Existence of limit cycle and stabilization of induction motor via new nonlinear state observer

In this paper the boundedness of the solutious 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 limit cycle. Utilizing these results a new bilinear and nonlinear reduced-order state observer, which is globally asymptotically stable, is constructed to estimate the unmeasurable 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.