EXISTENCE OF LIMIT-CYCLE AND STABILIZATION OF INDUCTION-MOTOR VIA NEW NON-LINEAR STATE OBSERVER

In this paper the boundedness of the solutions of the bilinear and nonlinear differential equations, which describe the dynamic behavior of an ideal three-phase squirrel cage induction motor, is shown using a Lyapunov function. It is then proved by sampling combined with a digital simulation that an unstable machine has a limit cycle. Utilizing these results a new bilinear and nonlinear reduced-order state observer, which is globally asymptotically stable, is constructed to estimate the immeasurable state variables. By using this observer a new two-step procedure for stabilizing an unstable machine, which has a limit cycle, is proposed. This scheme can be easily implemented resulting in an asymptotically stable overall system. These results are numerically verified by simulation. Copyright © 1979 by The Institute of Electrical and Electronics Engineers, Inc.