Generalized Projective Chaos Synchronization of Rotational Simple Pendulum Subjected to External Disturbance Using Fuzzy Sliding Mode Control

In this paper a robust control scheme is proposed for the generalized projective chaos synchronization between two identical rotational simple pendulum (RSP) systems subjected to external disturbance. By the Lyapunov stability theory with control terms, a suitable sliding surface is proposed to ensure the stability of the controlled closed-loop system in sliding mode. When the bound of external disturbance is unknown, a fuzzy logic tuning controller (FLC) is introduced into a sliding mode controller (SMC) so that a sliding mode controller is adjusted by FLC in response to any change in the input signal according to linguistic rules, then the SMC scheme is turned into the fuzzy sliding mode controller (FSMC) scheme. This method not only can approximately estimate the bound of external disturbance and allows us to arbitrarily direct the parameters α and β onto any desired values for different generalized projective chaos synchronizations, but also can resist the external disturbance and weaken the chatter phenomena in slave system. The results of numerical simulation are proved to show the effectiveness of the proposed methods.