sensor less control of im with on-line rotor time constant adaptation

8/14/2019 Sensor Less Control of IM With on-Line Rotor Time Constant Adaptation

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Sensorless Control of Induction Motors with On-LineRotor Time C onstant AdaptationShiu-Yung Lin, Hwa Wu, and Ying-Yu TZOU,Member, IEEE

Power E lectronics and Mechatronics Control Lab.,Department of Electrical and Control Engineering, National Chiao Tung University, Taiwan, R.O.C.Abstract-This paper presents a novel vector controlscheme for the sensorless control of induction m otors with

on-line rotor time constant adaptation. The motor speedcan be estimated using only phase currents and dc-linkvoltage. An adaptive voltage compensation scheme isproposed to compensate nonlinearities resulted by thePWM inverter and eliminate time delay of the sensingfilters. The proposed on-line rotor time constantadaptation scheme is developed from a power transferparameter identification algorithm to reduce sensitivitydu e to parameter mismatch and environment change. Theproposed auto-tuning sensorless control scheme has beenrealized using a single-chip DSP controller (TMS320C 14)from Texas Instruments. Experimental results reveals theproposed auto-tuning sensorless control scheme canachieve fast transient response and maintain a wide speedcontrol range.

NOMENCLATUREa,b, c4 44s, r subscripts denoting stator and rotor,

subscripts denoting motor three phase axessubscripts denoting the synchronous rotatingreference framesubscripts denoting the stationary referencerespectively

*A superscript denoting reference or commandquantities with 'lA"are estimated quantitiesP number of polesL,, L,, L, stator, rotor inductance per phase and mutualinductance

R,, R, stator and rotor resistance per phaseTr rotor time constant (L , / R,)i, v, A current, voltage, and flux linkagee,., Be rotor electrical and rotor flux angleU,, U, rotor electrical and rotor flux angularfrequencyT developed electrical torque0- leakage coefficient = (1 - L;/L,L, )KSI gain of rotor time constant (R , / L, )

status of a maturing technology in a broad range ofindustrial applications from low-cost to high-performance systems. In many industry applications, itis desired to eliminate thie speed sensor at the machineshaft without deteriorating the dynamic performance ofthe drive. Therefore, the development of shaftsensorless adjustable ac drive becomes an importantresearch topic [1]-[2]. These sensorless ac drives arerequired to achieve fasteir dynamic response with widerspeed control range than conventional open-loopcontrolled PWM inverter drives.During the past few years, various speed estimationalgorithms and sensorless control schemes have beendeveloped for sensorless induction drives [3]-[SI.Design challenges of sensorless drives are focused onthe pursuing of faster dynamic response, better speedregulation, elimination of sensory cables, lower cost,and increased reliability. Speed estimation anddecoupling control play key roles in the sensorlesscontrol of an induction motor. One m ajor difficulty inthe development of sensorless induction drives is thatthey may couple each other and are highly dependenton motor parameters. A well-decoupled induction drivecan simplify its speed estimation algorithm, while anindependent speed estimation algorithm is complex andhighly sensitive to parameter variations. An exactknowledge of the rotor time constant and mutualinductance of the induction motor is essential for ahigh-performance sensorless induction drive.

This paper presents a novel sensorless speed controlscheme for adjustable speed ac induction drive. Themotor speed can be estimated using only phase currentsand dc-link voltage to achieve fast dynamic responseand wide speed control range without any shafttransducer. An adaptive control scheme is d eveloped tocompensate nonlinearities resulted by the PWMinverter and to eliminate time delay resulted by sensingfilters. The dc-link voltage has been sensedinstantaneously to compensate speed estimation errordue to fluctuations in the dc-link voltage. The rotorresistance drifts with operating temperature and therotor inductance has a nonlinear relationship with itsWith great advances in power electronics , flux excitation. In order to overcome this problem, themicroelectronics, and control technology, development development of a flux compensating model with

of vector controlled ac moto r drives has reached the parameter identifica tion and adaptation is highlydemanded. This paper proposes an on-line rotor timetransfer parameter identification scheme [9]-[11, can

I . INTRODUCTION

This work W a s supported by the National Science Council, constant adaptation scheme, which is based on a powerTaipei, Taiwan, R.O.C. Project no. NSC 86-2622-E-009-006R.

1593-7803-4489-8/98/$10.00 0 1998 IEEE


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I :: AMPLIFIERI 1 AN DISERVO CONTROL CURRENT CONTROL

II Current LOOD I: SENSORS

' vdr VP l $$ 'dl TMS320F240-based digital controller :!

IIIII1III Squirrel-Cagei Induction Motor

IIIIIIIIIIIIIIIIIIIIIIIIIIIIII8IIIII

greatly reduce sensitivity due to parameter mismatchand environment change.Fig. 1 shows the block diagram of the proposedsensorless speed control scheme for induction drives.The proposed scheme consists of four major parts: (i) acurrent controller operating in the synchronous frame,(ii) a servo controller, (iii) a speed estimator based onstator flux model in synchronous frame, and (iv) a rotorflux oriented auto-tuning decoupling controller. Asingle-chip DS P controller (TMS320C14) from TexasInstruments has been used to realize the proposedcontrol scheme with on-line rotor time constantadaptation.11.SENSORLESSPEED STIMATION

The rotor or stator flux of an induction motor can beestimated from measured terminal quantities. The rotorflux and stator flux are related with the motor terminalquantities as follows

Equation (1 ) shows the rotor flux not only depends onthe estimated stator flux, it also requires the knowledgeof the leakage inductance of the induction motor. Onthe contrary, (2) shows the stator flux only depends on

c

DSP-basd Rotor SsetP Estimator Scheme

Fig. 2. Rotor speed estimation sch eme based on stator flux oriented.the stator resistance and measured stator voltages andcurrents. The stator resistance can be measured withaccuracy, therefore the stator flux oriented approach ismuch less sensitive to parameter variations andmeasurement noise. The estimation of the stator fluxcan be used to derive the synchronous frequency. Theelectrical angle of the stator f l u vmtor is

, U \

where the xm and ip an be calculated in terms ofmeasured stator voltages and currents. Theoretically,stator fluxes in the a-p coo rdin ate should besymmetric sinusoidal waveforms w ith 90 degree phase

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1 1 I l lDC-BuS Voltage I I Dead-TimeCompensator Compensator I

Adaptiv e Voltage Compensato r

Fig. 3. Adaptive voltage compensation scheme for PW M inverterdrive.shift during steady-state. However, a dc offset currentusually occurs due to nonlinearities of the PW Minverter. This dc current component will result speedripple and it may even lead to saturation of the statorflux in its worst case. Although this offset current canbe eliminated by using a high-pass filter with low cutofffrequency, it deteriorates dynamic response in lowspeed range at the same time.Fig. 2 shows the proposed speed estimation schemewhich is based on the stator flux model insynchronously rotating reference frame. T he derivativeof the stator flux angle gives the instantaneous electricalangular frequency

a; +a; (4)This estimated synchronous frequency is highlysensitive to the current ripples and a low-pass filtermust be used to smooth these current ripples. Thisimposes the requirement of a high bandwidth currentcontrol loop in the design of a sensorless inductiondrive.

111. ADAPTIVE OLTAGE OMPENSATIONTRATEGYFast and accurate estimation of the roto r flux angle isa key in the design of high-performance sensorlessinduction drives. The fhdamental component of PW Mvoltages applied to the stator windings is a keymeasured quantity for sp eed estimation. However, thisis hard to measure the fundamental component of aPWM voltage, especially when the PW M frequency is

low. The desired PW M voltages will be distorted bynonlinearities of the PW M inverter. Thesenonlinearities may come from the dead-time effect,non-ideal switching, and variation of the dc-linkvoltage. In order to have a better speed estimation toimprove low-speed performance, an adaptive voltagecompensation scheme as shown in Fig. 3 is developedto compensate these nonlinearities.

r r A

w1utv. BJead-''1nel741 n

I '*Fig. 4 . Dead-time effect in PFVM inverter drive: (a) ideal case, (b)the load current is positive, and (c) the load current is negative.

A. Dead-Time CompensationThe dead-time inserted to the PW M waveforms toprevent the PW M switches from short circuit will resultdistortion in its output waveforms. This nonlinearitybecomes more severe as the P W M uty ratio decreasesand the inductive nature of the motor also complicatesthis nonlinear behavior. 'The speed control range playsan important perform index of a sensorless inductiondrive and this imposes a challenge for lower speedregulation with full torque output. One major difficultyin low-speed sensorless lcontrol comes from distortionin speed estimation. The employment of a low-passfilter will only deterioraite its dynamic response. This

distortion is mainly resulted by the non-ideal switchingof the power device anld dead-time effect. We havedeveloped a simple dead-time comp ensation techniquefor better speed estimatioin.Fig. 4(a) shows the ideal PWM patterns to the samephase-leg of an inverter. Since both the u pper and lowerswitches in the same phase-leg are off during the deadperiod between transitions, the output voltage duringthis interval depends on the direction of phase current,as shown in Fig. 4(b) for i, 2 0 and in Fig. 4(c) fori,


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Fig. 5. Experimental results of the voltage command and outputvoltage: (a) without dead-time compensation and (b) with dead-timecompensation.

dead time D,,, if i 2 0Dmaxf i> 0

Ocm PWM perioddead time

PWM periodD*",=

where D,, is the duty ratio command and D,, is themaximum output duty ratio. Applying this dead-timecompensation scheme to the PWM inverter, thedistorted output voltage can greatly improved. Fig. 5 (a)shows the dead-time effect on the PW M output voltageand Fig. 5(b) illustrates the compensation effect of theproposed method.B. Forward Compensation Using DC-Link Voltage

The dc-link voltage fluctuates with the power gridand it also experiences large voltage variations due tointermittent start and stop operation of the drive. Thefluctuation of the dc-link voltage may be as large as50% and must be compensated for speed estimation.The estimated stator voltages can be compen sated as:

where vdc is the instantaneously measured dc-linkvoltage and F ( . ) denotes the computed stator voltagefiom given output duty ratios.

Iv. AUTO-TUNINGF ROTOR IM ECONSTANTIn the rotor flux oriented decoupling control schem e,

the slip estimator plays an impo rtant role in calculationof the rotor flux angle with respect to the stator MMF.An incorrect rotor time constant will result poor torqueresponse and low motor efficiency. An accurateknowledge of the rotor time constant is essential forboth decoupling control and speed estimation. Wedeveloped both off-line and on-line tuning techniquesfor the rotor time con stant. The off-line tuning is usedto determine an initial value when closing the torqueloop and the on-line tuning is used to compensate thedrifting effect due to temperature variation.

id s

Fig. 6 . The phasor diagram of stator current in real synchronousreference frame and estimated synchronous reference frame.

A . Off-Line Rotor Time Constant Tu ningThe phasor diagram of stator current in realsynchronous coordinate and estimated synchronouscoordinate is shown in Fig. 6 . The deviation angle CIbetween the real and estimated coordination representsthe degree of detuning, a well tuned rotor time constant

will result a=O. The relationships between slipfrequency, deviation angle, and rotor time constant inreal and estimated reference fiame can be written as:w , ~ , + tan(8)G ~ , F ~+ tan(@*> (7)(8 )

With a well tuned rotor time constant, (7) and (8) canbe rewritten as

id,

Ids

(9)

Fig. 7 shows the effect of rotor time constant on thedeviation angle. The torque equation of an inductionmotor as a function of the stator current vector can bewritten as

Tr - "8')- _Fr tan(8*+a)

3 P L* Sin(28)T =and the torque comm and with desired phase angle

Equations ( 1 0) and (1 1) can be combined to g etT=T*-=T*in(26) cor2a+---] sin 2a (12)

sin(28 ) [ tan28 ' .Fig. 8shows the variation of rotor time constant willhave a significant influence on the effect of torqueproducing current. In a well tuned condition, thegenerated torque will have a linear relationship with thetorque producing current. An incorrect rotor timeconstant will reduce its torque producing efficiency.The torque equation of a well decoupled inductionmotor can be w ritten as1596


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Fig.7. Deviation anglea as a fhction of rotor time constant.

0 I 2 3 4

Fig. 8. Influence of rotor time constant on torque producing current.

Te=-----P L i i2 2 Lr ds qs * (13)

The rotor time constant can be easily tuned during aconstant speed operation with constant load. We cantune the rotor time constant by searching for a linearrelationship of the developed torque between the fieldand torque producing currents. The product of the fieldand torque producing currents should be kept constantin a well-tuned condition. This tuning method is simpleand can be useful for the self-commissioning of aninduction drive when closing the torque loop.B. On-Line Rotor Time Constant Adaptation

The rotor resistance varies with the operatingtemperature and the rotor inductance is nonlinear withthe excitation current due to flux saturation. Therefore,the auto-tuning of the flux model is vital important in ahigh-performance sensorless induction drive. A correctflux model is especially important when the motor isrunning with low-speed high-torque or high-speed low-torque applications, To meet this requirement, an auto-tuning flux model with recursive parameteridentification must be d eveloped.Factors result the change of rotor time constantinclude: (i) the change of rotor resistance accompanieswith change of temperature, (ii) the variance of rotorinductance due to the flux saturation and other

I

Fig. 9. The block diagram of polwer transfer parameter identificationmethod.nonlinear variation effect,,and (iii) the rotor parametersmay be inherently incorrect by poor measurements.According to these detuning effects of rotor timeconstant, the method aQ power transfer param eteridentification is adopted to implement the on-lineadaptation of the rotor time cons tant. In steady state, therotor flux in d-qmodel can be written as

(14a)(14b)

'd p = Lmi* + os1T'qr 9'qr = LJqs -mslT'b .

Rewrite (14) in terms of their stator currentcompon ents, we can obtainab = ( Lm i dr L , w , T , i , , ) / ( 1 + w ~ T , 2 ) , ( Waqr= (Lmiqs ~ ~ u , , ~ , i , ) / ( l + w ~ , ~ , ~ ) .15b)

The active and reactive power transformed to the rotorarePa= vdridr+ vqsiqs- i i + i s ) R s , (1 6 4

(16b), = vqsidF Jqs - i i + i is)weL, .In steady state, the stator voltage equation is

v* = Rsidr-weLoiqs-o, ,Iqp, (17a)(17b)

Lrv , = RSih-w,L,i, -w e -Ab .mLr

Substitute (17) to (16), we obtainpa= (o, ,~,(weL; /L; (i: + ) / ( I + wS:r,'1, (18a)

(18b), = (o,LZ, /L:) ( i ; + i ; ) / ( I + w$T,z).From (18), a cost fimctilon in tuning the rotor timeconstant is defined as

F = p .-p14".. (19)Ids

The rotor time constant can be ob tained in searching fora minimum of the cost fimction by tuning the field andtorque producing currents. Fig. 9 shows the blockdiagram of the rotor time constant auto-tuning scheme,where To s the initial g u ess of the rotor time constant.

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Fig. 10. Experimental esults of off-line tuning of rotor time constant.

7^35

30

2 5

2Q

0 200 40 0 600 800 I000 1 2 0 0I S

Fig. 1 1. Experimental results of on-line tuning of rotor time constant.V. EXPERIMENTALERIFICATION

Experiment verification is carried out on a PC-baseddigital board using a single-chip DSP controller(TMS320C14) from Texas Instruments. All the controlfunctions were realized using assembly language andthe tuning functions were realized using PC-based high-level language. The motor to be controlled is a three-phase, four-pole, 220V, 1/2 HP, squirrel-cage inductionmotor manufactured by TEC O Co.Fig. 10 shows the rotor time constant tuningtrajectories from different initial guesses using the off-line tuning technique. It can be observed that the rotortime constant will indeed converge to a same value. Fig.1 1 shows the experimental result of on-line tuning whenthe rotor time constant of slip estimator has beensuddenly changed. It illustrates the rotor time constantof a slip estimator will converge to its correct value ifthe motor parameter are unchanged by the workingtemperature and operating point. Fig. 12 shows thedynamic responses of the constructed sensorlessinduction drive.

VI. CONCLUSIONThe key to a successful implementation of asensorless induction drive not o nly depends on fast andaccurate rotor speed estimation, it also requires a well-tuned decoupling control of the induction motor. Theproposed sensorless speed control scheme employsrotor-flux-oriented vector control with on-line rotortime constant adaptation to achieve well decouplingcontrol and stator-flux-based flux estimation withvoltage adaptation to achieve accurate speedestimation. The proposed sensorless control schem e isespecially suitable for squirrel-cage induction motorwith unknown or changing rotor dynamics.

REFERENCESK. Ohnishi, N. Matsui, and Y. Hori, Estimation,identification, and sensorless control in motion controlsystem, Proc. of the IEEE, vol. 82, no. 8, Aug. 1994.J. Holtz, Speed estimation and sensorless control of ACdrives, IEEE IECON Con$ Rec., vol. 2, pp. 649-654, 1993.J. H o b , Methods for speed sensorless control of ac drives,IEEE PCC-Yokohama Co nj Rec., pp. 415-420, 1993.

I I n i i I , I I I I I 1 I-0 1

Fig. 12. Experimental results of sensorless speed control for 2000rpm step response.

X. Xu and D. W. Novotny, Implementation of direct statorflux orientatin control on versatile DSP based system, IEEETrans. Ind. Appl., vol. 27, no. 4, pp. 694-700, 1991.L. Ben-Brahim and A. Kawamura, A fully digitized field-oriented controlled induction motor drive using only currentsensors, IEEE Trans. on Ind. Elec., vol. 39, no. 3, pp. 241-249, June 1992.B. K. Bose, M. G . Simoes, and et al., Speed sensorless hybridvector controlled induction motor drive, IEEE IAS AnnualMeetzngRec., pp. 137-143 , 1995.G. Yang and T. H. Chin, Adaptive speed identificationscheme for vector controlled speed sensorless inverterinduction motor drive, IEEE Trans. Ind. Appl., vol. 29, no. 4,C. Schauder, Adaptive speed identification for vector controlof indu ction motors without rotational transducers, IEEE IASCo nj Rec ., pp. 493-499, Oct. 1989.C . Wang, D. W. Novotny, and T. A. Lipo, An automated rotortime constant measurement system for indirect field-orienteddrives,IEEE Trans. Ind. Appl., vol. 24, no. 1, Jan./Feb. 1988.W. H. Kwon, C. H. Lee, K. S . Youn, and G. H. Cho,Measurement of rotor time constant taking into accountmagnetizing flux in the indution motor, IEEE IA S AnnualMeeting C onj Rec., pp. 88-92, 1994.M. Koyama, M . Ymo, I. Kamiyama, an d S . Yano,Microprocessor-based vector control system for inductionmotor drives with rotor time constant identification function.IEEE Trans. Ind. Appl., vol. 22, no. 3, pp. 453-459, MayIJune1986.M. Sumner and G. M. Asher, The experimental investigationof multi-parameter indentification methods for cage inductionmotors, Proc. EPE ConJ:Rec., vol. 3, pp. 389-394, 1991.

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sensor less control of im with on-line rotor time constant adaptation

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