Integral higher order sliding mode control for MIMO uncertain systems: Application to chaotic PMSM

This paper presents an integral high order sliding mode controller for a class of multi-input, multi-output nonlinear uncertain system. After transforming the system into high order input-output dynamic system, the idea is to define an integral sliding surface based on a nominal control law designed to stabilize in finite time the unperturbed system. By imposing some conditions on the controller parameter, the proposed method aims to stabilize the system although the presence of bounded uncertainties. In order to reduce the chattering caused by the discontinuous sign function in the controller, we replace this function by an hyperbolic tangent trigonometric function which is smooth and continuous. Stability of the proposed controller is proved based on Lyapunov approach. An illustrative example of perturbed chaotic permanent magnet synchronous motor demonstrates the effectiveness of this controller.