Elimination of limit cycle in unexcited Van der Pol system using fuzzy supported state space controllers

In this paper elimination of limit cycle in an unexcited Van der Pol system is done by stabilizing it asymptotically about the origin in a global sense. Fuzzy supported pole placement and linear quadratic regulator control is designed and verified to eliminate the limit cycle with a significantly smaller magnitude of the controller instantaneous input effort thus minimizing the actuator saturation phenomena in real world. A linearized state space model of an unexcited Van der Pol equation about the origin is employed to develop the state space controller design. Further a new fuzzy proportional rule-base based on Mamdani inference is constructed to support the state space controllers in order to eliminate the limit cycle with the least control effort required to stabilize the system. A comparative performance analysis of the fuzzy-supported state space controllers with its non-fuzzy counterparts is presented. The performance parameters are the magnitude of the instantaneous input controller effort and the settling time required to stabilize asymptotically about the origin in a global sense.