirectional control valve, position transducer and fuzzylogic control system. The position of the pneumatic cylin-der has been controlled by the voltage applied to the pro-portional directional control valve which has regulated theflow rate of the compressed air to the cylinder chambers.The position transducer has sensed the present positionvalue which has been used by the fuzzy controller tomanipulate the spool movement in the proportional direc-tional control valve.

2.2. Mathematical model of the system

The mathematical model of the positioning system hasbeen derived from physical laws and recent literatureinformation. The system constitutes the nonlinearities ofthe dead zone, the mass flow rate, the pressure dynamics,the motion equation and the friction dynamics.

In the modelling of the system, the following assump-tions are made:

� The gas is perfect.� The pressures and temperature within each chamber

are homogeneous.� Kinetic and potential energy terms are negligible.� Temperature changes inside the cylinders in neglected.� Tube length can be ignored when air supply is very

close to valve and cylinder.

� Valve dynamics is sufficiently faster than mechanicalsystems dynamics.

From Newton’s second law of motion, the equation ofmotion of piston and slide of the rodless cylinder is givenby (1).

€x ¼ 1M þm

ðAðP1 � P2Þ � Ffric þmg sin hÞ ð1Þ

where x is the piston position, M is internal mass of the pis-ton and slide, m is external load, A is internal cross sec-tional area of the cylinder chamber given by 0.785d2, d isthe internal diameter of the cylinder, P1 and P2 are theabsolute pressure inside cylinder chambers, Ffric is the fric-tional force, g is acceleration due to gravity and h is infla-tion angle of the piston with the horizontal axis.

The equation for absolute pressure in two cylinderchambers as per the law of conservation of energy is givenby (2) and (3) respectively.

_P1 ¼jAðl0 þ xÞðRT _m1 � P1A _xÞ ð2Þ

_P2 ¼jAðlþ l0�xÞð�RT _m2 þ P2A _xÞ ð3Þ

where j is adiabatic exponent, l0 is length of dead zone ofcylinder, l is full stroke length of the cylinder, R is specificgas constant, T is air temperature, _m1 and _m2 are the massflow rates to the cylinder chambers.

The mass flow rate inside the proportional valvedepends on the voltage applied to the coil. The equationof mass flow rates to the cylinder chambers from the pro-portional directional control valve is given by (4) and (5)respectively.

_m1 ¼ @0xrðC14Psw14 � C45P1w45Þ ð4Þ

_m2 ¼ @0xrðC23P2w23 � C12Psw12Þ ð5Þ

where @0 is air density, Ps is supply air pressure, xr is thespool position (expressed in %) in the valve depends onthe applied coil voltage u, C14, C45, C23 and C12 are sonicconductance consistent with the standard ISO 6358–2013for critical pressure ratio, w14, w45, w23 and w12 are nonlin-ear flow function (sonic flow and subsonic flow) dependingon the pressure ratio and on the critical pressure ratios b14,b45, b23 and b12 respectively.

The equation of frictional forces in cylinder is given by(6).

Ffric ¼ f1 _xþ Fksignð _xÞ þ Fpreð�_x

vsÞsignð _xÞ þ kpðP1 � P2Þ ð6Þ

where f1 is viscous coefficient of friction, Fk is kinetic coef-ficient of friction, vs are stribeck velocity, Fpr is break awayforce and kp is the friction coefficients due to seals.

2.3. Fuzzy controller

The highly nonlinear pneumatic system needs a feed-back controller to establish a servo closed loop control sys-tem. Fuzzy controller which basically work based on theknowledge base similar to a human operator is capableof controlling complex nonlinear system. So a sugeno type

D. Saravanakumar et al. / Measurement 54 (2014) 40–50 47

discrete fuzzy PD controller is designed for the positioningcontrol of the pneumatic cylinder. The controller has twoinputs – position error e(k) and change in position errorDe(k) and one output – voltage applied to the proportionalvalve u(k). The voltage applied to the proportional valveu(k) manipulates the mass flow rate to the cylinder cham-bers, thus controlling the position of the cylinder. The basicblock diagram of the closed loop position control systemusing fuzzy logic controller is shown in Fig. 2. The fuzzyPD controller is designed using fuzzy logic toolbox of Mat-lab-Simulink software. The fuzzy controller works on theknowledge base containing IF-THEN rules for undeter-mined predicates and fuzzy control mechanism.

The primary input variable – position error e(k) in therange �5 to 5 has five membership functions. They are NB(Negative Big), NS (Negative Small), ZE (Zero Error), PS (Posi-tive Small) and PB (Positive Big). The shape and range of themembership functions are shown in Fig. 3a. The next inputvariable – change in position error De(k) in the range �1to 1 has three membership functions namely NE (NegativeError), ZE (Zero Error) and PE (Positive Error). Fig. 3b showsthese membership functions shape and range. The outputvariable – control voltage to the proportional valve u(k)has the range 0–5 and posses seven membership functions.The values of the constant membership functions NB (Neg-ative Big), NS (Negative Small), NVS (Negative Very Small), Z(Zero), PVS (Positive Very Small), PS (Positive Small) and PB(Positive Big) are shown in Fig. 3c.

For convenience the rules of the fuzzy algorithm areshown in Table 1 in a matrix format and should be inter-preted as follows:

If eðkÞ is X and DeðkÞ is Y then uðkÞ is Z

where X, Y and Z are corresponding membership functions.The fuzzy inference method used is MAX–MIN method.The Defuzzification method used in the fuzzy PD controlleris Centroid method.

2.4. Simulation environment

The simulation model of the pneumatic cylinder posi-tioning system has been created based on the mathemati-cal model given by Eqs. (1)–(6) using Matlab-Simulinksoftware. The simulation model of the servo pneumaticpositioning system with the fuzzy PD controller is shownin Fig. 4. The constant parameters used in the simulationare shown in the Table 2. The external load applied, supplypressure and diameter of the cylinder are the parametersthat are considered for analysis. The three level values forthese parameters are shown in Table 3.

The system is subjected to a step change in desiredposition (setpoint) from 0 m to 0.1 m at simulation time0 s. From the simulation response, the settling time Ts (s),maximum overshoot OSmax (%) and Integral of the time-weighted absolute error ITAE (ms) are computed. Theseparameters are considered as output parameters for opti-mizing the system parameters. The maximum force gener-ated inside the cylinder has been computed from thesimulation. Settling time is the time required for theresponse curve to reach and stay in final steady state value[18] with an error band of ±2%. Thus settling time refers to

speed of the positioning system. Overshoot refers to anoutput exceeding its final steady-state value. The maxi-mum deviation from the steady-state value is the maxi-mum overshoot which will be expressed in percentage.The maximum overshoot is considered as a measure ofaccuracy of the system. ITAE is the integral of the timeweighted parameter which is accumulation of errordepending on time [18] which is combined measure ofboth speed and accuracy of the system.

3. Results and discussions

The simulation results have been evaluated to analyzethe effects of pneumatic system parameters on the perfor-mance measures such as settling time, maximum over-shoot, integral time absolute error and maximum forcegenerated using response surface methodology with thehelp of Minitab software package. The design layout andthe pneumatic system parameters have been tabulated inTable 4. Fig. 5 shows the simulation responses of the sys-tem for few trials in the design of the experiments.

3.1. Influences of pneumatic system parameters on settlingtime (Ts)

The result of ANOVA table for analyzing the pneumaticsystem parameters is shown in Table 5, which has illus-trated the degrees of freedom (DF), sum of squares (SS),mean squares (MS), F-values (F) and probability (P) in addi-tion to the percentage contribution (C%) of each factor andtheir interactions. A low P-value (60.05) indicates statisti-cal significance for the source on the correspondingresponse (i.e., a = 0.05%, or 95% confidence level). Thisdemonstrates that the obtained model is considered to bestatistically significant effect on the response. The coeffi-cient of determination (R2) in the ANOVA table is definedas the ratio of the explained variation to the total variationand which is a measure of the fit degree. When R2

approaches to unity, it indicates a good correlationbetween the experimental and the predicted values. It isclear from the results of ANOVA that the external loadaffects the settling time in a considerable way which has48.51% of the contribution. The second dominant factoron influencing settling time has been supply pressurewhich has the contribution of 47.19%. The diameter ofthe cylinder has less influent nature among the electricalprocess parameters with the contribution of 1.62%. Thecoefficient of correlation R2 has the value of 97.32% whichhas been more than the confidence level. Three dimen-sional (3D) Surface plots between settling time and pneu-matic system parameters is shown in Fig. 6 which hasbeen obtained using response surface methodology (RSM)according to their mathematical models with the help ofMinitab software package.

3.2. Influences of pneumatic system parameters on maximumovershoot (OS)

The ANOVA table for analyzing the maximum overshootis shown in Table 6. It is clear from the ANOVA table thatthe supply pressure greatly influences the maximum over-

Fig. 8. Surface plots between integral time absolute error and pneumatic system parameters.

48 D. Saravanakumar et al. / Measurement 54 (2014) 40–50

shoot which has 67.52% of the contribution. The seconddominant factor on influencing OS has been external loadwhich has the contribution of 24.78%. The diameter ofcylinder has less influent nature among the pneumatic

system parameters with the contribution of 4.18%. Thecoefficient of correlation R2 has the value of 96.48% whichhas been more than the confidence level. Three dimen-sional (3D) Surface plots between maximum overshoot

Fig. 9. Surface plots between maximum force generated and pneumatic system parameters.

D. Saravanakumar et al. / Measurement 54 (2014) 40–50 49

and pneumatic system parameters is shown in Fig. 7 whichhas been obtained using response surface methodology

(RSM) according to their mathematical models with thehelp of Minitab software package.

50 D. Saravanakumar et al. / Measurement 54 (2014) 40–50

3.3. Influences of pneumatic system parameters on integraltime absolute error (ITAE)

The ANOVA table for analyzing the integral time abso-lute error is shown in Table 7. It is clear from the ANOVAtable that the supply pressure greatly influences the inte-gral time absolute error which has 37.06% of the contribu-tion. The second dominant factor on influencing ITAE hasbeen external load which has the contribution of 34.68%.The diameter of cylinder has less influent nature on ITAEamong the pneumatic system parameters with the contri-bution of 2.78%. The coefficient of correlation R2 has thevalue of 95.42% which has been more than the confidencelevel. Three dimensional (3D) Surface plots between inte-gral time absolute error and pneumatic system parametersis shown in Fig. 8 which has been obtained using responsesurface methodology (RSM) according to their mathemati-cal models with the help of Minitab software package.

3.4. Influences of pneumatic system parameters on maximumgenerated force (Fmax)

The ANOVA table for analyzing the maximum generatedforce is shown in Table 8. It is clear from the ANOVA tablethat the diameter of cylinder greatly influences the maxi-mum generated force which has 58.73% of the contribu-tion. The second dominant factor on influencing Fmax hasbeen supply pressure which has the contribution of26.91%. The external load has very less influent nature onITAE among the pneumatic system parameters with thecontribution of 0.12%. The coefficient of correlation R2

has the value of 95.78% which has been more than the con-fidence level. Three dimensional (3D) Surface plotsbetween maximum generated force and pneumatic systemparameters is shown in Fig. 9 which has been obtainedusing response surface methodology (RSM) according totheir mathematical models with the help of Minitab soft-ware package.

4. Conclusion

In the present work, an analysis has been made to eval-uate the influence of system parameters on pneumaticactuator using fuzzy rule base model and response surfaceplots. From the simulation results, the influence of eachsystem parameter on speed, accuracy and force generationhas been discussed by optimizing the pneumatic actuatorparameters. Based on the results, the following conclusionshave been made.

(i) The external load has given more contributionamong the pneumatic system parameters on settlingtime.

(ii) The supply pressure has considerably affects maxi-mum overshoot and integral time absolute error.

(iii) The cross sectional area of cylinder has most signif-icant effect on maximum generated force.

Acknowledgement

The authors express their sincere thanks to Departmentof Production Technology, Anna University, Chennai forfunding this research.

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