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New approach to field orientation control of a CSIinduction motor driveJie Zh ang, MScV. Thiagara jan, MScT. Grant, MEngT.H. Bar ton, DEng, FIEE

Indexing term: Induction motors

Abstract: An improved approach to the fieldorientation control of a CSI-IM drive is devel-oped. The primary current variables in the syn-chronous reference frame are acquired directlyfrom the DC-link current and the phase angle ofthe stator current. Flux position estimation is per-formed by feedback of the primary currents. Thissubstantially reduces the matrix co-ordinate trans-formations, and simplifies the control strategy. Aninnovation in the positioning control of the statorcurrent vector is provided by a binary gatingpattern in combination with a real-time interrupttechnique. A new control scheme, incorporating anonlinear current controller, has been developed.The analysis and control scheme are verified byexperimental results.

List of principal symbolsa, /? = designate ortho gon al axes in the synchro -nous reference framer l 5 r2 = stator and rotor resistancesh, l2 = stator and rotor leakage inductancesLlt L2 = stator and rotor airgap inductancesM = stator-rotor mutual inductancen = number of pole pairs&>! = radian frequency of the supplycosl = radian frequency of the rotor currentss = slipp = the differential operator, d/dtvi*> vip alpha and beta components of the applied

voltagehathfi = alpha and beta co mp onen ts of the stato rcurrentha > hp = alpha and beta components of the rotorcurrenti M = magnetising current in the alpha-beta frame*P = angle of the alph a axis with respect to thestator reference direction6 = angle of the stator M M F vector relative tothe alpha axisX = airgap flux linkage v ectorX2l = rotor leakage flux linkage vector

Paper 5728B (PI, P6), received 20th February 1987The authors are with the Department of Electrical Engineering, TheUniversity of Calgary, 2500 University Drive NW, Calgary, Alberta,Canada, T2N 1N4

X 2 = rotor flux linkage vector^2a> ^2/? = com po ne nt s of X2 along the alpha and betaaxesIdc, Idcref = DC-link current and reference DC-linkcurrenth* ha p = magnitude of the actual and reference statorcurrentTe, T t = electromagnetic torque and load torqueT2 = ro tor t ime cons tant , (l2 + L2)/r2Tm = mechanical time constant7^ = sampling period

a.ref = convertor reference delay angleK r numeric factor

1 IntroductionField orientation control of induction motors [1] is oneof the most important topics in the variable speed drivearea today; its key technique is the acquisition of fluxposition. Any direct flux sensing scheme requires aspecial machine with a flux sensing device. Indirect fieldorientation by Hasse [2], for which the flux position isestimated based on machine electrical input quantities aswell as machine parameters, is preferred in most applica-tions today. As an exact practical realisation of the indi-rect me tho d is extreme ly difficult, consid erable effort hasbeen made to attain it and remarkable results have beenachieved [3-10, 15].Most field orientation schemes in the literature arebased on variable transformations. Several mathematicalco-ordinate transformations are required to translate theAC electrical quantities of the induction motor to the DCquantities of the two-phase model in the synchronous ref-erence frame. This results in much calculation, and asophisticated control task. It also leads to difficulties insystem design and implementation. Alternatively, fieldorientation control of an induction motor fed by acurrent source inverter can manipulate the DC-linkcurrent in proportion to the magnitude of the statorcurrent vector. Together with phase angle control of thestator current, this provides a direct variable transform-ation and a simple realisation of field orientation control.Although the inductor interposed between the rectifierand the current source inverter is a substantial com-ponent which introduces lag into the system, its presenceis substantially compensated by the simplicity androbustness of the system and the ease of regeneration.This is accomplished by a single rectifier without anyspecial control measures.

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2 Theory of field orientationBased on two-axis machine theory, the differential equa-tions of an induction motor can be written by the use ofa (} variables in the synchronous reference frame. Themathem atical m odel of a cage induction motor is

00

i + p{lx + L J(/i + > i

pMMco sl

(/t + Li)a>i pMr i + P('i + ^1) McOi-Mco s/ r 2 + p ( / 2 - tpM (l2 + L2)

The number of effective turns of the stator and rotorwindings is normalised so that Lt = L2 = M.The electromagnetic torque isTe = 2n(k2p i2a2a (2)

Let the a axis of the synchronous reference frame coin-cide with the space vector of the total rotor flux linkage,k2 = k + kn. Then k2p = 0 and k2a = k2. The flux canbe related to the currents in the synchronous referenceframe:Mila

andMi 1/?

L2)i2a = k

L2)i2tl = 0

(3)

(4)Several imp ortan t relations result from this ideal fieldorientation.

-pk2

120= -

k, =

r2si

M

kr 22 l2

M+ L2 he

(5)

(6)

(7)The slip angular frequency is related to the stator cur-rents by

(8)and the torque equation becomes

^2a l2PM M

I, + (9)

F i g . 1 Block diagram of an induction motor from the viewpoint of fieldorientation

The block diagram representation of a cage inductionmotor which arises from these equations is illustrated inFig. 1, where iM is the actual magnetising current, and Tmis the mechanical time constant corresponding to thetotal moment of inertia on the drive shaft. k2 is constant Mco^

pM- ( / 2 + L2)to slr2 + p(/ 2 + L2)

Hahe

-l2P _

(1)

if ila is maintained constant. The instantaneous torqueresponse can be achieved by controlling only the statortorque current, iip. The transient vector diagram whichappears in field orientation control is given in Fig. 2a . Inthe steady state, dkjdt = 0 and the vector diagram isshown in Fig. 2b. Under ideal field orientation, theinstantaneous orientation of the reference frame *F andthe phase angle 0 of the stator current vector are adjusteduntil the rotor current vector is along the negative /? axisand there is no magnetisation of the motor along this /?axis. At the same time, the magnitude of the statorcurrent is adjusted so that the stator torque current isequal to its desired value as indicated in Fig. 2b . The

1

2CX/9- 2/9

Fig. 2 Current variables in the synchronous reference framea Dynamic conditionsb Steady state

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position of the total rotor flux is the most importantinformation for field orientation control.

3 New control schemeThe total rotor flux position can be estimated by slip fre-quency angle, and a feedback of rotor position angle. Theestimation of the slip frequency angle has to be based onthe stator currents since the rotor currents are not acces-sible. A block diagram of a field orientation scheme,based on the above analysis and which is well suited tothe current source inverter drive, is shown in Fig. 3. Inorder to acquire accurate information, the estimation ofslip frequency angle in the diagram is based on the actualprimary currents, ila and i1/?, instead of their commandvalue [11] since it normally takes tens of milliseconds forthe actual current to respond to a step reference input.During the transient, the command slip frequency value,co*,, which is calculated from the current command valuedeviates from the actual value, cosl, which is desired forcorrect field orientation. Obviously, the deviation is largeespecially at the beginning of the transient. A excessive orinadequate slip then results. The excessive or inadequateslip adversely affects the torque response of the drive[10].

Field orientation theory is essentially based on vari-able transformations. In order to obtain ila an d iip, anumber of mathematical co-ordinate transformations arerequired to translate the AC electrical quantities to theDC quantities of the 2-phase model in the synchronousreference frame. This results in much time consuming cal-culation and leads to difficulties in system design andimplementation. However, it can be shown that in theCSI induction motor drive the DC-link current, IDC , hasan analytical relation with the magnitude of the statorcurrent phasor, Iu provided that the commutation effectis neglected. If commutation is included this relationshipis a complex one. Fortunately the commutation period isnormally brief [12, 13] and can be neglected. Our systemhad a maximum commutation angle of 10 and the errorin neglecting it did not exceed 0.6%. Should a correction

rectangular

KXref

10C

MT2

M

UJ S ,1p

Fig. 3 Proposed polar form realisation offieldoriented controlbe deemed necessary, a linear one proportional to thesize of the DC-link current will reduce the residual errorto extremely small levels, well under 0.1%. Field orienta-tion control of a CSI induction motor drive can thereforemanipulate the DC-link current in proportion to the

magnitude of the stator current phasor [11] and complexmathematical co-ordinate transformations are not neces-sary.ha = COS V = DC CO S

*I/J = ^1 sin 6 = DC sin

(10)

(11)The direct variable transformation substantially reducesthe conventional matrix calculation for the co-ordinatetransformation. It is not affected by the machine param-eter variation and no synchronous sampling facility isrequired compared with the conventional co-ordinatetransformation. It provides an accurate primary currentcontrol and permits a simple and economical realisationof field orientation. The new control scheme is illustratedin Fig. 4.

One way to set the reference value of stator magne-tising current, ilaref, is to have a flux observer to providea magnetising current feedback [9] . This results in acomplex control scheme. Furthermore, the accuracy ofthe conventional flux observer and the effect of the feed-back control of the magnetising current are affected bythe motor parameter variation. In the control schemeshown in Fig. 4, the reference value of the magnetisingcurrent, ilaref, is provided by the ila calculator block.haref *s equal to ila0 , which is a constant in the normaloperating range below the basic frequency, 60 Hz, and isinversely proportional to the excitation frequency duringthe field weakening range, above 60 Hz. Since there is nodirect feedback control of the magnetising current, theactual flux of the machine may not always equal the ref-erence value. In fact, the actual flux must be reduced atlight load [15]. Therefore, it is necessary to reduce thereference value of the magnetising current under this con-dition. This is the reason for the input of the torque com-ponent of current, i1/Jre/, to the ila calculator. In Fig. 4,Ks = M/T2X2 is the slip gain and i l a0 is the rated valueof the magnetising current in the synchronous referenceframe. The latter can be predetermined via the RM Svalue of magnetising current per phase, the relationbetween the a /? value and the phase RMS value being

(12)

4 Simple nonlinear current regulatorBecause of the large variation of induction motor inputimpedance as slip frequency changes, a linear PI currentcontroller may not be sufficient to achieve high per-formance. A nonlinear current controller [14, 11] hasbeen designed. The schematic diagram of the current con-troller is illustrated by F ig. 5. The DC-link current isadjusted to a given level by controlling the rectifier com-mutation point. The commutation point is in turn con-trolled by inhibiting or applying gate pulses to therectifier at appropriate times.

When Idc < Idcref, the inhibit signal is off and the con-vertor controller advances normally, emitting gate pulsesto the converter thyristors at suitable instants. An appro-priate reference delay angle, ocref, is calculated by themicroprocessor according to the required value of theDC-link current to reduce the overshoot and ripple of theoutput current [11]. As soon as Idc ^ Idcref the inhibitsignal goes on, and the convertor controller is inhibited

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from further progress. In this situation, conductionremains through a pair of thyristors and the rectifieroutput voltage and current decrease with time until

signals are acquired with the aid of an analogue inputmultimodule board, iSBX 311. The output of the manip-ulated variables, including the DC-link current

3-phasesupply

'a O'10ccalculator locref '1O/9

Jsle speedcontroller11/9 ref

currentcontroller convertor

' d clowpassf i l ter

-T c s

vdcldcLf

rectangular

lowpassf i l t e rFi g . 4 Block diagram of control sch eme

' iO c /9

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The CPU is interrupted when an interrupt request is pro-vided by the interrupt controller and control is passed tothe interrupt service routine. An appropriate gatinghex

T h 1110000

T h 2011000

T h 3001100

000110

T h 5000011

T h100001

patternpointer

a> a>u "w o- ^ a> 6-

Fig. 7 Binary gating pattern for current source inverterpattern is fed into the drive circuit array of the CSIthrough the PPI and the outgoing binary gating patternis updated by the interrupt service routine. The statorcurrent frequency is varied simply by varying the inter-rupt interval.5.2 Phase angle control of stator currentOne of the key techniques of field oriented control isphase angle control of the stator current. Without anappropriate phase angle control, field orientation control

degenerates into conventional slip-frequency control andthe dynamic characteristics deteriorate.The implementation of phase angle control is trouble-some, Usually a complex phase angle control loop isemployed. However, the binary gating pattern in com-bination with the real-time interrupt technique justdescribed provides a simple and effective means of phaseangle control [11]. The phase angle of the stator currentphasor can be instantaneously decreased or increased byincreasing or decreasing the interrupt interval. This isdone by first converting the increment of the phase angleinto the corresponding time increment which must elapsefor the phase angle change at the given frequency, thenadding six times the time increment to the interrup t inter-val to change the phase angle. The increment of thephase angle is limited to n/3 in this project. The interruptinterval can be controlled in real time by loading the cor-responding number into the programmable counter. Inthis way, a highly accurate and rapid phase angle andfrequency control of stator current is easily achieved.5.3 General description of softwareThe general flowchart of the program is shown in Fig. 8.The program is written in such a way as to make it com-pletely interactive from the terminal. System parameters

C start ji n i t i a l i za t ion interruptservice routinetable look-up

closed- loopoperat ioncommunicat ion keyboardcommand andparameter interpreter

y e s

cur rent - looptest w i thfrequency control

save processorstatus andregisters

call SFWINV

restoreprocessorstatus andregisters

return frominterrupt

n = n*1

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and operating commands can be input from the key-board in real time and in arbitrary sequence. The inputinformation is interpreted as the correspondingcommand or parameter by either the operation modeinterpreter or system parameter interpreter. The inputparameters are converted from ASCII format into float-ing point numbers by a subroutine. The video terminaldisplays an appropriate message after a parameter orcommand is received by the program. Normally, thedrive is in close-loop operation (OPMDO). The oper-ational model 1 (OPM D1) and model 2 (OPM D2) areprovided for test purpose. The interrupt service routineprovides control of phase angle and frequency of statorcurrent as presented above.During transient response to a speed or load step ref-erence input, the speed PI controller reaches its limitrapidly. The current loop produces the maximum allow-able current to provide maximum torque for acceleration.Thus, optimal control of the speed response is realised.The optimisation is based on the index of the minimumrise time of the speed response under the constraint ofldc ^ Idcmax The limit value of the output of the speedcontroller corresponds to the DC-link current limit. It, aswell as all necessary system parameters, can be adjustedin real time by a keyboard command. The algorithm ofthe speed PI controller is given in Appendix 10.1.6 Experimental resultsThe experimental cage induction motor is coupled to aDC dynamom eter consisting of a 20 hp D C m otor. Itsnameplate data and parameters are listed in Appendix10.2. The total moment of inertia on the drive shaft is0.88 kgm 2, which is quite large for the 10 hp inductionmotor and slows down the speed of response. In closedloop operation, the speed reference signal is given fromthe k eyboa rd. The system sampling frequency is 375 Hz.

The speed response to a step reference input from 500-1500 r/min with 69% rated load is shown in Fig. 9, with

the whole speed range, of a step load disturbance. Themaximum speed deviation due to the step load dis-turbance is about 24 r/min and the speed recovery time is

Fig . 9 Speed response to a sudden change in speed reference from 500r/min to 1500 r/mina Vertical scaleb Horizontal scale 200 r/min/div1 sec/diva settling time of about 2 s and very small overshoot. Themaximum transient DC-link current is limited to 2.4times the rated value. The step down speed response from1500-500 is shown in Fig. 10. The settling time is within1 s and the response is very well damped.Fig. 11 demonstrates the speed response to step loaddisturbance. The system shows excellent rejection, over

Fig . 10 Speed response to a sudden change in speed reference from1500 to 500 r/mina Vertical scaleb Horizontal scale 200 r/min/div1 sec/div

Fig. 11 Speed response to a sudden application of rated load at 1750r/mina Upper trace dynam ometer referenceb Middle trace Speed, 100 r/min /divc Lower trace DC link curre nt, 40 A/div.d Horizon tal scale 1 sec/div.

less than 1 s. The performance is identical at differentoperating points.Fig. 12 depicts 10 continual speed reversals between+ 1750 r/min which takes about 45 s. At the beginning ofthe each reversal, the output of the speed regulatorreaches its limit value, i 1 /? immediately. The drive thenaccelerates with maximum torque and quickly reachesthe steady-state value. After the 10th reversal, the drivereturns to the normal operation mode automatically. Theload torque provided by the DC dynamometer is slightlylarger in the reverse direction and the DC-link currentduring regeneration is higher then that in motoring.These, and friction, account for the nonlinearity of thespeed response curve during the reversals.The mean speed regulation over the entire speedregion is 0.116%. Even at very low speed, 50 r/min (1.6Hz), the drive provides good performance with a speedregulation of 0.17%. The overall system performance iscomparable with or better than other well designed

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induction motor drives which have so far appeared in theliterature [6-7, 15-18].

7 ConclusionAn improved approach to field oriented control of a CSIinduction motor drive has been presented. The direct

Fig. 12 Ten speed reversals from 1750 to -1750 r/min at 57% ofrated loada Upper traceb Lower tracec Horizontal scale

speed, 1000 r/min/div.DC link current, 40 A/div.5 sec/div.variable transformation greatly reduces the conventionalmatrix calculations for translating the AC stator phasequantities to DC quantities in the synchronous referenceframe. A new rotor flux position estimation scheme and asimple control strategy is developed. The binary gatingpattern in combination with real-time interrupt tech-nique, which is another feature of the system, provides ahighly accu rate and rapid phase angle and frequencycontrol of the stator current without any complex controlloop. To overcome the variation of motor input imped-ance and to achieve high performance, a simple nonlinearcurrent controller is designed. The experimental resultsare very satisfactory a nd surpass all desired specificationsof the project with considerable performance margins.

8 AcknowledgmentWe gratefully acknowledge our indebtedness to the Uni-versity of Calgary for the provision of facilities and to theKirloskar Electric Company of India who financed thisproject. We also wish to recognise the advice and help ofG.S. Hope, G. Hancock and E. Evanik of the Depart-ment of Electrical Engineering, The University ofCalgary. The first author would like to thank V. Thi-agarajan and T. Grant for their contribution to the hard-ware realisation of the project.

9 References1 BLASCHKE, F.: 'New method for the structure decoupling of ACinduction machines'. Second IFAC Symposium on multivariabletechnical control systems, 1971, pp. 11-132 HASSE, K.: 'Zum dynamischen Verhalten der Asynchronmaschinebei Betrieb mit variabler Staenderfrequenz und Staenderspannung'('On the dynamic behavior of induction machines driven by variablefrequency and voltage sources'), ETZ Arch., 1968, 89, pp. 77-813 GABRIEL, R., LEONHARD, W., and NORDBY, C : 'Field orien-tation control of a standard AC motor using microprocessor'. IEEEIndustry Applications Society, Conference Record, 1979, pp. 910-9164 SCHUMACHER, W., LETAS, H.H., and LEONHARD, W.:'Microprocessor-controlled AC-servodrives with synchronous and

asynchronous motors'. IEE Conference Publication 234, Power Elec-tronics and Variable-Speed Drives, 1984, pp . 233-2365 AKAMOTSU, M., IKED A, K., TOMEI, H., and YANO, S.: 'Highperformance IM drive by co-ordinate control using controlledcurrent inverter', IEEE Trans., 1982, IA-18, pp. 382-3926 KAIMOTO, M., HASHII, M., YANASE, T., and NAKANO, T.:'Performance improvement of current source inverter-fed inductionmotor drive', IEEE Trans., 1982, IA-18, (6), pp. 703-7117 KRISHNAN, R, LINDSAY, J.F, and STEFANOVIC, V.R.:'Design of angle controlled current source inverter-fed inductionmotor drive', IEEE. Trans. Ind. Appl, 1983, IA-19, pp. 370-3788 MATSUO, T., and LIPO, T.: 'Rotor parameter identificationscheme for vector controlled induction motor drives', IEEE Trans.Ind. Appl, 1985, IA-21, (4), pp. 624-6329 KAZMIERKOWSKI, M.P., and KOPCKE, H.J.: 'Simple controlsystem for current source inverter-fed induction motor drives', IEEETrans. Ind. Appl, 1985, IA-21, (3), pp. 617-62310 LORENZ, R.D.: 'Tuning of field oriented induction motor control-lers for high performance applications'. IEEE-IAS ConferenceRecord, 1985, pp. 607-61211 ZHANG, JIE: 'Field oriented control of induction motor speed'.MSc. Thesis, Dept. of Electrical Eng., The University of Calgary,198512 LIPO, T.A., and CORNELL, E.P.: 'State-variable steady-stateanalysis of a controlled current induction motor drive', IEEE Trans.Ind. Appl, 1975, IA-11, (6), pp. 704-71213 FARRER, W., and MISKIN, J.D.: 'Quasi-sine wave fully regener-ative inverter', IEE Proc. B, 1973,120, (9), pp. 969-976

14 ZELENKA, K.R., and BARTON, T.H.: 'Fast acting current limitfor DC motor drive', IEEE Trans. Ind. Appl, 1986, IA-22, (5), pp.798-80315 ITO, T., YAMAGUCHI, T, UEDA, R., MOCHIZUKI, T., andSIGEO, T.: 'Analysis of field orientation control of current sourceinverter drive induction motor system', IEEE Trans. IAS, 1983,IA-19, (2), pp. 206-20916 SIVAKUMAR, S., SHARAT, A.M., and NATARAJAN, K.:'Improving the performance of indirect field orientation schemes forinduction motor drives', IEEE-IAS, Conference Record, 1986, pp.147-15317 KEIJI, S., KENZO, K., TAKASHI, S., TAKAYUKI, M., andTOSHIAKI, O.: 'Multi-processor-based, fully digital, AC drivesystem for rolling mills', IEEE-IAS, Conference Record, 1986, pp.36-4118 DEFORNEL, B., BACH, J.L, HAPIOT, J.C., and PIERTRZAK-DAVID, M.: 'Numerical speed control of a current-fed asynchro-nous machine by measurement of supply voltages', IEE Proc. B,1984,131, (4), pp. 165-169

10 Appendix10.1 Algorithm of speed controllerBy the use of a rectangular integration method, thedigital algorithm of the PI speed controller, with theinput of x(k) and the output of y(k), is given by

y(k) = y(k -where

/a - x(k - 1)]

T = 0.053 (s)K = 1.2Ts = the sampling period

10.2 Machine parameters10 hp; 230 V; 26.2 A; 60 Hz; 4 pole; 1750 r/min.Parameters of the experimental motor are

rl 0.242 filx + Lx 35.012 mHr2 0.144 fil2 + L2 35.574 mHM 33.888 mH

Parameters of the dc-link filter arer, 0.105 fiLf 55 mH

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