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CURRENT LIMITATION IN THE ADAPTIVE NEURAL SPEED CONTROLOF A DC MOTORM Minkova', D Minkov2, J L Rodgerson' and R G Harley'

1 Department of Electrical Engineering, 2- Department of Electronic EngineeringUniversity of Natal, Private Bag X10Dalbridge, 4014, South AfricaCorresponding author: Dr.D .Minkov: email:[email protected]. c.za

ABSTRACTA simple design is proposed for a current limitation inthe adaptive neural speed control of a DC motor. Thedesign is based on using a current feedback from theoutput of the motor to the output of the ANN, and asimple logical operation between the end of the currentloop and the input of the motor. Simulations are madeof the performance of the controller with a currentlimitation and without a current limitation, for differenttypes of reference speed trajectories. The controlsimulations are made for a DC motor with givenparameters, and white noise is superimposed on boththe rotor speed and the armature current at the outputof the motor.

INTRODUCTIONThe dynamics of a DC motor is described by thefollowing equations [l]:

di( t)diK o ( i ) = -Ri( t)-L-+v( i) (1)

Ki( i ) = J- d o ( f )+Do( )+ T,( t) (2)dt- rotor speed (rad/s)- armature resistance ( Q )- armature inductance (H )- armature voltage (V)- armature current (A)- load torque (N.m)- rotor inertia (kg.m2)- torque and back emf constant (V drad)- viscous friction coefficient (N.m.s/rad)

In order to digitally control a plant, a discrete timemodel of the plant is required. The following discretetime models of a DC motor can be derived fromeqn.(l) and eqn.(2):

(3)( k + l ) = A , o ( k ) + A , o ( k - l ) ++& ( k , - 1) +A4V( k)i ( k ) = A ,w ( k ) + A ,o ( k - i ) + (4)

+A,( k- 1) +A8V ( k)

where k indicates the k-th discrete time moment, A ,, A,,A, , A,, A,, A,, A,, A,,, and A , , are real constants, andA,, A, , andA,, are real parameters which depend on theload of the motor.There are two approaches for application of artificialneural networks (ANNs) for plant control. For certainuncomplicated plants, it is possible to train the ANNoff-line, before its use in non-adaptive controller. Inthis case, pre-control training of the ANN isperformed, but the connection weights of the ANN arenot updated during the control action. In the alternativeapproach, the connection weights of the ANN areupdated on-line, during the control action, and thecontroller is adaptive [2]. The non-adaptive neuralcontrol of a DC motor has been investigated by El-Sharkawi et a1 [1 ,3 ,4] . An adaptive neural speedcontroller of a DC motor has been proposed by Buja eta1 [SI. t is assumed in [5] that the motor parameters KandJ are known, but determination of these parametersis not indicated.An adaptive neural speed controller of a DC motorwhich does not require knowledge of any motor/loadparameters has been proposed by Minkova et a1 [6].The idea for the design of this adaptive speed controllerof a DC motor is based on the work of Henaff andMilgram [7] for adaptive robot control by afeedforward ANN trained by the onlinebackpropagation algorithm. It can be deduced from [7]that in cases where the desired output of the ANN isnot known, the error at the output of the subsequent

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In this paper a current limitation is proposed for theadaptive neural speed controller of a DC motordeveloped by Minkova et a1 [6]. The performance ofthe controller with a current limitation is simulated fordifferent reference speed trajectories. A comparison ismade between the armature current of the motor for thecontroller with a current limitation and the controllerwithout a current limitation.All the computations in this paper are made for a DCmotor with the following parameters:R = 1.2 QL = 2 5 m HJ = 0.208 kg.m2K = 1.21 V.s/radD = 0.008 N.m.s/rad (14)T, = 0 i.e the DC motor is used without a loadv, = 240 VP, = 5 kWi, = P,/v, = 20.83 AU , = 1800 rev/min = 188.5 rad/swhere v, is the rated voltage, P, is the rated power, i,is the rated armature current, and U, s the rated rotorspeed.

CURRENT LIMITATION IN THE ADAPTIVESPEED CONTROLLER

The computed rotor speed trajectory and armaturecurrent trajectory are shown in Fig.1 for a particulararmature voltage trajectory applied to the DC motorconsidered. It is seen that the changes of the armaturevoltage over the time result in fast changes of thearmature current. This indicates that if the armaturecurrent at the output of the motor reaches too largeamplitude in a given discrete time moment, then thearmature current amplitude could be limited in thefollowing moment by applying of an armature voltagewith the same direction and with a slightly smalleramplitude, compared to the moment considered, to theinput of the motor.The topology of the adaptive neural speed controller ofa DC motor, proposed by Minkova et a1 [6], andequipped with a current limitation feedback is given inFig.2. Fig.3 shows a flowchart of the controller withcurrent limitation. The current limitation in thiscontroller of a DC motor is performed byimplementation of the following logical operation:

where i,w is the maximum allowed amplitude of thearmature current, i.e. i gives the current limitation.Eqn.(l5) shows that if the amplitude of the armaturecurrent at step k-I becomes larger than 80%i,, thenthe armature voltage applied to the input of the motorin the following step k has a prescribed value of 98%of its value at step k-I . It turns out that such a decreaseof the amplitude of the armature voltage for suchamplitudes of the armature current limits the amplitudeof the armature current below iM independently fromthe reference speed trajectory. If the amplitude of thearmature current is less than 80% i then the armaturevoltage is supplied from the output of the ANN to theinput of the motor.The topology of the ANN used in the controller isgiven in Fig.4. The choice of the parameters y, , ndZi of the ANN training depends on the reference speedtrajectory and the DC motor parameters, and isdiscussed in [ 6 ] . t should be noted that the ANN of thecontroller does not require any preferential trainingbefore the beginning of the control process, and thecontroller does not require any knowledge of themotor/load parameters.

COMPUTED RESULTSControl processes are simulated for the DC motor withparameters introduced by eqn.(14). White noise with amagnitude of 0.5 rad/s is superimposed on the rotorspeed at the output of the motor, and white noise witha magnitude of 0.1 A is superimposed on the armaturecurrent at the output of the motor in all controlsimulations.The performance of the controller with currentlimitation of i M = 5 A is illustrated in Fig.5 for asinusoidal type of reference speed trajectory RSTlwhich leads to slow motor dynamics. Thecorresponding variation of armature current as afunction of the time is shown in Fig.6. The variation ofthe armature current appears in Fig.7 for thecorresponding controller without current limitation (thecontroller from [6]), and the reference speed trajectoryRSTl . The comparison between Fig.6 and Fig.7 showsthat the armature current reaches an amplitude ofapproximately 9 A for the controller without currentlimitation, and Ii(t) < M = 5 A for the controller withcurrent limitation.Fig.8 illustrates the performance of the controller withcurrent limitation of i 12 A for another sinusoidaltype of reference speed trajectory RST2 which leads tofast motor dynamics. The change of the armaturecurrent with the time is shown in Fig.9 for the samecontrol simulation. Fig. 10 gives the dependence of the

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armature current as a function of the time for thecorresponding controller without current limitation, andthe reference speed trajectory RS72. The comparisonbetween Fig.9 and Fig.10indicates that the introductionof current control decreases the amplitude of thearmature current from 1 i(t) =45 A for the controllerwithout current limitation to 1 i ( t ) < M=12 A for thecontroller with current limitation.The performance of the controller with currentlimitation of i,=4 A is illustrated in Fig.11 for asigmoidal type of reference speed trajectory RST3. Thecorresponding change of the armature current with thetime is given in Fig.12. The comparison betweenFig.5, Fig.8, and Fig.11 shows that the controller withcurrent limitation has a good performance for all thereference speed trajectories considered.

CONCLUSIONSThe fast changes of the armature current of a DC motorand the use of an adaptive neural speed controller leadto a significant amplitude and noise of the armaturecurrent of the motor. It indicates that current limitationhas to be performed during the control process. Adesign is proposed which limits the amplitude of thearmature current of a DC motor below a prescribedvalue during the adaptive neural speed control of themotor. The current limitation is achieved by using of acurrent feedback from the output of the motor to theoutput of the ANN, and a simple logical operationbetween the end of the current feedback and the inputof the motor. The current limitation functions well, andthe controller with current limitation has a goodperformance, independently of the speed of the motordynamics.

ACKNOWLEDGEMENTThe financial support of the Foundation for Researchand Development FRD s greatfully acknowledged.

REFERENCES[l] Weerasooriya, S and El-Sharkawi, M.A:Identification and control of a DC motor usingback-propagation neural networks, ZEEETrans.Energy Conversion, 1991, 6, pp.663-669.[2] Antsaklis, P. ; Atherton, D P and Warwick, K:Neural networks for control and systems (ShortRun Press, UK , 1992), pp.31-68.

trajectory controller for a DC motor, ZEEETranr.Energy Conversion, 1993, 8 , pp. 107-113.El-Sharkawi; M A and El-Samahy, A A: Highperformance drive of DC brushless motors usingneural network, IEEE Trans.Energy Conversion,1994, 9, pp.317-322.Bertoluzzo, M ; Buja, G S and Todesco, F:Neural network adaptive control of a DC drive.Proceedings of the Conference IEEE IndustrialElectronics Society, Italy, 1994, pp. 1232-1236.Minkova, M; Minkov, D; Rodgerson, J L andHarley, R G: Adaptive neural speed controller ofa DC motor, Submitted for publication to IEEEProceedings Electric Power Applications.Henaff, P and Milgram, M: Adaptive neuralcontrol with backpropagation algorithm.Proceedings of he IMACS InternationalSymposium on Signal Processing, Robotics an dNeural Networh, France, 1994, pp.395-398.Krose, B J A and van der Smagt, P P: Anintroduction to neural networks, (University ofAmsterdam, Netherlands, 1993), pp.30-37.Ogata, K: ]Modem control engineering,(Rentice-Hall, USA, 1990), pp. 118-120.

LIST OF ]FIGURECAPTIONS

4 ~ -t,

I0-; 0.1 1.s 2 2s 91 8)

Fig.1 Computed rotor speed trajectory (- - ),and armature current trajectory (- - -), foran armature voltage trajectory ( ) appliedto the DC motor.[3] Weerasooriya, S and El-Sharkawi, M A :Laboratory implementation of a neural network

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Fig.2 A schematic diagram of the adaptive neuralspeed controller of a DC motor with currentlimitation.

N d

INTRODUCE THE REFERENCE SPEED TRAJECTORYSAMPLING PERIOD T AND CALCULATE THE INPUTr(k) TO THE REFERENCE MODEL FROM eqn.11.THE NO OF THE CONNECTION WEIGHTS VECTOR

A f THE ANN IS INSIDE THE SPHERE WI TH ARAOUlS 0.1 IN THE WEIGHT SPACE. k= 1

W ( k ) DEFINED IN THE INTERVAL [ 0. tc ] FOR A

It

THE DISCRETE TIME IS t=kT. MEASURE THEROTOR SPEED w(k) AND THE ARMANRECURRENT i(k-1) OF THE MOTOR.CALCULATE THE CONTROL ERRORt ( k ) 0 U,&) - d k )

tBACKPROPAGATE THE ERROR %(k) THROUGHTHE ANN AN0 UPDATE ITS CONNECTION WEIGHTS,OR ONE TRAlNlNC EPOCHCALCULATE THE ROTOR SPEED a k + l ) IN THE

DISCRUE TIME MOMENT t=(k+l)T FROM eqn.12I FOR A j z 0 . 6 AN0 A vr0 . 2RECALL THE ROTOR S PEED FOP. THE LAST TwoD lS C R E E TIME MOMENTS AND SUPPLY Q(k+l).w(k)AND d k - 1 1 TO THE THREE INPUTS OF THE ANN1 IW R E T HE CONTROL VOLTAGE V(k) FROM THEOUTPUT O F THE ANN

THE INPUT TO THE

Fig.3 A flowchart of the operation of the adaptiveneural speed controller of a DC motor withcurrent limitation.

U / \ \

INPUT HIODEWLAYER LAYER

mapping*Fig.4 Topology of the A N N of the controller.

Fig.5 Performance of the controller with currentlimitation for the reference speed trajectoryRSTI. T=200ms, r=0.25, ( r=0 .7 , andli=0.2.

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Fig.6 Variation of the armature current for thecontroller with current limitation and R STI .T=200ms, y=0.25, a=0 .7 , and Ii=0.2.

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1 (aFig.7 Variation of the armature current for thecontroller without current limitation and RSTI .T=200ms, y=0.25, a=0 .7 , and fi=0.2.

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Fig.10 Variation of the armature current forcontroller without current limitation and RST2.T=40ms, y=0.25, (r=0.25, and l i=0.6.

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Fig.8 Performance of the controller with a currentlimitation for the reference speed trajectoryR S E . T = 4 0 m , y = 0 . 2 5 , ~ ~ ~ 0 . 2 5 ,ndli =O . 6 .

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Fig.9 Variation of the armature current for thecontroller with current limitation and R S l 2 .T = 4 0 m , y = 0 . 25 , a = 0 .2 5 , and I i=0.6.

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Fig.11 Performance of the controller with currentlimitation for the reference speed trajectoryRST3. T=20Oms, y=0.25, a=0.7, andli=0.2.

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Fig.12 Variation aif the armature current forcontroller with current limitationR S T 3 . T =2 0 0 m , y = 0 . 2 5 , a=0.7, and k = 0 . 2 .

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