an improved two-stage control scheme for an im

8/14/2019 An Improved Two-Stage Control Scheme for an IM

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. _ , i .. .,IEEE 1999 International Conference on Power Electronics and Drive Systems, PEDS99, July 1999, Hong Kong.

An Improved Two-stage Control Scheme for an Induction MotorK. L. Shi, T. F. Chan, Y. K. Wong, and S . L. Ho

Department of Electrical Engineering, Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong

Abstract - In this paper, an improved two-stage controlscheme (previou sly developed by the authors) is presented. Aslip-frequency controller operates together with a current-magnitude controller to yield the desired values of current andfrequency during the acceleration/deceleration stage and thesteady-state stage. Simulation studies on a 7.5kW inductionmotor are performed using Matlab/Simulink. The simulationresults indicate that the performance of the two-stage controlscheme is comparable with that obtained using field-orientedcontrol. Besides, the improved control scheme is much simplerto implement and the performance is less sensitive to machineparam eter changes.I. INTRODUCTION

In order to control accurately the magnitude and phase ofthe stator current, field-oriented control has to dep end on themotor parameters and the complicated calculations involved[ I ] . In practice, accurate current-phase cont rol is impossible,due to uncertainty in motor parameters and controllers timedelay. Two features of field-oriented control, however,deserve attention. Firstly, although the field-orientedcontroller does not control the frequency directly, its slipfrequency is constant during the acceleration1 decelerationperiod. Secondly, when the torque command is constant, thesupply current magnitude will remain constant. The firstfeature may be explained using the slip frequencyformulation of field orientation [2]:

where w, is slip frequency, R, is the rotor resistance, P is thenumber o f poles, T* denotes the torque command, and Xdr*denotes rotor flux command. If r* an d AF1,,*are maintainedconstan t during acceleration, w, s also constant.

The second feature may be proved using the fieldorientation conditions. The fl,,say be expressed as:

where k,,=PLM/3Lr, LM is mutual inductance, and L, s rotorinductance.The equation of the stator flux vector in the excitationreferen ce frame can be written as [2]:

Stator phase current magnitude I i,$can be expressed by:

Substituting Eqs.(2) an d (3 ) into Eq.(4),

When the torque command T* and flux command Xdr*are both constant, Eq.(5) becomes:2 ._I i.,= &5$const.

The above two features o f field-oriented control have beenemployed by the authors to design a two-stage controller [3]for an induction motor. In this paper, the two-stage controlleris improved with a simpler slip frequency control.

11. TWO-STAGE CONTROL STRATEGY FOR ANINDUCTION MOTOR

The current-input induction motor model [4]-[5] shown inFig. 1 has three inputs, namely the stator current magnitudeZs, upply frequency w, and load torque TL. t has an output,namely the rotor speed U,,. The relationship between theoutpu t and inputs may be expressed as:

Current -speedInduction...motor

Fig.1 An inductionmotor model with current input

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The speed response of the motor may be divided into twostages, an initial acceleration/ deceleration stage (the speedresponse to rise from about 3% to about 97% of speedcommand), and a final steady-state stage (the speed responseerror is during ab out 3%), as shown in Fig.2.

Steady-state Constant change

1.5 2 2.5 3 3.5kAcceleration period Final steady state period

I eliminateI

Fi g2 Typical speed response of an induction motor

The basic principle of the two-stage controller may bedescribed as follows.

1)During the accelerationldeceleration stage, the statorcurrent magn itude is maintained constant and the inputfrequency depends on the slip frequency orand the rotorspeed.

2)During the final steady-state stage, the input frequency Uis held constant and the speed of rotor U , s maintainedconstant by controlling the stator current magnitude IZJ.

In the two-stage speed control scheme, the relationshipbetween inputs and outputs is described by Table 1.

I oscillationsonstant

In this paper, the control strategy between the two stagesis designed as follows.When (wl,* ml , (13, ontrol is from a steady-state stag e toan acceleration stage.When 2.5


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(12), {k 37.80.2 1q. accelerationldeceleratbt?,stagesteady - state stageThe slip-frequency control scheme to implement Eq.(l1)

can be constructed by a sim ple controller whose output islimited to k37.8 by an output saturation [7]. For the variableload of Eq.(lO), simulation program of the slip-frequencycontroller consists of the blocks Suml, Sum2, Gain, andSaturationl, as illustrated in Fig.3.

mcrSumZ Saturation1 SlipSpeedcommand frequency

Rotor04rcum lspeed

Fig. 3. Simulation blocks of slip-frequency control for the varied load

Similarly, for a constant load, simulation program of th eslip-fre quen cy control ler expr essed by Eq.( 12) can beconstructed as shown in Fig.4.

Saturation1 Slipfrequencyommand

R d c r Sum1speed

Fig. 4. Simulation blocks of slip-frequency control for a constant load

IV . CURRENT MAGNITUDE SATURATIONCONTROLDuring the steady-state period, the slip frequency ismaintained constant, while the stator current magnitude isadjusted to control the rotor speed. Fig.9 shows the process

of controlling the speed w , a', b' c') by stator currentamplitude according to the speed error. The decayingoscillations of speed about the final operating point havebeen eliminated.

400 ~

Fig5 Speed is controlled by stator current amplitude.

The follow ing proportional-and-integral PI) control withoutput satura tion is used in the non linear control.

In this paper, coordination of the current magnitudecontrol for the tw o stages is achieved using the followingstrategy:1) When l0,*-w,~123, the current magnitude controlchanges from a steady-state stage to an accelerationstage.2) When 2.533 , then [,of Eq.(13) islarger than lOOA, hen ce the prop ortion al coeff icient K p maybe chosen as 35.

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The maximum value of the integral part of Eq.( 13) can beestimated from an acceleration process with U,,*= IZO,w,,(t=Os)=O, assu mi ng that the rotor speed rises at uniformacceleratio n an d w,(t=O.Zs)=IZO, i.e.,0.2

j(o,, * -w,,)d.r = 12r = OWhen the current magnitude controlacceleration stage to a steady-state stage, changes from ansubstituting (U,,*-w,,)=2.5, Kf, 35, and Eq.(15) into Eq.(13), and let Z,


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variance of 10) demo nstrates that the two-stage con troller hasgood disturbance rejection.

VII. CONCLUSION

Tom ( son41

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1Og.Two-stage controller

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Fig.10. Simulation results of two-stage controller and VW z controller

3) Efects ofparameter variations: The simulation of thetwo-stage controller for the variable load is repeated with therotor resistance and mutual inductance changed to 2R, an d0.7LM respectively. A comparison between Fig. 11 an dFig.9g shows that the speed response of the two-stagecontroller is insensitive to param eter variations.

Fig.1 1. Speed response withmotor parameter variation Fig.12. Speed response withspeed and current noises

4) Effects of noise in the measured speed and inputcurrent: In order to evaluate the effects of the noise of speedsensor and the no ise of the input current, distributed randomnoises are added into the feedback speed and input currentof the two-stage controller in Fig.7. The simulation isachieved using the random number blocks of Simulink,which generates a pseudo-random, normally distributed(Gaussian) number [ 6 ] . As shown in Fig.12, the speedresponse with the measured speed noise (mean of zero andvariance of 3) and with the current noise (mean of zero and

The improved two-stage controller has almost the samefrequency and current characteristics as the field-orientedcontroller. During the acceleratioddeceleration stage, thestator current magnitude is maintained at the maximumpermissible value to give a large torque, and during thesteady-state stage, the stator current magnitude is adjusted tocontrol the rotor speed. Because the two features of field-oriented control are exploited, the performance of theimproved two-stage controller is obviously superior to ascalar controller [SI. Besides, the new controller has theadvantages of simplicity and insensitivity to motorparameter changes. Very encouraging results are obtainedfrom a com puter simulation using Matlab/Simulink.

VIII. ACKNOWLEDGEM ENTThe work reported in this paper wa s funded by the HongKong Po lytechnic University research grant V157.

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IREFERENCESK.S. Rajashekara, A. Kawamura, and K. Matsuse, Speed sensorlesscontrol of induction motors, Sensorless Control of AC Motor Drives,IEEE Press, pp. 1-19, 1996.A.M. Trzynadlowski, The Field Orientation Principle in Control ofInduction Motors, Kluwer Academic Publishen, 1994.K.L. Shi, T.F. Chan, and Y.K. Wong, A Novel Two-Stage SpeedController for an Induction Motor, Record of The 1997 IInternational Electric Machines and Drives Conference, USA, Ma y1997, pp.MD2-4.K.L. Shi, T.F. Chan, and Y.K. Wong, Modelling of the Three-phaseInduction Motor Using SIMULMK, Record of The 1997 IInternational Electric Machines and Drives Conference, USA, Ma y1997, pp.WB3-6.M. Chee, Dynamic Simulation of Electric Machinev Using Matlab/Simulink Prentice-Hall, Inc., 1998Using SIMULINK, mnamic System Simulation for MATLAB, Th eMathworks Inc. 1997.S . Wade, M. W. Dunnigan, and B. W.Williams, Modeling andSimulation of Induction Machine Vector Control with RotorResistance Identification IEE Transactions. Power Hecfronics,vol.12, No.3, pp.495-505, May 1997.GO. Garcia, R.M. S tephan , and E.H. Watanabe, Com paring theIndirect Field-Oriented Control with a Scalar Method, IEEETransactions on Industrial Electronics, vo1.41, No.2, pp.201-207, 1994.

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an improved two-stage control scheme for an im

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