Pii: 0005-1098(96)00070-2

Field orientation, in one of its many forms, is an established control method for high dynamic performance AC drives. In particular, for induction motors, indirect fieldoriented control is a simple and highly reliable scheme which has become the de facto industry standard. In spite of its widespread popularity no rigorous stability proof for this controller was available in the literature. In a recent paper (Ortega et al., 1995) [Ortega, R., D. Taoutaou, R. Rabinovici and J. P Vilain (1995). On field oriented and passivity-based control of induction motors: downward compatibility. In Proc. IFAC NOLCOS Cont. Tahoe City, CA.] we have shown that, in speed regulation tasks with constant load torque and current-fed machines, indirect field-oriented control is globally asymptotically stable provided the motor rotor resistance is exactly known. It is well known that this parameter is subject to significant changes during the machine operation, hence the question of the robustness of this stability result remained to be established. In this paper we provide some answers to this question. First, we use basic input-output theory to derive sufficient conditions on the motor and controller parameters for global boundedness of all solutions. Then, we give necessary and sufficient conditions for the uniqueness of the equilibrium point of the (nonlinear) closed loop, which interestingly enough allows for a 200% error in the rotor resistance estimate. Finally, we give conditions on the motor and controller parameters, and the speed and rotor flux norm reference values that insure (global or local) asymptotic stability or instability of the equilibrium. This analysis is based on a nonlinear change of coordinates and classical Lyapunov stability theory. Copyright 01996 Elsevier Science Ltd. Received 14 February 1995; revised 7 February 1996; received in final form 23 March 1996. This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Darren Dawson under the direction of Editor Yaman Arkun. Corresponding author Dr Paul A. S. de Wit. Tel. +31 53 489 2520; Fax +31 53 489 3631; E-mail [email protected]. t Faculty of Mechanical Engineering, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands. * URA C.N.R.S., Universitt de Technologie de Compiegne, 817, BP 649, 60206 Compiegne, France ([email protected]). g Department of Systems Engineering, Australian National University, Canberra, ACT 0200, Australia. 1. PROBLEM FORMULATION In this paper we carry out the stability analysis of an indirect field oriented controller (FOC) that regulates the velocity and the rotor flux norm of a current-fed induction motor in the presence of an unknown constant load torque and rotor resistance uncertainty. For further details and motivation of induction motors and FOC the reader is refered to Bose (1986), Leonhard (1985), in the electrical machines literature, and to Bodson et al. (1994) Ortega et al. (1995), Taylor (1994) in the control journals. The dynamic model of the current-fed induction motor in its simplest formulation expresses the rotor flux and the stator currents in a reference frame rotating at the rotor angular speed. * 1 Lnl i:=--_X+ z r y-u = -Rrx+ R,u, (1) jJ = +(T TL) = T TL, (2) T= uTL,,,Jx= u'Jx, (3)