A new fuzzy sliding mode control scheme

In this paper, a new fuzzy sliding mode control scheme is proposed for second-order linear time-varying 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-wise. 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 second-order system