Habetler Et Al

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IEEE TRANSACTIONSON INDUSTRY APPLICATIONS,VOL. 28, NO. 5, SEPTEMBER/ OCTOBER 1992 1045

Direct Torque Control of InductionMachines Using Space VectorModulation

Thomas G. Habetler, Member, IEEE, FrancescoProfumo, Senior Member, IEEE, Michele Pastorelli,and Leon M. Tolbert, Member, ZEEE

Absfruct-This paper describes a control scheme for directtorque and flux control of induction machines based on thestator flux field-orientation method. With the proposed predic-tive control scheme, an inverter duty cycle has directly calcu-lated each fixed switching period based on the torque and fluxerrors, the transient reactance of the machine, and an estimatedvalue of the voltage behind the transient reactance. The paperdescribes a method by which a voltage space vector can becalculated in order to control the torque and flux directly in adeadbeat fashion. The inverter duty cycle can then be calculatedusing the space vector PWM technique. With this scheme, therequirement of a separate current regulator and proportional-integral (PI) control of the flux, torque, and/or current error iseliminated, thereby improving transient performance.An alter-native modulation scheme is presented in which transient per-formance is improved by specifying the inverter switching statesU priori, then calculating the required switching instants tomaintain deadbeat control of the f lux while reducing the torqueerror during the entire switching interval. A similar approach isused for a transient in the flux. The implementation of thecontrol scheme using DSP-based hardware is described, withcomplete experimental results given.

INTRODUCTIONN MANY VARIABLE-speed drive applications, torqueI ontrol is required or desired, but precise, closed-loop

control of speed is not necessary. The advantages oftorque control in this type of application include greatlyimproved transient response, avoidance of nuisance over-current trips, and the elimination of load-dependent con-troller parameters. An example of an application wheretorque is to be controlled, without precise speed control,is traction drives for electric vehicles. Here, the torquecommand comes directly from the user input. Speed con-trol, if used at all, needs not be precise. In tractionapplications, as well as applications that currently useopen-loop, constant V/f drives, a torque control scheme

Paper IPCSD 92-12, approved by the Industrial Drives Committee ofthe IEEE Industry Applications Society for presentation at the 1991Industry Applications Society Annual Meeting, Dearbom, MI, Septem-ber 28-October 4. Manuscript released for publication March 1, 1992.T. G. Habetler is with the School of Electrical Engineering, GeorgiaInstitute of Technology, Atlanta, GA 30332.F. Profumo and M. Pastorelli are with the Dipartimento di Elettro tec-nica, Politecnico di Torino, Torino, Italy.L. M. Tolbert is with Martin Marietta Energy Systems, Oak RidgeNational Laboratory, Oak Ridge, TN 37831.IEEE Log Number 9203303.

that does not require motor speed information is veryadvantageous.Stator flux field orientation (SFO) 111, 121 has gainedinterest as an induction machine torque control schemedue to the fact that speed feedback is not required tocontrol the torque produced by the machine. The flux andtorque a re calculated (estimated) from the stator voltage,current, and resistance. A torque-producing component ofcurrent and a flux-producing component of current can beidentified without knowledge of the rotor speed, position,or flux.

SFO drives typically derive a stator current command inthe stationary dq reference frame based on the calculatedtorque and flux error. A current regulator is then used togenerate the appropriate gating signals to the inverter.This scheme, however, requires a decoupling of thetorque-producing component of current and the statorflux.

The problem of decoupling the stator current in adynamic fashion can be avoided. Reference [3] presents amethod of stator flux orientation in which the torque andflux errors are directly sent through proportional-integral(PI) regulators to generate a dq voltage reference. Avoltage space vector PW M scheme [ 6 ] is then used tocontrol the inverter. The transient response of this torquecontrol method is still limited by the PI regulators in boththe torque and flux loops.

The method of direct self control [4],5] was introducedto control the torque and flux directly based solely on theinstantaneous errors in torque and flux. This method isvery well suited to high-power drives with low switchingfrequency. The inverter is switched in a hysteresis (orband-bang) fashion based directly on the torque and fluxin the machine. This method, however, results in a vari-able switching frequency due to the hysteresis control.

The scheme proposed in this paper is also based ondirect control of the torque and flux but has the advan-tage of a fixed switching period. Like the other directtorque controlled schemes, no inner current regulationloop is used. The proposed scheme calculates the inverterswitching pattern (i.e., duty cycle) directly in order tocontrol the torque and flux in a deadbeat fashion over aconstant switching period. This is accomplished by calcu-lating the voltage space vector required to control the

0093-9994/92$03.00 0 1992 IEEE


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1046 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 28, NO . 5 , SEPTEMBER/OCTOBER 1992

torque and flux on a cycle-by-cycle basis using the calcu-lated flux and torque errors sampled from the previouscycle and an estimate of the back EMF in the machine.The back EMF of the machine is estimated from the fluxand voltage vectors, which are already-available quantitiesin the SFO controller. Voltage space vector PWM is thenused to find the switching intervals (duty cycle). A n alter-native control method is used under transient conditionssince the space vector PWM does not yield a solutionwhen the torque and/or the flux cannot be driven to thereference value in a single switching period. A blockdiagram of the direct torque controlled drive is shown inFig. 1.

ESTIMATIONF MOTOR UANTITIESIt is convenient in SFO drives to convert the systemquantities to a stationary, two phase dq reference frame.

An arbitrary three-phase quantity fa , f b , f , can be trans-formed to the stationary dq reference frame by

The stator flux dq vector is determined from the statorvoltage vector E , the stator resistance R,, and the statorcurrent vector r, by

Induction Machine

stator Flux ~ I 1Magnitude ReferenceFig. 1. Block schematic of d irect torque and flux controlled inductionmachine drive.

Fig. 2. Equivalent circuit of inverter-driven induction machine in thedq stationary reference frame.

As is the case with any SFO drive scheme, the calculationof the stator flux requires knowledge of the stator resis-tan=, Particularly at low speed below about 5 Hz.There-fore, the speed range of the drive is limited unless someform of resistance estimator or tuning is incorporated.

The electromagnetic torque produced by the machinecan be written in terms of the stator current and flux as

Therefore, the change in torque Over a period can bepredicted from the stator voltage and current and thevoltage behind the transient reactance E . This voltage canbe estimated from the stator flux and current. Using (2)and the dq equivalent circuit of the induction machinedrive system shown in Fig. 2, the voltage behind thetransient reactance is

where p is the number of poles in the machine. A nequivalent circuit in the stationary reference frame of theinverter-driven induction machine is shown in Fig. 2. From Fig. 2, the change in stator current vector A j , overa constant period T, is given by

(4 )The period T, is constant in the proposed scheme in orderto maintain a constant switching frequency. At speedsabove a few Hertz, the stator IR drop can be neglected, inwhich case v* s equal to E*. t is assumed that the statorelectrical time constant is much longer than T,, andtherefore, the change in current over the period T, islinear. The corresponding change in electromagnetictorque over the period T, is then

3 p - - v - EA T = - - (A , x AZ,) =-- A, x- ,2 2 2 2p [ - L ,

If it is assumed that E is sinusoidal, thenE = j w e ( A , - LII,) (7)

The excitation frequency we in (7) can be estimated usingthe stator fluxvector and the terminal quantities, as in [ 3 ] .In order to find the average stator frequency, it is as-sumed that h, is sinusoidal, then

Therefore, the change in torque over the period T, can befound from (5)-(8). The change in flux over some periodT, is simply given by

(9)The control scheme described in the next section uses theestimated or predicted values of the change in flux and

I


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HABETLER er al.: DIRECT TORQUE CONTROL O F INDUCTION MACHINES

torque ((5) and (9)) to determine the switching state of theinverter.

DEADBEATORQUEND FLUXONTROLThe proposed control scheme is based on a predictive

calculation of the stator voltage vector, which will drivethe torque and flux magnitude to the reference value in adeadbeat fashion over a constant period. A fixed timeperiod equal to half the switching period is denoted by T,.Let t , be the time at the beginning of an arbitrary T,period. The torque is controlled in a beat manner if, overthe T, period

AT =T * - T(t , ) (10)where T* is the reference or command value of torque.Equation (10) is then substituted into ( 5 ) to yield

3 P T s -2 2 L ,* - T(t , ) =--,(As X ( V * - E ) ) (11)

where p* s the voltage vector (minus the stator IR drop),which results in deadbeat control of the torque. In termsof d and g components

Let K, be defined as

Then, the q component of voltage is

The stator flux magnitude is controlled such thatAIAI = A :Ix(t,)l (15)

where A is the command value of stator flux magnitude.Using (9), the voltage V * required for deadbeat control ofthe flux magnitude is found from

orA =(Vd"T, +A,,)' +(V,*T, + Ad,)' (17)

where A, is assumed to be the value of flux vector at thebeginning of the period T,. Equations (11) and (17) repre-sent two equations with two unknowns and Vz .Sub-stituting (14) into (17) gives a quadratic equation with V,*

Lu- I--%+ k = lFig. 3. Inverter switching states and stator voltage vectors.

as the unknown.

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Equation (18) yields two solutions for V:. The solutionwith the smallest absolute value is chosen since it repre-sents the smallest d-axis voltage necessary to drive thetorque and flux to thzir reference values. Equation (14)then gives V,*. Once V* s found from (18), the referencevalue of stator voltage is obtained by adding on the statorIR drop, that is

v,* =v* +R , J , ( t , ) . (19)Note that in (19), the stator IR drop from the previouscycle is added to v*. s stated earlier, the change instator current is assumed to be linear since the stator IRdrop is very small compared with the voltage drop acrossL:. In addition, (19) is justified since the change in statorcurrent vector over T, is very small compared with themagnitude of the stator current vector.The switching state of the inverter is determined fromE* using space vector PWM [6]. v,* represents the aver-age value of the stator voltage vector OVF the period T, .The instantaneous stator voltage vector V , takes on oneof seven values depending on the switching state k of theinverter. This is depicted in Fig. 3. The stator voltage isgiven by

k = 0 , 7 .The reference voltage is realized in an average sense bycomputing the duty ratio (fraction of the switching period)for the two voltage vectors K ( k ) and K ( k + I ) , which areadjacent to E Let Tk and T k + l be amount of time spenton and I / ( k + * ) , respectively. Then, Tk and T k + l are


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1048 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS,VOL.28, NO. 5, SEPTEMBER / OCTOBER 1992

found by solving

The remainder of the switching period is spent on thezero state, that is

where To is the time spent on the zero state ( k =0 or 7) .Switching from the zero state to two adjacent statesinvolves commutating each of the inverter legs exactlyonce. Therefore, T, is a half period of the switchingfrequency. This implies that the torque and flux are con-trolled twice per switching cycle. In addition, the spacevector PWM results in reduced current ripple in steady-state operation as compared with sine-triangle PWM cur-rent regulator-based controllers [61, [71.

TORQUEND FLUXONTROL UNDER TRANSIENTCONDITIONSIt is important to maximize the dynamic response to

transients in the torque and/or flux command. With asufficiently large torque error in one switching period,such as that which occurs with a step change in fluxcommand, the simultaneous solution of (21) and-(22)yields the sum Tk +T k + lgreater than T,, that is, V,* istoo large to be synthesized in a single switching period.Therefore, an alternative control method must be derived.In the case of a transient in the torque command, thecontroller must cause the torque to be driven toward itsreference value while still maintaining deadbeat control ofthe flux. Just the opposite is true in the case of a fluxreference transient. Then, the flux magnitude is driventoward the reference value while maintaining deadbeatcontrol of the torque.

Consider first the case of a transient condition in thetorque, that is, the torque cannot be driven to the refer-ence value in a single T, period. This is generally the mostimportant and most frequently encountered transient con-dition. In this case, the inverter states are chosen a priori,which causes the torque to be driven in the desireddirection while still allowing for deadbeat control of theflux, To illustrate this state selection, consider an examplewhere the angle of the flux vector is between - ~ / 6 nd+ ~ / 6 . his is illustrated in the vector diagram of Fig. 4.States 2 and 3 cause the current in quadrature with thestator flux, and therefore the torque, to increase. Like-wise, states 5 and 6 cause the torque to decrease. Inaddition, from Figs. 3 and 4, states 2 and 6 cause the fluxmagnitude to increase, and states 3 and 5 cause the fluxmagnitude to decrease. Therefore, states 2 and 3 can beused to control the flux to its reference value over the Tsinterval while continuously increasing the torque over theentire interval. Table I summarizes the state selection fora transient in the torque command. Once the states k andk +1 are identified, the flux is controlled by substituting

fq

1ed

Fig. 4. Vecto r diagram illustrating the state selection process for tran-sient operation.

TABLE ISELECTIONF INVE RT E RTATES AND k +1 UNDE R RANSIENTCONDITIONST( 2 n - ) -


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HABETLER et al.: DIRECT TORQUE CONTROL OF INDUCTION MACHINES

3 p 1 -2 2 L ,T = - - y ( A , X ( vk T k+~ k + , T k + ,ET,) ) . (25)

Equation (25) is solved simultaneously with (24) for T,and T k + l .This accomplishes the deadbeat control of thetorque while driving the flux in the desired direction.Here, again, the zero state is not used. This is perfectlyreasonable since skipping the zero state while still switch-ing between adjacent states is equivalent to pulse dropping in conventional sinusoidal modulation.

The only remaining possibility is a transient in both thetorque and the flux. In this case, a single state is selectedfor the entire period, which drives both the torque andflux in the desired directions as quickly as possible. Thestate selection is given in Table I. The selected statescause both the torque and flux to be driven in the properdirection. Selecting a single state for the entire T , periodis essentially pulse dropping on all three phases (six-stepoperation).

REALIZATIONND SIMULATIONF THE CONTROLSCHEMEThe realization of the direct torque control scheme is

outlined idthe flowchart in Fig. 5. The switching states ofthe inverter and the corresponding dwell times are deter-mined each half switching period. The controller reads inthe stator voltage and current at the beginning of aparticular switching period. The stator flux is then calcu-lated. In the actual implementation done here, analoghardware is used to find the stator flux due to the ease ofperforming analog integration, thereby relieving the mi-croprocessor from this duty. Details of the experimentalhardware are given in the next section. It is assumed inthis paper that the stator resistance and transient reac-tance are known quantities. The stator flux and torque arethen used to calculate the present value of torque andsynchronous speed. The back EMF of the machine is thencalculated from the speed, flux, and current.Equation (18) is then solved for V,* using the quadraticformula. The square root is found using a Taylor seriesexpansion. The Taylor series expansion is done about theprevious intervals solution. In this way, it has been foundthat only three terms in the expansion yield a solutionwith less than 5% error. Using a truncated Taylor seriesexpansion with a good initial estimate of the solutionallows (18) to be solved within a very reasonable computa-tional time.

The two inverter states adjacent to p* re then found,and finally, the switching intervals are found by solving(21) and (22). If a positive solution does not exist, then atransient condition is encountered. In this case, it is firstassumed that a transient exists in the torque command.Table I(a> is used to determine the adjacent inverterstates, and then, (23 ) and (24) are solved. If a positivesolution for Tk and T k + does not exist, then (24) and (25)are solved using the states given in Table I(b). If asolution still does not exist, the inverter is switched to thestate indicated in Table I(c).

Read inh a . 1b, Va, Vb, Ia and Ib.( fm4/Dconvcners IConm o stator dq referem frame

4Calculate presentvalue of toqueI I

I CalculateKe, em (13)

Ad d s ta to r IR drop, q n 19)

Lookupkandk+l

Solveq n s (23) and (24)

f nnnTable l(c)@Output switching tate and switching- intervalstobasedrives 1

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Fig. 5. Flowchart of direct torque control scheme .

As with any predictive control scheme, as this one is, asingle T , period steady-state error exists since the torqueand flux calculations are based on input data from thepreceding period. A one-period delay is necessary to allowtime to calculate the switching pattern. An ideal deadbeatcontroller would require the calculations to be done inzero time. Furthermore, the controller is based solely oninstantaneous errors in the torque and flux. This fact,combined with the one-period delay, results in a steady-state error in the commanded torque. If the torque regu-lator is used together with an outer speed control loop,this does not present a problem. However, if the steady-state error in the torque is not tolerable, an outer loopthat adjusts the torque reference based on the averageerror (i.e., the integral of the torque error) can be added.It is important to note that this additional outer loop inno way compromises the dynamic performance of thedirect-torque controller.

The proposed control system is implemented using adigital signal processor (DSP) to perform the requisitecalculations. The DSP, which is characterized by hardwaremultiplication capability, allows for a large number ofarithmetic operations to be performed during each T,period. The transient control scheme in addition to theaforementioned deadbeat control increases the computa-tional burden quite significantly. This is not a problemwith a relatively low switching frequency (in this case, 2kHz). However, at higher switching frequencies, depend-ing on the speed of the processor and the A/D convert-


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1050 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 28, NO. 5, SEPTEMBER / OCTOBER 1992I

0.5

I:ir-05

e9 0

-1 -1 4.5 0 0.5 1d-&flux @U)

0 1 2 3 4 5 6 1(b)

. . . .4 0.625fz.ti

.ov4 -0.625-

-1.25

(e)Fig. 6. Simulation results: (a) Electromagnetic torque; (b) stator line current; (c) stator flux; (d) line-line switching function;(e) stator current vector.

ers, sufficient time may not be available to implement thetransient computations. In this case, the stator voltage canbe set equal to a voltage proportional to the calculatedI/* by setting the actual inverter switching times T i andT i + l equal to

T

This method results in satisfactory performance butdoes not give deadbeat control under transient conditions.

This is due to the fact that the zero state is not used, andtherefore, (22) is not satisfied.

The simulation results are shown in Fig. 6.The switch-ing frequency is 2 kHz, he transient reactance is 0.14 puat 60 Hz, nd the dc bus voltage is 3.0 pu. The fluxreference is 0.8 pu. The simulation results illustrate boththe steady-state and transient performance of the pro-posed torque control scheme. Note the good dynamicresponse of the system to a step change in torque com-mand. It is also clear from Fig. 7(c) that the flux regula-tion is quite good, even during the torque transient.


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HABETLER et al.: DIRECT TORQUE CONTROL O F INDUCTION MACHINES 1051

Fig. 7. Experimental waveforms. Top trace: mechanical speed, 600r/min /div. Bottom trace: estimated torque, 210 N .m/div. Horiz: 10ms/div. ms/div.Fig. 8. Experimental waveforms. Top trace: estimated flw magnitude, 1V . /div. Bottom trace: mechanical speed, 600 r/min/div. Horiz: 200

EXPERIMENTALESULTSThe experimental setup includes a complete motor drive

consisting of a three-phase bipolar inverter with a switch-ing frequency of 2 kHz and a 15-hp induction motor. Themain switches are rated at 1000 V and 200 A. Thecomplete 'control scheme, including the space vectorPWM, is performed by a single TMS 32010 digital signalprocessor that has only 4 k of memory. The total timeavailable to read in the data, execute the software, andoutput the switching state to the inverter is T, =250 ps.The steady-state control scheme (without the transientcomputations) consumes approximately 150 ps. This in-cludes 10 ps, minimum, for A/D conversion. The com-plete control scheme, including transient operation, canbe easily implemented within the 250-ps period. It shouldalso be noted that the actual software has not beenoptimized in any way for speed and that significant im-provements in computing time could be realized by fullyutilizing the high level of pipelining available in the DSP.As stated earlier, the stator flux is calculated usingsimple analog integrator. The line-neutral voltages used

to determine the flux are found from the dc bus voltageand the inverter switching state. The space vector-basedcontroller is very convenient to implement in digital soft-ware since no digital-to-analog converters are required, asis the case with sine-triangle PWM controllers. The exper-imental controller uses a tachometer speed feedback togenerate the torque reference. The speed error is sentthrough a PI controller, which gives the torque reference.

The experimental results are shown in Figs. 7-11. Vari-ous tests have been carried out to characterize the perfor-mance of the proposed control system. First, a speedreference alternating between f300 r/min is applied tothe system. The response of the controller is shown in Fig.7. The bottom trace shows the calculated torque readoutfrom the controller through a D/A converter. It can beseen from the oscillogram that the torque regulation isquite good. In Fig. 8, the stator flux magnitude is depicted.Note the stator flux magnitude remains constant evenwith large changes in the speed (torque). Fig. 9 shows the

Fig. 9. Experimental waveforms. Top trace: estimated synchronousfrequency, 125.6 rad/s/d iv. Bottom trace: mechanical speed, 600r/min/div. Horiz: 500ms/div.

output of the synchronous speed estimator in comparisonwith the actual motor speed. In Fig. 10, the estimatedd-axis flux is shown with a large change in the speed.Finally, Fig. 11shows the stator line current in the steadystate.

CONCLUSIONSThis paper has presented a direct induction machine

torque control method based on predictive, deadbeat con-trol of the torque and flux. By estimating the synchronousspeed and the voltage behind the transient reactance, thechange in torque and flux over the switching period iscalculated. The stator voltage required to cause the torqueand flux to be equal to their respective reference values iscalculated. Space vector PWM is then used to define theinverter switching state. A n alternative approach to dead-beat control was also presented for use in the transient orpulse-dropping mode.

This type of torque control has several advantages.First, the torque and flux are controlled twice per switch-ing period. Therefore, the steady-state delay, which is


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1052 IEEE TRANSACTIONSON INDUSTRY APPLICATIONS, VOL. 28, NO. 5, SEPTEMBER/OCTOBER 1992

Fig. 10. Experimental waveforms. Top trace: estimated d-axis statorflux, 1 V . /div. Bottom trace: mechanical speed, 60 0 r/min/div. Ho rk200 ms/div.

Fig. 11. Experimental waveforms. Top trace: stator line current, 15A/div. Bottom trace: speed reference, 30 0 r/min/div. Horiz: 50 ms/div.

present in any predictive scheme, is only equal to half theswitching period. Second, the space vector PWM resultsin reduced line current ripple in comparison with sine-triangle PWM-based controllers. The direct torque con-trol scheme results in very good performance without therequirement for speed feedback. The estimation of themachine back EMF allows the controller to accuratelypredict the change in torque over the switching period.This type of predictive control scheme is superior toconventional current-regulated PWM torque controlleddrives that are not based on a complete model of themachine, that is, the current is regulated without knowl-edge of the motor parameters. The back EMF estimatorwas shown to operate quite satisfactorily through bothsimulation and experimental results.

The scheme presented in this paper is certainly compu-tationally intensive. However, with present microcom-puter hardware, this control scheme is easily realized insoftware with a 2-kHz switching frequency, which is typi-cal of hard-switched transistor inverters. The experimen-tal results clearly demonstrated the feasibility of such acomputationally intensive control scheme.

APPENDIXMOTORDATAThe characteristics for the machine used in the simula-

Rated output power 15 hpRated voltage 380 VRated current 21.6 AMaximum torquePoles 4Rated speed 1430 r/min3000 r/minax speedStator resistance 0.371 RRotor resistance 0.415 RStator leakage inductance 2.72 mHRotor leakage inductance 3. 3 mHMutual inductance 84.33 mH

tion study and the experimental work is given below.

205 N * m

REFERENCESX. Xu, R. DeDoncker, and D. W. Novotny, A stator flux orientedinduction machine drive, in PESC I988 Conf Rec., pp. 870-876.-, Stator flux orientation control of induction machines in thefield weakening region, in ZEEE-IAS Conf Rec., 1988, pp.437-443.X. Xue, X. Xu, T. G. Habetler, and D. M. Divan, A low coststator flux oriented voltage source variable speed drive, in IEEE-ZASAnn. Mtg. Conf Rec., 1990, pp. 410-415.M. Depenbrock, Direct self control (DSC) of inverter-fed induc-tion machines, IEEE Trans. Power Electron., vol. 3, no. 4, pp.I. Takahashi and T. Noguchi, A new quick-response and high-efficiency control strategy of an induction motor, IEEE Trans.Indus@ Applications, vol. IA-22, no. 5, pp. 820-827, 1986.H. W. van der Broeck, H. C. Skudelny, and G. Stanke, Analysisand realization of a pulse width modulator based on voltage spacevectors, in IEEE-US Conf Rec., 1986, pp. 244-251.T. G. Habetler, A space vector-based rectifier regulator forac/dc/ac converters, in Proc. Euro. Power Electron. Conf., 991.I. Boldea and S. A. Nasar, Torque vector control-A classof fastand robust torque/speed and position digital controllers for elec-tric drives, Elec. Machines Power Syst. J., vol. 15, pp. 135-147,1988.I. Boldea and J. A. Trica, Torque vector controlled (TVC)voltage-fed induction motor drives-Very low speed performancevia sliding mode control, in Proc. Int. Conf Elec. Machines, 1990,

420-429, Oct. 1988.

pp. 1212-1217, pt. 3.

Thomas G. Habetler (S82-M83-S85-M89)received the B.S.E.E. degree in 1981 and theM.S. degree in 1984, both in electrical engheer-ing, from Marquette University, Milwaukee, WI,and the Ph.D. degree from the University ofWisconsin-Madison, in 1989.From 1983-1985, he was employed by theElectro-Motive Division of General Motors as aProject Engineer. While there, he was involvedin the design of switching power supplies andvoltage regulators for locomotive applications.In 1985, he was awarded the General Motors Fellowship to attend theUniversity of Wisconsin-Madison. He is currently an Assistant Professorof Electrical Engineering at the Georgia Institute of Technology. Hisresearch interests are in switching converter technology and electricmachine drives.


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1053ABETLER et al.: DIRECT TORQUE CONTROL OF INDUCTION MACHINES

Dr. Habetler was co-recipient of the 1989 First-Prize Paper Awardand the 1991 Second-Prize Paper Award of the Industrial Drives Com-mittee of the IEE E Indust ry Applications Society. He is chair of theMembership and Publicity Committee of the IEEE Power ElectronicsSociety and is a member of the IEEE-IAS Industrial Power Converterand Industrial Drives Committees.

Francesco Profumo (SM90) was bom in Savona,Italy, in 1953. He received the laurea (withhonors) in electrical engineering from thePolitecnico di Torino, Italy, in 1977.From 1978 to 1984, he worked as a Researchand Development Senior Engineer for theAnsaldo Group, Genoa, Italy. He then joinedthe Department of Electrical Engineering of thePolitecnico di Torho,where he is now an Asso-ciate Professor of electrical drives. He was Visit-ing Professor in the Department of Electrica land Computer Engineering of the University of Wisconsin-Madison,from 1986 to 1988. His fields of interes t are power electronics conver-sion, integrated electronic/eletromechanial design, high response speedservo drives, and applications of new power devices. He published morethan 60papers in technical joumals and conference proceedings.Dr. Profumo is the secretary of the IEEE-PELS/IES Italian Chapter,and he was the Secretariat of the EPEP1 Conference held in Florence ,Italy, in September 1991. He is a Registered Professional Engineer inItaly.

Mr. Pastorelli is a R

Michele Pastorelli was born in Novara, Italy, in1962. He received the degree in electrical engi-neering from the Politecnico di Torino, Italy, in1987.He joined the Department of Electrical Engi-neeringof the Politecnico di Torh o in 1988. Heis working towards the Ph.D. degree in electricalengineering, and his fields of interest are powerelectronics and high-performance servo drives.He has published more than 10 papers in tech-nical joumals and conference proceedings.egistered Professional Engineer in Italy.

LeonM. olbert(S88-M91) received the B.E.E.and the M.S. degrees in electrical engineeringfrom the Georgia Institute of Technology, At-lanta, in 1989 and 1991, respectively.He is currently employed by Martin MariettaEnergy Systems at the Oak Ridge National Lab-oratory in Tennessee. His interests include con-trol of electri c machines and power electronicsapplications.

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Habetler Et Al