Design and implementation of fuzzy sliding mode controllers for generalized projective synchronization of chaos horizontal platform systems

This paper presents robust chattering-free fuzzy sliding mode control (FSMC) as a way to achieve generalized projective synchronization (GPS) of two horizontal chaos platform vibration systems with system uncertainty and external disturbance. An appropriate sliding surface is acquired through an SMC design such that the error state trajectories of a master–slave system will reach such a sliding surface and approaches to the origin. Based on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. As a consequence, the system is simulated and experimented to demonstrate that the error state tends to be stabilized and the chattering problem can be thus resolved, implying that the slave horizontal platform system (HPS) is GPS with the master HPS.