Optimal design of the shifted switching planes for VSC of a third-order system

Abstract

In this paper, a new sliding mode control algorithm for a third-order uncertain, non-linear and time-varying dynamic system subject to unknown disturbance and input constraint is proposed. The algorithm employs a time-varying switching plane. At the initial time tt0, the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the plane moves with a constant velocity to the origin of the space. Two methods of switching plane parameter selection are presented. The first one ensures the minimization of the integral of the absolute error (IAE) over the whole period of the control action and the second one minimizes the integral of the time multiplied by the absolute error (ITAE). In both cases the input constraint is satisfied. The switching plane is chosen in such a way that the reaching phase is eliminated, insensitivity of the system to the external disturbance and the model uncertainty is guaranteed from the very beginning of the proposed control action and fast, monotonic error convergence to zero is achieved.