Controller design of multivariable variable structure systems with nonlinear switching surface

Abstract

The variable structure systems are a special class of nonlinear systems characterized by a discontinuous control action which changes the structure upon reaching a set of switching surfaces. If a system is forced to constraint its evolution on the predetermined switching surfaces, it results in a dynamical behaviour that is largely determined by the design parameters and equations defining the switching surfaces. Consequently, new properties which are not present in the original system can be obtained for the controlled motions. Therefore the system is robust and insensitive to the disturbances and parameter variations. A sliding mode control for the multivariable systems in the presence of disturbances and parameter variations is considered. In the previous sliding mode control, the switching surfaces ar linear functions and therefore the speed of response is relatively slow. To overcome this problem, a new method using nonlinear switching surfaces with multiple polynomials is proposed to improve the speed of response and the good transient response can be obtained. Simulation results are presented and show the advantage of the proposed nonlinear switching surfaces.