ITAE optimal switching plane design for VSC of continuous-time third order systems with state constraints

In this paper the design of a time-varying switching plane for the sliding mode control of the third order system subject to velocity and acceleration constraints is presented. Initially, the introduced plane passes through the system representative point in the error state space and then it moves with a constant velocity and a constant angle of inclination to the origin of the space. Having reached the origin the plane stops moving and remains fixed. The plane parameters (determining angles of inclination and the velocity of its motion) are selected to ensure the minimum integral of the time multiplied by the absolute error (ITAE) without violating velocity and acceleration constraints simultaneously. The switching plane is chosen in such a way that the reaching phase is eliminated, insensitivity of the system with reference to the external disturbances and the model uncertainty is guaranteed from the very beginning of the proposed control action. Furthermore, fast and monotonic error convergence to zero is achieved.