Design of sliding mode control of nonlinear system based on Takagi-Sugeno fuzzy model

In this paper, a sliding mode control algorithm based on Takagi-Sugeno (T-S) fuzzy model for a class of nonlinear systems is discussed. For a complex physical system represented by an aggregated fuzzy global model which compromises a set of linear models, conditions for the fuzzy sliding mode control to stabilize the global fuzzy model are given. Firstly, we choose the sliding surface which gives a good behaviour during sliding mode. It is formulated as an assignment of the poles of uncertain nonlinear system in a convex optimization area. Secondly, we design a nonlinear control law leading the state trajectory on the sliding surface in a finite time. A numerical application of a flexible joint manipulator is given to validate the theoretical results of our approach.