Proceedings of the American Control Conference San Diego, California June 1999 A Simple Robust Control for Induction Motors zy Gerardo Guerrero-Ramirez and Yu Tang National University of Mexico DEPFI-UNAM, P.O. Box 70-256, 04510 Mexico D.F., Mexico e-mail zyxwvu : gerardo@control. fi-p .unam.mx tang@servidor .unam. mx fax: (525)6161073, tel: (525)6223013 Abstract This paper presents a simple robust control for induc- tion motors. The control is robust to uncertainties in the rotor and stator winding resistances, and a bounded load torque perturbation. In the proposed scheme, zyxwvu as- suming that a nominal control law, designed with the knowledge of the plant parameters, ensures the expe nential stability of the closed-loop system in the a b sence of parameter uncertainty, we use the Lyapunov redesign technique to design an additional feedback sig- nal that is added to the control signal to guarantee the uniform ultimate stability in the presence of uncertain- ties. Simulation results are included to illustrate the performance of the control scheme. Key words: Robust control, Lyapunov redesign, pas- sivity, induction motor. 1 Introduction Induction motors are widely used in industrial ap- plications that require high power constant speeds. An induction motor is simple in operation, rugged, maintenance-free and generally less expensive than other machines. However, its model is complicated due to its inherent nonlinear dynamics and not all states are measurable for feedback control. These effects make in- duction motors more difficult to control than DC me tors. In recent years, thanks to the advances in power electronics and microprocessor technology, induction motors have found applications in precision electrome- chanical systems. In particular, many control strate- gies have been proposed for induction motor drives to achieve better dynamic performance and induction mo- tors have been gradually replacing the DC motors. Among these control strategies, the field oriented con- trol [I] [SI is widely used in industry applications, which involves the transformation of electrical variables into the zyxwvutsrqp dq frame rotating with the rotor flux vector and a nonlinear feedback. Provided that the rotor flux is not identically zero, and the desired rotor flux amplitude is constant, an asymptotic linearization and decoupling are obtained. The input-output linearization control [9] [2] achieves exact linearization and decoupling be- tween the flux and speed dynamics. In this approach, a nonlinear transformation is performed on the state variables, such that in the new coordinates the speed and rotor flux magnitude are decoupled by feedback ( see also [13] ). The backstepping design [6], based on integrator backstepping and nonlinear damping, results in a not globally defined controller [13]. The passivity-based design [lo] [4] on the other hand, incorporates at a fundamental level the system physical structure and thus avoids the cancelation of the nonlin- ear terms as required in the (asymptotical and exact) input-output linearization approach . It was extended to torque regulation of the induction motor, and a glob- ally defined and stable controller was found, but exact model knowledge zyxw was assumed. In this paper, following the passivity-based approach developed in [5], [ll], and assuming that a nominal control law, designed with the knowledge of the plant parameters, ensures the exponential stability of the claed-loop system in the absence of parameter uncer- tainty, we use the Lyapunov redesign technique [7] to design an additional feedback signal that is added to the control signal to guarantee the uniform ultimate stability in the presence of uncertainties . The rest of the paper is organized as follows. After the problem statement in Section 2, the controller design is given in Section 3. Section 4 illustrates the perfor- mance of the proposed controller by means of simula- tion. The paper ends up with the concluding remarks in Section 5. 2 Problem Statement We consider a standard single pole pair, 34 induction motor represented in the zyxw CY@ model [5], with the ba- sic assumption about the linear relationship between fluxes and currents. Both electrical and mechanical 0-7803-4990-6/99$10.00 zyxwvut 0 1999 AACC 936