Self-constructing recurrent fuzzy neural network forDSP-based permanent-magnet linear-synchronous-motor servodrive

F.-J. Lin, S.-L. Yang and P.-H. Shen

Abstract: A self-constructing recurrent fuzzy-neural-network (SCRFNN) control system isproposed to control the position of the mover of a field-oriented control permanent-magnetlinear-synchronous-motor (PMLSM) servodrive system to track periodic reference trajectories.The proposed SCRFNN combines the merits of self-constructing fuzzy neural network (SCFNN)and the recurrent neural network (RNN). Moreover, the structure and the parameter-learningphases are preformed concurrently and on-line in the SCRFNN. The structure learning is based onthe partition of input space, and the parameter learning is based on the supervised gradient-decentmethod using a delta-adaptation law. Further, all the control algorithms are implemented in aTMS320C32 DSP-based control computer. The simulated and experimental results due to periodicreference trajectories show that the dynamic behaviors of the proposed SCRFNN control systemare robust with regard to uncertainties.

1 Introduction

Fuzzy neural networks (FNNs) combine the capability offuzzy reasoning in handling uncertain information [1, 2] andthe capability of neural networks in learning from processes[3, 4]. Generally, learning for most FNN applications isonly parameter learning based on a supervised back-propagation algorithm, in which the parameters of themembership functions and the connected weights areadjusted and the structure of the FNN has been determinedin advance and fixed. Though the control performance ofthe fixed-structure FNNs with the ability of on-lineparameter learning are usually acceptable [2], large numbersof nodes are usually needed in the hidden layers for complexcontrolled plant. On the other hand, several approachesconsist of structure- and parameter-learning phases for theFNNs have been proposed in [5–8]. These two-phaselearning algorithms not only extract the fuzzy-logic rulefrom input data with adjustment of fuzzy partitions for theinput and output spaces but also adjust the parameters ofthe FNNs. Traditionally, these two phases are donesequentially [6], i.e. the structure-learning phase is employedto decide the structure of fuzzy rules first, and then theparameter-learning phase is used to tune the coefficients ofeach rule (e.g. membership functions). The disadvantage ofthis sequential learning scheme is its suitability only for off-line instead of on-line operation [6], and a large amount ofrepresentative data should be collected in advance forimplementation of this scheme. Moreover, the independentrealisation of the structure and parameter learning usuallyrequires a lot of time. To overcome these problems and to

achieve the purpose of fast learning, a self-constructingneural fuzzy-inference network (SONFIN) was proposedin [8] to perform the structure- and parameter-learningphases concurrently. However, the network-structure andparameter-learning algorithms are both complicated. There-fore, the SONFIN is difficult to implement for practicalapplications. To solve this difficulty, a self-constructingfuzzy neural network (SCFNN) is proposed in [9]. Thestructure-learning phase and the parameter-learning phaseare done concurrently and on line in the SCFNN. Inaddition, the structure-learning algorithm of the SCFNN,which is based on the partition of the input space, is simplerthan using SONFIN, and the parameter-learning algorithmof the SCFNN is based on the supervised-gradient-decentmethod [2–4] using the delta-adaptation law proposedin [10]. Since a recurrent neuron has an internal feedbackloop to capture the dynamic response of a system withoutexternal feedback through delays, the recurrent neuralnetworks (RNNs) have superior capabilities than thefeedforward neural networks. The RNNs have the abilityto deal with time-varying input or output through their ownnatural temporal operation [11]. Moreover, the RNNsare dynamic mapping and demonstrate good controlperformance in the presence of unmodelled dynamics,parameter variations and external disturbances [11, 12].Therefore, a self-constructing recurrent fuzzy neural net-work (SCRFNN) is proposed in this study. The proposedSCRFNN combines the merits of the self-constructingfuzzy neural network (SCFNN) and the recurrent neuralnetwork (RNN). Moreover, the structure and the para-meter-learning phases are preformed concurrently and online in the SCRFNN.

The direct-drive design of mechanical applications basedon PMLSM is a viable candidate to meet the increasingdemands for higher contouring accuracy at high machinespeeds. The direct-drive design based on PMLSM has thefollowing advantages over its indirect counterpart: nobacklash and less friction; high speed and high precisionin long-distance location; simple mechanical construction,E-mail: linfj@mail.ndhu.edu.tw

The authors are with Department of Electrical Engineering, National DongHwa University, Hualien 974, Taiwan, ROC

r IEE, 2006

IEE Proceedings online no. 20050359

doi:10.1049/ip-epa:20050359

Paper first received 5th September and in final revised form 3rd November 2005

236 IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006

resulting in higher reliability and frame stiffness; and highthrust force [13]. At the same time, the end effect ofPMLSM can be controlled more easily than with linearinduction motor. Therefore, the PMLSM is suitable forhigh-performance servomotor applications and has beenused widely for the industrial robots, machine tools,semiconductor-manufacturing systems, X-Y driving devicesetc. [13–16]. However, the servomotor performance of thePMLSM is greatly affected by the uncertainties in the drivesystem since it is not equipped with auxiliary mechanismssuch as gears or ball screws. Moreover, since the operationof LSM involves two contacting bodies, a friction force isinevitably among the forces of motion. Furthermore, thisfriction characteristic may be easily varied owing to changesin normal forces in contact, and also through changes intemperature and humidity. In a closed-loop control system,the friction force results in a steady-state error, a limit cycleand a low bandwidth [17, 18]. Unfortunately, friction is anatural phenomenon that is quite difficult to model, and itis not completely understood. Since for compensation theabove mentioned nonlinear force disturbances, includingthe friction force quickly and directly, is very important indirect drive applications, a sophisticated control strategyis often required to achieve accurate tracking in high-performance position-control systems [15, 16].

In this study, a field-oriented control PMLSM servo-motor drive using a SCRFNN position controller isdesigned to track periodic sinusoidal, triangular andtrapezoidal reference inputs for the mover position withrobust and accuracy tracking performance. The proposedSCRFNN control system and the field-oriented mechanismare implemented in a control computer that is based on a32-bit floating DSP (TMS320C32). Floating-point DSPsoffer all the advantages of conventional DSPs in combina-tion with precise floating-point arithmetic. Highly precisecalculations can be done without bothering about taskssuch as scaling of integer value or overflow. Thus DSPs canfeasibly be used for precise measurement-data processing.Moreover, with on-board analogue-to-digital converters(ADCs), digital-to-analogue converters (DACs), parallelinput/output (PIO) and encoder interfaces, these DSPboards have greatly simplified the task of implementingdigital controllers.

2 Modelling of PMLSM

The PMLSM used in this study comprises a long stationarytubular ‘secondary’ that is supported at both ends housing asequence of Neodymium–Iron–Boron (NdFeB) permanentmagnet with guidance rail and linear scale, and a movingshort ‘primary’ which contains the core armature windingand Hall sensing elements [16]. The adopted PMLSM is a110V 2.9A 46W 57.8N type. The machine model of aPMLSM can be described in a synchronous rotatingreference frame as follows [13]:

vq ¼ Rsiq þ plq þ oeld ð1Þ

vd ¼ Rsid þ pld � oelq ð2Þwhere

lq ¼ Lqiq ð3Þ

ld ¼ Ldid þ lPM ð4Þ

oe ¼ npor ð5Þand vd, vq are the d–q axis voltages; id, iq are the d–q axiscurrents; Rs is the phase-winding resistance; Ld, Lq are thed–q axis inductances; or is the angular velocity of the

mover; oe is the electrical angular velocity; lPM is thepermanent-magnet flux linkage; np is the number ofprimary pole pairs; and p denotes the differential operator.Moreover,

or ¼ p v=t ð6Þ

ve ¼ npv ¼ 2tfe ð7Þwhere v is the linear velocity of the mover; t is the polepitch; ve is the electric linear velocity; and fe is the electricfrequency. The developed electromagnetic power is given by

Pe ¼ Feve ¼ 3np ld iq þ Ld � Lq� �

id iq� �

oe=2 ð8ÞThus, the electromagnetic force is

Fe ¼ 3pnp ld iq þ Ld � Lq� �

id iq� �

=2t ð9ÞThe configuration of a field-oriented PMLSM servomotordrive system is depicted in Fig. 1, where dm is the positioncommand; d is the position of the motor; em is the positionerror; Dem is the time derivative of the position error; i�a, i�band i�c are the three-phase command currents; ia and ib arethe A- and B-phase currents; Ta, Tb and Tc are the switchingsignals of the inverter; i�d is the flux-current command; andi�q is the force-current command. The drive system consists

of a PMLSM, a ramp-comparison current-controlledPWM VSI, a field-orientation mechanism, a co-ordinatetranslator, a speed-control loop, a position-control loop, alinear scale and Hall sensors. The flux position ye of the PMis detected by the output signals of the Hall sensors denotedU, V and W, and the mover-position signal d. Differentsizes of iron disk can be mounted on the mover of PMLSMto change the mass of the moving element. With theimplementation of field-oriented control, the electromag-netic force can be simplified as follows:

Fe ¼ Kf i�q ð10Þ

Kf ¼ 3pnplPM=ð2tÞ ð11Þwhere Kf is the thrust coefficient; np is the number ofprimary poles; and lPM is the permanent-magnet fluxlinkage. The mover dynamic equation is

Fe ¼ M _vþ Dvþ FL þ f ðvÞ ð12Þwhere M is the total mass of the mover; D is the viscousfriction and iron-loss coefficient; FL is the externaldisturbance term; and f (v) is the friction force. ConsideringCoulomb friction, viscous friction and the Stribeck effect,the friction force can be formulated as follows [17, 18]:

f ðvÞ¼FC sgnðvÞ þ ðFS � FCÞe�ðv=vsÞ2 sgnðvÞ þ Kvv ð13Þ

where FC is the Coulomb friction; FS is the static friction;vs is the Stribeck-velocity parameter; Kv is the coefficientof viscous friction; and sgn( � ) is a sign function. All theparameters of f (v) are time-varying.

A curve-fitting technique based on the step responseof the mover position is applied here to find the model ofthe drive system. For convenience of controller design,the position and speed signals in the control loop are setat 1V¼ 0.063662m and 1V¼ 0.063662m/s. The majorsystem parameters are

Kf ¼ 20 N=A

M ¼ 1:97 kg ¼ 0:1254Ns=V

D ¼ 83:2245 kg=s ¼ 5:2982 N=V

9>>=>>; ð14Þ

The overbar symbol represents the system parameter in thenominal condition. Though the electromagnetic force can besimplified as (10) via the field-oriented control, considering

IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006 237

the variations of system parameters and external nonlinearand time-varying disturbance including friction force, thePMLSM servomotor drive system is a nonlinear time-varying system in practical applications.

3 Self-constructing recurrent fuzzy neuralnetwork

3.1 Structure of the SCRFNNThe model of the suggested SCRFNN is given as follows:

Rj: IF x1 is Aj1 and . . . xn is Aj

n;

THEN uj is oj and hjðt þ 1Þ is yjð15Þ

where Rj is the jth rule; x¼ [x1, x2,y, xn]T is the input

vector to the model; n is the number of external inputs; hj isthe internal variable; uj is the jth output of the local model

for rule Rj; and Aji is a fuzzy set in which i¼ 1yn. yj is the

consequent parameter for output hj.The structure of the SCRFNN is shown in Fig. 2.

Basically, it is a four-layer neural fuzzy network embeddedwith dynamic feedback connections. To give a clearunderstanding of the mathematical function of each node,the function of SCRFNN will be described layer by layer asfollows:

Layer 1: Each node in this layer is an input node, whichcorresponds to one input variable. These nodes only passthe input signal to the next layer. In this study, the inputvariables are x1¼ dm� d¼ em (the position error) andx2¼Dem (the derivative of position error).

Layer 2: Each node in this layer acts as a linguistic label ofone of the input variables in layer 1, i.e. the membershipvalue specifies the degree to which an input value belongsto a fuzzy set is determined in this layer. The Gaussian

function is adopted as the membership function as follows:

uAji¼ exp �

xi � mji� �2

s2ji

( )ð16Þ

where mji and sji are the mean and standard deviation,respectively, of Gaussian functions of jth term associatedwith ith input variable.

Layer 3: This layer includes rule layer and recurrent layer.For the internal variable hj in the recurrent layer, thefollowing sigmoid membership function is used:

fj ¼1

1þ expð�hjÞð17Þ

where hj¼ ujyj is the recurrent unit acting as memoryelement, and yj is the recurrent weight. Moreover, theneurons in the rule layer represent the preconditioning partof one fuzzy-logic rule. Therefore, the neuron in this layeris denoted by P, which multiplies the incoming signalsfrom layer 2 and the recurrent layer and outputs theproduct result, i.e. the firing strength of a rule. For the jthrule node,

uj ¼ fj

Yn

i¼ 1

uAji¼ 1

1þ exp �hj� �Yn

i¼ 1

exp �xi � mji� �2

s2ji

( )

ð18Þ

Layer 4: The final output of the model y* is calculated inlayer 4, and the output node, together with related links,acts as a defuzzifier. The mathematical function is

y� ¼XMj¼ 1

ujoj ð19Þ

110 V

60 Hzrectifier

L

CPWM

inverter

co-ordinatetranslator

+

+ _d

iq∗

ia∗ ib

∗ ic∗

Tb Tc

rampcomparison

currentcontrol

Ta

ia

ib

sin /cosgenerator

id∗ = 0

cos �e sin �e

U,V,W,d

PMLSM

linearscale

&Hall

sensors

self-constructingrecurrent

fuzzy-neural-network(SCRFNN)

position controller

d/dt

on-line learningalgorithm using

delta adaptation law

em +

_

d

dm

em

∆em

d/dt

−

Σ

Fig. 1 System configuration of field-oriented control PMLSM servodrive

238 IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006

where uj is the output of jth neuron of the rule layer; y� isthe output of the SCRFNN; M is the number of rules; andthe link weight oj is the output-action strength associatedwith the jth rule. The consequent part of one fuzzy-logicrule is implicitly contained in oj.

3.2 Learning algorithm for the SCRFNNTwo types of on-line learning algorithms, the structurelearning and the parameter learning, are developed toconstruct the SCRFNN. The structure learning is used tofind proper input-space fuzzy partitions and fuzzy-logicrules subject to minimising the number of rules generatedand the number of fuzzy sets on the universe of discourse ofeach input variable. The parameter learning is based onsupervised learning algorithms to adjust the link weights inthe consequent part and the parameters of membershipfunctions using the backpropagation algorithm to minimisea given energy function. Initially, there are only input andoutput nodes in the SCRFNN without any membership,rule and recurrent nodes. The membership, the rule and therecurrent nodes are generated automatically and dynami-cally in the learning process according to the on-lineincoming data by performing the structure- and parameter-learning processes.

3.2.1 Structure learning algorithm: The firststep in the structure learning is to determine whether ornot to perform the structure learning. If eminr 7em7 orDeminr 7Dem7, where emin and Demin are preset positiveconstants, then the structure learning is necessary. Next, itwill further decide whether or not to add a new node(membership function) in layer 2 and the associated fuzzy-logic rule in the rule layer and recurrent layer. Since onecluster formed in the input space corresponds to one

potential fuzzy-logic rule, the firing strength of a rule foreach incoming data xi can be represented as the degree thatthe incoming data belong to the cluster. The firing strengthobtained form (18) is used as the degree measure

Dj ¼ uj j ¼ 1; . . . ;MðtÞ ð20Þwhere M(t) denotes the number of existing rules. Accordingto the degree measure, the criterion for generating a newfuzzy rule for new incoming data is described as follows.Find the maximum degree Dmax

Dmax ¼ max1�j�M

Dj ð21Þ

If Dmax � D, then a new rule is generated, where D 2 ð0; 1Þdenotes a prespecified threshold that could decay during thelearning process, thus limiting the size of SCRFNN. Next,the mean and standard deviation of the new membershipfunction are assigned with preset values using heuristic orprior knowledge as follows:

mðnewÞi ¼ xi ð22Þ

sðnewÞi ¼ p ð23Þ

where xi is the new incoming data; p is a prespecifiedconstant.

To avoid the newly generated membership functionbeing too similar to the existing one, the similaritiesbetween the new membership function and the existingones must be checked. The similarity measure proposedin [8] is used to check the similarity of two membershipfunctions. Suppose that there are two fuzzy sets A and B

with membership functions uAðxÞ ¼ expf�ðx� m1Þ2=s21gand uBðxÞ ¼ expf�ðx� m2Þ2=s22g, respectively, to bemeasured. Assume m1Zm2. It follows that 7A\B7 can

…

x1 x2

…

…

…

…

h3(t )h2(t )h1(t )

layer 4

layer 3

layer 2

layer 1

�3 �2 �1h1(t + 1)h2(t +1)h3(t +1)

y∗

u1u2 u3

�1 �2�3

z−1 z−1 z−1

Π Π Π

Σ

A11(x

1)u A

12(x

1)u A

13(x

1)u A

21(x

2)u A

22(x

2)u A

23(x

2)u

Fig. 2 Structure of SCRFNN

IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006 239

be computed by [8]

A \ Bj j ¼ 1

2

h2ðxÞ m2 � m1 þ ppð Þ s1 þ s2ð Þf g

ppð Þ s1 þ s2ð Þ

þ 1

2

h2ðxÞ m2 � m1 þ ppð Þ s1 � s2ð Þf g

ppð Þ s1 þ s2ð Þ

þ 1

2

h2ðxÞ m2 � m1 þ ppð Þ s1 � s2ð Þf g

ppð Þðs1 � s2Þ

ð24Þ

where h(x)¼max{0, x}. Then a suitable similarity measure[8] is given using the entropy En(A, B)

EnðA;BÞ ¼A \ Bj jA [ Bj j ¼

A \ Bj js1 pp þ s2 p

p � A \ Bj jj j ð25Þ

The similarity checking was performed on all inputvariables in [8]. However, this increases the complexity ofthe algorithm significantly and is not a practical realisation.Therefore, in this study, the similarity check is performedonly on the first input variable, i.e. the position error. Thesimilarity measure En between the new membershipfunction and all existing ones is calculated and themaximum one Emax is found as follows:

Emax ¼ max1�j�MðtÞ

En u mðnewÞi ; sðnewÞ

i

n ou mji; sji� �h i

ð26Þ

where uðmji; sjiÞ represents the Gaussian membershipfunction with mean mji and standard deviation sji; andM(t) is the number of membership functions of the ith inputvariable. If Emax � En, where En 2 0; 1ð Þ is a prespecifiedthreshold value, then the new membership function isadopted and the number M(t) is incremented by one. Sincethe generation of a membership function corresponds to

the generation of a new fuzzy rule, the link weights oðnewÞj

and yðnewÞj associated with a new fuzzy rule have to be

decided. Generally, the link weights are selected withrandom or prespecified constants.

3.2.2 Parameter-learning algorithm: The pro-blem in parameter learning can be stated as follows: giventhe training input data x¼ [x1,y,xn] and the desiredoutput value dm, to adjust optimally the parameters of themembership functions and feedback weights. The centralpart of the parameter-learning algorithm for the SCRFNNconcerns how to obtain a gradient vector recursively inwhich each element in the learning algorithm is defined asthe derivative of an energy function with respect to aparameter of the network. This is done by mean of thechain rule, and the method is generally referred to as thebackpropagation learning rule, because the gradient vectoris calculated in the direction opposite to the flow of theoutput of each node. To describe the on-line parameter-learning algorithm of the SCRFNN using the supervisedgradient-descent method, first the energy function E isdefined as

E ¼ 1

2dm � dð Þ2¼ 1

2e2m ð27Þ

The update rules for the parameters in the SCRFNN aredescribed as follows:

Layer 4: The error term to be propagated is computed as

d4 ¼ � qEqy�¼ � qE

qem

qem

qy�

� �¼ � qE

qem

qem

qdqdqy�

� �ð28Þ

Layer 3: In this layer, only the error term needs to becalculated and propagated:

d3j ¼ �qEquj¼ � qE

qy�

� �qy�

quj

� �¼ d4oj ð29Þ

Layer 2: The error term is computed as follows:

d2ji ¼ �qEquAj

i

¼ qEqy�

qy�

quj

� �quj

quAji

" #¼ d3j fj ð30Þ

linear scale&

Hall sensor

ia

ib

ic

DSP-based control computer

D/Aconverter

1 2 3 A

4 5 6 B

7 8 9 C

∗ 0 B# D

LCD

flashEPROM

TMS320C32

parallelport

encoderinterface

i a∗

i b∗

i c∗

PMLSM drive

PMLSM

U,V,W,d

Fig. 3 DSP-based control system for the field-oriented PMLSM servodrive system

240 IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006

Update rule of oj

Doj ¼ �ZoqEqoj¼ � Zo

qEqy�

� �qy�

qoj

� �¼ Zod

4uj ð31Þ

The update of mji is

Dmji ¼ �ZmqEqmji

¼ �ZmqEquAj

i

quAji

qmji

" #¼ Zmd

2ji

2 x2i � mji� �

sji� �2ð32Þ

The update sji is

Dsji ¼ �ZsqEqsji¼ �Zs

qEquAj

i

quAji

qsji

" #¼ Zsd

2ji

2 x2i � mji� �2

sji� �3ð33Þ

The update yj is

Dyj ¼ �ZyqEqyj¼ �Zy

qEquj

quj

qfj

qfj

qhj

qhj

qyj

� �

¼ Zyd3j fj 1� fj� �

ujðN � 1ÞYn

i¼ 1

uAji

ð34Þ

where Zo, Zm, Zs and Zy are the learning-rate parameters ofthe link weights, means, standard deviations and feedbackweights, respectively. The mean and standard deviation ofthe membership functions and weights are updated asfollows:

ojðN þ 1Þ ¼ ojðNÞ þ Doj ð35Þ

mjiðN þ 1Þ ¼ mjiðNÞ þ Dmji ð36Þ

sjiðN þ 1Þ ¼ sjiðNÞ þ Dsji ð37Þ

yjðN þ 1Þ ¼ yjðNÞ þ Dyj ð38Þwhere N denotes the iteration number of the jth link.

The exact calculation of the Jacobian of the systemqd=qy� which is contained in qE=qy� cannot be determinedowing to the uncertainties of the plant dynamic such asparameter variations and external disturbances. To over-come this problem and to increase the online learning rateof the network parameters, the delta-adaptation lawproposed in [19] is adopted as follows:

d4 ¼ em þ ADem ð39Þwhere A is a positive constant.

4 Simulated and experimental results

The block diagram of the DSP-based computer controlsystem for the field-oriented control PMLSM servo-motor drive system is shown in Fig. 3. A TMS320C32

encoderinterface

ISR

motor-speedcalculation

field-orientedmechanism &

axistransformation

end

control

SCRFNNcontrol

algorithm

main

parametersinitialisation

I/Oinitialisation

interrupt-intervalsetting

detection ofrotor-fluxposition

servo on

enableinterrupt

end

monitordata & check �

disableinterrupt

�̂s

d

v

iq∗

Ts = 0.2 ms

encoderinterface

end� = �+1

� = 5

yes

� = 0

control

noTs = 1.0 ms

D/A conversion

d

ic∗ib

∗ia∗

Fig. 4 Flow charts of control algorithms

dist

ance

, mm

referencemodel

moverposition

time, s

a

curr

ent,

A control effort i∗q

number of rules

tracking error

dist

ance

, mm

time, s

b

time, s

c

time, s

d

−5

0

5

−10

10

−2

−6

−4

02

4

6

2 2018161412108640

2 2018161412108640

2 2018161412108640

2 2018161412108640

0

2.0

−0.50

0.5

1.51.0

2.53.0

12

3

4

5

6

Fig. 5 Simulated responses of SCRFNN control system due toperiodic sinusoidal commanda Tracking responseb Control effortc Number of rulesd Tracking error

IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006 241

floating-point DSP is the core of the control computer;moreover, the control computer includes multiple channelsof ADC, DAC, PIO and encoder interface. The current-controlled PWM VSI is implemented using an intelligent-power-module (IPM) switching component with a switchingfrequency of 15KHz. Digital filters and frequency-multi-plied-by-four circuits are built into the encoder interfacecircuits to increase the precision of position feedback. Theresulted resolution is 1mm. The field-oriented mechanismand the proposed SCRFNN control algorithm are realisedin the DSP using the ‘C’ and ‘Assembly’ languages. All theprograms are developed under the Windowst environmentin the PC and are then downloaded to the EPROM. Afterplugging the EPROM in the DSP control computer, onecan manipulate the computer- control system via akeyboard and LCD. Three-phase command currents aresent to the motor drive using DACs. The methodologyproposed for real-time control and SCRFNN implementa-tion are composed of the main program, one interrupt

service routine (ISR) and one subroutine (Control) in theDSP, as shown in Fig. 4. In the main program, parametersand input/output (I/O) initialisation are set first; thenthe interrupt interval for the ISR is set. After enabling theinterrupt, the ISR with 0.2ms sampling rate (TS) is usedfor the encoder interface and field-oriented mechanism.The ISR reads the mover position from the encoder andgets the control effort i�q from the subroutine (Control) to

calculate the three-phase current commands via the field-oriented mechanism, and then sends the calculated com-mands to the motor drive via DACs. Since the DSP controlcomputer has only one hardware interrupt available, aparameter x in the ISR is used to record the execution timesof the ISR. When the parameter x is equal to 5, thesubroutine (Control) begins to execute so that it has a1.0ms sampling rate. The subroutine (Control) first readsthe mover position from the encoder and then calculatesthe motor velocity v and the control effort i�q according to

the proposed SCRFNN control algorithm.

referencemodel

moverposition

control effort i∗q

number of rules

tracking error

time, s

a

time, s

b

time, s

c

time, s

d

−5

0

5

−10

10

2 2018161412108640

dist

ance

, mm

curr

ent,

Adi

stan

ce, m

m

−2

−6

−4

0

2

4

6

0

2.0

−0.50

0.5

1.51.0

−1.0

2.5

1

2

3

4

5

6

2 2018161412108640

2 2018161412108640

2 2018161412108640

Fig. 6 Simulated responses of SCRFNN control system due toperiodic triangular commanda Tracking responseb Control effortc Number of rulesd Tracking error

referencemodel mover

position

curr

ent,

A

control effort i∗q

number of rules

tracking error

dist

ance

, mm

dist

ance

, mm

time, s

a

time, s

b

time, s

c

time, s

d

−6

−4

−2

0

2

4

4

4

4

1

1

−1

3

3

5

0

0

0

2

2

2

−2

6

16 201814121086420

6

6

8

16 201814121086420

16 201814121086420

16 201814121086420

Fig. 7 Simulated responses of SCRFNN control system due toperiodic trapezoidal commanda Tracking responseb Control effortc Number of rulesd Tracking error

242 IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006

4.1 SimulationTo investigate the effectiveness of the proposed SCRFNNcontrol algorithm, two simulated conditions includingparameter variations and external disturbance are consid-ered in the following:

Condition 1:

M ¼ M ; FL ¼ 0N 0�5 s ð40Þ

Condition 2:

M ¼ 10M ; FL ¼ 0N after 5 s ð41Þ

Condition 3:

M ¼ 10M ; FL ¼ 50N after 10 s ð42Þ

The simulation is carried out using the ‘Matlab’ package.To demonstrate the control performance of the controlsystem with different reference trajectories, the simulated

results due to periodic sinusoidal, triangular and trapezoidalcommands are given. The control objective is to control themover to move 75mm periodically for sinusoidal andtriangular reference trajectories. When the command is atrapezoidal reference trajectory, the control objective is tocontrol the mover to move 5mm periodically.

The threshold values and learning rates of the proposedcontrol scheme are

emin¼0:001 Demin¼0:005 D¼0:8 En¼ 0:5

Zo¼1:9 Zm¼0:003 Zs¼0:005 Zy¼0:005

)

ð43Þ

All the threshold values and learning rates in the proposedcontrol system are chosen to achieve the best transientcontrol performance in both the simulation and experi-mentation. In addition, the coefficients of the friction model

c

2 s2

number of rules

a

moverposition

5 mm

0 mm

referencemodel

2 s

−5 mm

dist

ance

d

tracking error

2 s400 µm

dist

ance

b

2 s0.5 A

0 Acurr

ent

g

2

number of rules

2 s

e

moverposition 5 mm

0 mmreferencemodel

2 s

−5 mmdi

stan

ce

h

tracking error

400 µm 2 s

dist

ance

f

2 s0.5 A

0 A

control effort iq∗

control effort iq∗

curr

ent

time time

time

time

timetime

time

time

Fig. 8 Experimental results of SCRFNN control system due to periodic sinusoidal commanda Tracking response at nominal conditionb Control effort at nominal conditionc Number of rules at nominal conditiond Tracking error at nominal conditione Tracking response at parameter-variation conditionf Control effort at parameter-variation conditiong Number of rules at parameter-variation conditionh Tracking error at parameter-variation condition

IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006 243

used in this study are selected as follows:

FC ¼ 0:08 FS ¼ 1:2 vS ¼ 0:08 Kv ¼ 0:8 ð44ÞIn the simulation, condition 1 is simulated first, thenchanging to condition 2 at 5 s and changing to condition 3at 10 s. The simulated results of the tracking response,control effort, number of rules and tracking error for theproposed SCRFNN control system due to periodicsinusoidal command are depicted in Fig. 5. From thesimulated results, excellent tracking responses and robustcontrol characteristics can be obtained for the SCRFNNcontrol system. Moreover, the abrupt large control effortsand tracking errors, as shown in Figs. 5b and 5d, are causedby the change of simulated condition at 10 s. Further, tofurther verify the control performance of the SCRFNNcontrol system, the simulated results of the trackingresponse, control effort, number of rules and tracking errorfor the proposed SCRFNN control system due to periodictriangular and trapezoidal commands are shown in Figs. 6and 7, respectively. Perfect tracking responses and robustcharacteristics can still be obtained with regard to parametervariation and external disturbance, as shown in Figs. 6a and 7a.

In addition, effective structure learning of the SCRFNNdue to change in simulated condition can be observedby the variation of the number of rules shown in Figs. 6cand 7c.

4.2 ExperimentationTwo test conditions are provided in the experimentation:the nominal condition and the parameter-variation condi-tion. The parameter-variation condition is the addition ofone iron disk of mass 7.32kg to the mass of the mover. Theexperimental results of the tracking response, control effort,number of rules and tracking error using the proposedSCRFNN control system due to periodic sinusoidal,triangular and trapezoidal commands at the nominalcondition are depicted in Figs. 8a–d, 9a–d and 10a–d.Moreover, the experimental results of the tracking response,control effort, number of rules and tracking error usingthe proposed SCRFNN control system due to periodicsinusoidal, triangular and trapezoidal commands at theparameter-variation condition are depicted in Figs. 8e–h,9e–h and 10e–h. From the experimental results, good

moverposition

5 mm

0 mm

referencemodel

a

2 s

c

b

2 s0.5 A

0 A

control effort i∗q control effort i∗

q

2

number of rules

−5 mm

tracking error

400 µm

d

2 s

2 s

moverposition 5 mm

0 mm

referencemodel

e

2 s

g

f

2 s

2 s0.5 A

0 A

2

number of rules

−5 mm

tracking error

2 s400 µm

h

dist

ance

curr

ent

dist

ance

dist

ance

curr

ent

dist

ance

Fig. 9 Experimental results of SCRFNN control system due to periodic triangular commanda Tracking response at nominal conditionb Control effort at nominal conditionc Number of rules at nominal conditiond Tracking error at nominal conditione Tracking response at parameter-variation conditionf Control effort at parameter-variation conditiong Number of rules at parameter-variation conditionh Tracking error at parameter-variation condition

244 IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006

tracking responses of the mover shown in Figs. 8a, 8e, 9a,9e, 10a and 10e can be obtained at both the nominal andthe parameter-variation conditions. Owing to the complex-ity of both structure and parameter learning, the trackingerrors only converge after two cycles of the on-line trainingprocess for both the sinusoidal and the trapezoidalcommands. Furthermore, effective structure learning ofthe SCRFNN can be observed clearly as the changingof the number of rules depicted in Figs. 9g and 10g. Inaddition, the robust control characteristics of the proposedcontrol scheme during the occurrence of parametervariation can be clearly observed.

5 Conclusions

This study successfully demonstrates the application of aSCRFNN control system to control the mover positionof a field-oriented PMLSM servomotor drive for periodicreference trajectories. First, the principle of the field-oriented control PMLSM servomotor drive was introduced.Then, the network structure and theoretical bases of the

proposed SCRFNN control system were described in detail.In the design of the SCRFNN control system, noconstrained conditions and prior knowledge of thecontrolled plant are required. Finally, simulation andexperimentation were carried out using periodic sinusoidal,triangular and trapezoidal trajectories to test the effective-ness of the proposed control schemes.

The major contributions of this study are: (i) thesuccessful development of a new self-constructing neuralnetwork, the SCRFNN; (ii) the successful derivation ofthe structure and parameters learning algorithms for theSCRFNN; and (iii) the successful application of theSCRFNN control system on a PMLSM servodrive systemto track different reference trajectories with robust controlperformance.

6 Acknowledgments

The author acknowledges the financial support of theNational Science Council of Taiwan, ROC through grantNSC 93-2213-E-259-002.

a

c

b

d

2 s2

number of rules

moverposition

5 mm

0 mm referencemodel

2 s

dist

ance

tracking error

2 s400 µm

dist

ance

2 s0.5 A

0 A

control effort iq∗

curr

ent

e

g

f

h

2 s2

number of rules

mover position 5 mm

0 mm referencemodel

2 s

dist

ance

tracking error

400 µm 2 s

dist

ance

2 s0.5 A

0 A

control effort iq∗

curr

ent

Fig. 10 Experimental results of SCRFNN control system due to periodic trapezoidal commanda Tracking response at nominal conditionb Control effort at nominal conditionc Number of rules at nominal conditiond Tracking error at nominal conditione Tracking response at parameter-variation conditionf Control effort at parameter-variation conditiong Number of rules at parameter-variation conditionh Tracking error at parameter-variation condition

IEE Proc.-Electr. Power Appl., Vol. 153, No. 2, March 2006 245

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