Sliding Mode Control Scheme

Absrrucr In this paper, a new fuzzy sliding mode control scheme is proposed for second-order linear timevarying systems in order to obtain faster error convergence and desired error dynamics. It is well known that a second-order linear time-varying system can be used to model higher order linear time invariant systems piece-wisely. Therefore, it is necessary to do deep investigation for the stability and robustness analysis and the design of advanced tracking controllers for second-order linear time-varying systems. It is shown that the design of sliding mode control system is divided into two steps. A linear sliding mode controller is designed first to speed up the error convergence when the error is greater than one. A terminal sliding mode controller is then designed to guarantee that the error can converge to zero in a finite time when the error is around the system origin. In order to have a smooth switching from the linear sliding mode control to the terminal sliding mode control, a fuzzy logic technique.is used to connect two sliding mode surfaces. The stability of the proposed fuzzy sliding mode controller is analyzed, and the convergence and robustness properties are demonstrated in a simulation example with a secondorder system.