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Speed Regulation of an InductionMotor Using Model Reference
Adaptive ControlAkira Kumamoto, Satoshi Tada, and Yoshihisa Hirane
ABSTRACT: A novel approach of con-structing a robust variable-speed drive sys-tem using an induction motor supplied froma voltage-source-type PWM inverter is dis-cussed. The inverter is controlledso as togenerate the fabricated terminal voltagesbased on the voltage-decoupled transvectorcontrol theory where neither a current feed-back lo op n or a current lim iter circuit is re-quired. Although the hardware for this de-coupling method becomes simplified, it stillhas omedisadvantages, uch as the dis-crepancy between the command currents andactual currents. Incorporated into the drivesystem described herein is the optimal-speedregulator adopting the exact model-matchingmethod, which fulfills the function of a com-pensator for unfavorable errors.The oper-ating characteristics of the proposed drivesystem are compared with conventional PIcontrol to verify the effectiveness under var-ious conditions by investigating the transientresponses for the step change of the speedcommand, the load torque, andso forth.
IntroductionRecent advances in power electronics
technology have made various variable-speeddrive systems available in the last decade.Among the newly developed methods, themost outstanding scheme is the variable-speed induction motor drive based on trans-vector control theory [1]-[3]. It achieves fastspeed response using an economical induc-tion motor. Although an almost linear trans-fer function is obtained by introducing vectorcontrol 121, [3], there are still some uncertainfactors that disturb the ideal linearization.
While transvector control is usually im-plemented with a primary current control,thus far some authors have presented an ap-plied-voltage control method for an induc-tion motor drive [3]-[6], which is the naturalextension o f a current control in the sensethat the direct output of the frequently uti-
Presented at the International Conference on In-dustrial Electronics,Control, and Instrumenta-tion, San Francisco.C A , November 18-22. 1985.A k i n Kumamoto,Satoshi Tada and YoshihkaHirane are with the Faculty of Engineering,Kan-saiUniversity. 564 Yamatecho 3-3-35, Suita,
Osaka, Japan.
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lized PWM inverter is the motor terminalvoltage. The voltage-decoupled transvectorcontrol method described in [4] eliminatesany current feedback and/or sensing. sincemotor leakage inductances are usually ofsmall value. The resulting circuit construc-tion, therefore, becomes simplified.
This elimination of a current control loopis based on the fact that both actual torqueand flux current components follow the cor-responding current commands in the orderof the motor time constant. In an actual sit-
uation, however, the flux current componentmay be varied to realize field control. In suchacase, the discrepancy between the com-mand and actual currents suggests the ne-cessity of some additional strategy to assurestable operation of the inverter.
This paper proposes the utilizationof anoptimal-speed regulator [7] designed bymodel reference adaptive control (MRAC)theory [8].The resulting system exhibitsgood performance characteristics by adop-tion of the exact model-matching method.together with maintaining a simplified circuit
construction of voltage decoupling, whichuses only a speed loop.
Voltage-Decoupled TransvectorControl
Control Principle 141. [j]
The electrical and mechanical instanta-neous characteristics of an induction motoron the cr-p axis. rotating synchronously withthe source angular frequencyw , ~ , re givenby Eqs. 1)- 4).
where
In an ordinary current-controlled transvec-tor system. Eqs. ( 5 ) and 6) are used to can-cel the mutual interference of current andflux level in the generated torque.
Contrary to the current-controlled type, thevoltage-decoupling method requires two ad-ditional equations, which are necessary toeliminate the cross term in the input level:
The result is a linearized firs-order model,shown in Fig. 1 which assumes a constant-
flux current i l Q .Simulation Exarnple
The voltage-decoupled vector controlmethod describedso far utilizes only a speedloop. The automatic speed controller (ASR)computes the necessary current commands,
and is, nd then transforms these valuesinto the applied voltage values consideringmotor parameters using Eqs. 7) and 8). Inorder to investigate the effect of the expectedcurrent discrepancy. which is unavoidablebecause of neglecting the leakage induc-
tances, a closed-loop ASR incorporating an
ref
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Optimal-Speed Regulator Design
Exact Model-Matching 181
The exact m odel-matching method assuresthat the closed-loop transfer function coin-cides with that of the reference mod el. Thecontrolled plant f s) and the model t d b ) aredenoted as shown. where P ( s ) , r ( s ) , p d ( s ) ,
and rd(s) are monic polynomials of ordern ,m , nd. and md. respectively, with (n, nd)n m).
[ ( S I ~ ( s ) / r c ( s ) g r ( s )P - ' ( s ) (9)
f, s) y s ) / u s ) gdrd(b)Pdi(s) 10)
Figure 4 illustrates the block diagram ofthe exact model-matching control system ob -tained by introducing the input dynamics ofriN s) s shown. where P * ( s ) and r*(s ) arearbitrary stable monic polynom ials of ordern and m.
The control law is given by
~ s ) gkds) ~ s )+ h d s ) ~ s ) )
y s) r * ( s ) g + g,V s)/g (11)where kh(s)and hb s) satisfy the relation
T
Fig. 1. Ideal first-order model of induction motor.
TableMotor Parameters and Control Gains
r~ _ _ _ _ _ _
1 k W, 100 V , 8.4 A , 60 H z , 4 poles, 1710 rpm
Primary resistanceSecondary resistancePrimary self-inductanceSecondary self-inductanceMutual inductanceTotal inertiaViscous-friction coefficientRated w ax is primary
Rated P-axis primarycurrent
current
Proportional gainIntegral gain
0.49 Q0.45 12
38.8 mH35.4 mH35.1 mH
0.024 Nm-sec lrad0.001 1 Nm-seclrad
6.83 A
11.54 A
0.011 o
appropriate PI control is established for the o o o ttest motor, with the constants listed in thetable.
In thecase where voltage decoupling isapplied, actual currents exhibit a slight ex-
cursion from the respective commands.asshown in Fig. 2 . which assumes the contin-uous inverter output voltage. The fluctuationof actual cuvents around command currentsin this case doesnot cause serious problems,and the speed response is almost the sameas that of the ideal case.
The transient responses for a higher speeddrive over the base speedof 1710 rpm sshown in Fig. 3. The field current commandiri is decreased as an inverse proportion tothe actual motor speed of w , over the basespeed. Note that comparatively large over-
shoot and undershoot can be seen in the ac-tual current levelat the beginningof the tran-sient. This means that stable operation of aninverter may be disturbed because of the re-quirement to protect the switching devices.Therefore, some type of proper protectionscheme, f or example, a current-limiting cir-cuit, is required fof safeguarding, which re-sults in a complexity of system construction.
The voltage-decoupling m ethod is an ex-cellent control principle but it still has somedisadvantages, as we have seen thus far.Iathe ollowing , the application of an exact
model-matching method based onthe mod-e m control theory of MRAC is studied.
_ - -
00]
3 0a 1 5
.I 1 s-30
0 0 5 1 0 1.5t, sec
Fig. 2 . Step response for base-speed comm and assuming continuousinverter output (PI control).
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-10
3 01 50
- 1 5- 3 0
r e f
l0 . 2 0 . 4 0 . 6 0 . 8
t , sec
Fig. 3 . Step response for high-speed command. with field controlassuming continuous inverter output (PI control).
Fig. 4. Block diagram of exact model-matching.
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The unknow n parametersg and 0 in Eq. (17)depend upon the varying controlled plant andare to be adjusted by the adaptive law. Theadaptive errore(t) , defined by y ( r ) yln(t)?is given by
e(r) l / P * ( P ) g r * ( P )~ t )
er r* (P) - ,(t) 18)
The basic strategy of adaptation is toin-troduce an error dynamics identifier, who seoutput c r)is calculated similar toEq. (17)except that g and 0 are replaced with theirestimates g ( t ) and &t). It is guaranteed thatan appropriate adaptive law, which realizest?(t) &), also assures e ( t ) 0.
ImplemmtingMotor Control [7]
The indu ction motor s transfer function isdirectly written from the block diagram ofFig. 1 to give
rlM S) (s)/i;e;(s)
pM'i , , / (L,J(s D / J ) ) (19)
The reference modelrIMD(S) is a closed-looptransfer function obtained by optimal regu-lator theory, and is given by
rIMD s) Wnz(s)/ '(s)
g d / ( s2 Pdls + PdO) (20)Considering the order oftiM s) nd f IM D s ) ,
the parameters to b e estimated here are thetwo scalarsg(t) and /io(?). Th e adaptive con-trol system is constructed using the straight-forward process described previously, bychoosing arbitrary polynomials as
P*(s ) s + P,r*(s) 1 , y(s) 1 (21)
Figure 5 show s the final drive system in-corporating an optimal adaptive-speed reg-ulator.
Simulation Results of Drive System
A digital simulation program to investigate
the dynamic behavior of the resulting closed-loop control system using an optimal-speedregulator is given. A voltage-source-typePWM operation of an nverter s adoptedhereafter. Illustrated in Fig.6 is the step re-sponse from standstill to the ratedspeed atthe no-load condition.
In the early stage of speed build-up, actualmotor speed w , does not coincide with thereference speed w, because of the software-limited acceleration torque. However, wsoon follows the reference speed and the at-isfactory transient characteristics are ob-tained. In the case of the conventional PI
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UJ:,0 4-knput
Fig. 5. Proposed variable-speed drive system of induction motor incorporating MRAC.
30
10
.p 0- lo
30
.> 15-30
a 2
0 0 . 5 1.0 1.5t , sec
Fig. 6. Step response for base speed of proposed system at theno-load condition.
controller, a sudden increase in load torquewill cause an impact drop in the m otor speed.The applied load torque is sensed as a dropof the speed, but s done via the filteringeffect of motor inertia. Therefore, speedcompensation for load torque change is un-avoidable to some amount of time delay.Thus, it is a commonly accepted method to
equip anadditional torque compensatoror tomake a compromise between the responsesfor speed command and load torque varia-tion. On the contrary, a moderate responseis obtained in the proposed system, as shownin Fig. 7 . which indicates the smooth returnto the speed reference even in the case of theapplication of the full-load torque from theno-load condition.
Another factor to be considered when de-signing the control system is the variation ofmotor parameters. Increasing R? up to 2.0times from the initial value as a ramp fun c-
tion of time during 1.5 sec revealed that thedrop of the motor speed is limited within a
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small range and the robustness of the systemhas been recognized. In the high-speedop-eration over the base peed, he MRACmethod exhibits a satisfactory transient re-sponse. The reference model outputo rad-ually increases according t o the second-orderproperty. This avoids the sudden change ofi necessary fo r acceleration. T herefore, thevariation of the current commands becomesmoderate, resulting in a slight discrepancybetween the actual and command currents.
Conclusion
A newly proposed variable-speed drivesystem utilizing an optimal-speed regulatorbased on the exact model-matching methodis described. The system is investigated un-der various conditions, and is recognized tohave satisfactory operating characteristics,especially for the load torque change. pa-rameter variation. and a wide speed range
operation. Th e design process of the controlloop is simple enough and the w ell-designedC A D program can be utilized, which eman-cipates the designer from troublesome rep-etition of control parameter tuning.
The application of modem control theoryto power electronics technology is becomingan unavoidable process to attain a high-qual-ity control system, and is studied extensivelyto improve the conventional control meth-ods. Described herein is the trial to realizethe robust and simplified controller for aninduction motor drive. and almost all of the
necessary calculations maybe realized byintroducing a high-speed microprocessor inan actual system.
References
[ I ] F. Blaschke. The Principle of Field Ori-entation as Applied to the New TransvectorClosed-Loop Control System for RotatingField Machines. Siemens Review,vol. 31,pp. 217-220, 1972.
[2] A . Nabae and R. Kurosawa, A New ln-duction Motor Drive System Having a Con-stant Torque ransfer unction, Trans.
[3] S. Sugimo to and E. Ohno. A New Induc-tion Motor Drive System Having a LinearTransfer Function, Trans. IEW. vol. 103B,pp. 31-38, 1 983.
[4] K. Ohnishi. H. Suzuki. and K. Miyachi.Decoupling Control of Secondary Flux andSecondary Current in Induction Motor Drivewith a Controlled Voltage Source and ItsComparison with VoltlHertz Control,ConRec. of IEEEIIAS. pp. 678-685. 1982.
IS] M erashima, M omura, T. Ashikaga, T.Nakamura. and K. Ohnishi, Fully DigitalControlled Decoupled Control System in In-duction Motor Drive, Cot Rec. ofICOX84,pp. 845-850, 1984.
[6] B. K. Bose, Scalar Decoupled ControlofInduction Motor. E E E Trans. on Indrrs-trial Application s.vol. 1A-20. pp. 216-225,1984.
[7] S . Tada, A. Kumamoto. andY . Hirane, An
Optimal Drive System of a Vector-Con-trolled Induction Motor Using Exact ModelMatching, Preprint of IEET (Institute ofElectrical Engineers of Japan ), SPC-85-49,1985.
[SI K. Ichikawa, Construction of AdaptiveControl System Based on an Exact ModelMatching Technique, Trans. SICE. vol. 20,
I E W. VOI 98B, pp. 303-309, 1978.
pp. 926-931.. 19 M .
Akiraumamoto re-ceived the.S.E.E..M.S.E.E., and Ph.D. de-grees in 1968. 1971, and1983. respectively, fromKyoto University. Kyoto.Japan. Since 1971. he hasbeen engaged in rescarchand development in powerelectronics at Kansai Uni-versity. Osaka, Japan. Hiscurrent interest is in theapplication of control the-
ory to pow er electronics and intelligent flexibleautomation. He is also interested in knowledge-based engineering. Dr. Kumamoto is currentlywith the Information ProcessingBranch, Facultyof Engineering. Kansai University.
Satoshi Tadareceived the
I was in digital-controlledinduction motor drivesystem research applyingmodel reference adaptivecontrol theory. He hasbeen with Nissin ElectricCo., Ltd., Kyoto, Japan,
since April 1986. His current interest is in the
application of modem control theory to electricaland mechanical power control systems.
Yoshihisa Hiranegradu-ated from Hosei Univer-sity in 1956 and receivedthe M.S.E.E. and Ph.D.degrees in 1959 and 1974,respectively, both fromthe University of OsakaPrefecture, Osaka, Japan.In 1959. he joined KansaiUniversity where he hasbeen working in the fieldof power electronics as aProfessor in the Depart-
ment of Electrical Engineering. He workedonsabbatical leave at the University of Bradford, E n-gland. from 1976 to 1977. as an Hono rary VisitingResearch Fellow on thyristor control of electricalmachines. He is currently interested in magneticcircuit application of power electronics.
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