Self-Sustaining Oscillations With an Internal Two-Fuzzy Inference System Based on the Poincaré-Bendixson Method

The generation of self-sustaining oscillations at the output of nonlinear systems without tracking a reference signal is under investigation. In this study, we proposed an internal double fuzzy inference system to generate an asymptotically stable limit cycle or self-oscillations for the second-order systems. The fuzzy system has been synthesized by invoking the Poincaré-Bendixson theorem, which states sufficient and necessary conditions of existence of an attracting periodic orbit at the output of the closed-loop system. This theorem was also used for design; that is, we set the tuning rules of the fuzzy controller. The effectiveness of the proposed controller is corroborated by numerical simulations and experiments made in a single-link pendulum system.