IEEE TRANSACTIONS ON POWER ELECTRONICS VOL. PE-2, NO. 1, JANUARY 1987 55 Instantaneous Torque Control of Electric Motor Drives MARIJA ILIC-SPONG, SENIOR MEMBER, IEEE, TIMOTHY J. E. MILLER, SENIOR MEMBER, IEEE, STEPHEN R. MACMINN, MEMBER, IEEE, AND JAMES S. THORP, SENIOR MEMBER, IEEE Abstract-In the control of adjustable speed drives, the performance mutator motors and ac sine-wave motors because the in- of inexpensive digital integrated circuits is approaching the stage where stantaneous torque is ideally constant in the steady state traditional control algorithms may be displaced by new algorithms that and is therefore indistinguishable from the average better exploit their speed and the functional capabilities of their soft- . ware. The concept of "instantaneous torque control" is introduced as torque However, there is now a great increase in the use an objective worth pursuing in the application of such digital IC's to of drives based on motors that do not have constant in- drive systems. Instantaneous torque control would in principle permit stantaneous torque: for example, ac motors fed with the fastest possible response and the elimination of torque ripple, along square-wave current or voltages; brushless dc motors with with many other advantages not possible with conventional control al- square-wave excitation; stepper motors; and many single- gorithms, most of which are set up to control a time-averaged torque. . v Some of the fundamental principles of instantaneous torque control are phase ac motors with some form of electronic speed con- developed for the switched reluctance motor, which is used as an ex- trol. ample because, like the brushless dc permanent-magnet motor with This suggests the possibility of controlling the instan- concentrated windings, it has the potential for rapid response, but it taneous currents or flux linkages in such a way as to pro- can have appreciable torque ripple with unfavorable firing angles. A duce constant instantaneous torque. In this paper the pos- reference frame transformation that would eliminate the rotor position from the voltage and torque equations is not known for either of these sibility for such instantaneous torque control is machines. This opens up a number of interesting questions as to the explored for a switched reluctance (SR) motor, which is generality of instantaneous torque control algorithms, and whether they a conventional variable-reluctance stepper motor pro- can be incorporated into the general or unified theory of electrical ma- vided with a shaft position transducer. The SR motor is chines. chosen because of the relative simplicity of the elemen- tary theory describing torque production in the absence of INTRODUCTION magnetic saturation and mutual coupling between phases. r HE SPEED and functionality of digital integrated cir- It is known to be susceptible to torque ripple if the firing I cuits now suggests the development and evaluation of angles are unfavorable. new algorithms for the control of adjustable speed drives. The control of torque in dc commutator motors is based This paper introduces the concept of "instantaneous on the classical theory in which torque is proportional to torque control" as an objective worth pursuing in the ap- the vector product of armature current and flux. Under plication of such IC's to drive systems. Instantaneous sufficiently light load the commutator maintains the spa- torque control would, in principle, provide the fastest tial orthogonality of these quantities so that the vector possible response and would permit the elimination of product becomes a scalar product. Since both the flux and torque ripple along with a wide range of instabilities and the current are normally constant, the instantaneous torque even shaft resonances, by software techniques alone. It is is also constant. There is ideally no torque ripple, and the even conceivable that some of these features could be torque is varied by changing the current or the flux or automatic. both. In sine-wave ac machines the situation is similar. In most ac and dc drives the control algorithms are set The actual phase currents and flux linkages are not con- up to control a time-averaged torque rather than the in- stant but can be made to appear constant by means of a spta contaneous toq. tiseapproach works well for dc co- reference-frame transformation that has appropriately been called the commutator transformation; (an example Manuscript received September 27, 1985; revised May 5, 1986. This is Park's transformation). The instantaneous torque of an paper was presented at the Power Electronics Specialists Conference, Tou- ideal sine-wave ac machine is constant and is proportional louse, France, June 24-28, 1985, under the title, "Nonlinear Torque Con- to the vector product of current and flux linkages in the trol of Electric Motor Drives." M. Ilic-Spong is with rthe Department of Electrical and Computer En- transformed reference frame. The transformation unifies gineering, University of Illinois at Urbana-Champaign, 1406 West Green the theory of the dc and ac systems for dc and ac drives Street, Urbana, IL 61801, USA. that have closely similar structures when viewed from the T. J. E. Miller is with the General Electric Company, P.O. Box 43, aporteefenerm.Thspicplsreutno Room 380, Building 37, Schenectady, NY 12301, USA. aporaerfrnefae hs rnllsaept1t S. R. MacMinn is with the General Electric Company, Corporate Re- practice in the so-called "vector control" of ac motor search and Development, 1 River Road, Schenectady, NY 12345, USA. drives. J. S. Thorp is with the School of Electrical Engineering, Cornell Uni- Sic th SR moo.sdul aiet ti adrt versity, Ithaca, NY 14853, USA. ncthSRmtr1dobysle, Shaero IEEE Log Number 8609966. construct a reference frame transformation that will elim- 0885-8993/87/0100-0055$ 1.00 ©C 1987 IEEE