Sliding mode control with ellipsoidal sliding surface

This paper introduces sliding mode control with ellipsoidal sliding surface which have the characteristic of finite convergence time to the equilibrium point from any initial condition. The proposed method is more robust than conventional method because it has no reaching phase. It converge to the equilibrium point faster than conventional method. The conventional linear sliding surface can not guarantee finite convergence time, but our method can derive finite convergence time analytically. Since, the proposed ellipsoidal sliding surface is smooth function without cusp, chattering was reduced. To verify the advantages of the proposed method, we compared with the proposed ellipsoidal sliding surface and the conventional linear sliding surface by simulation for a simple second order uncertain dynamic system.