Indirect field oriented control of induction motors is robustly globally stable

For induction motors indirect field oriented control is a simple and highly reliable scheme which has become an industry standard. We have previously 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 give necessary and sufficient conditions for uniqueness of the equilibrium point of the (nonlinear) closed loop, which interestingly enough allow for a 200% error in the rotor resistance estimate. Then, we give conditions on the motor and controller parameters, and the speed and rotor flux norm reference values that insure either global boundedness of all solutions, or (global or local) asymptotic stability or instability of the equilibrium. The analysis is carried out using classical Lyapunov stability theory and some basic input-output theory