ITAE optimal transient performance in SMC of third order systems with state and input constraints

This paper presents a time-varying switching plane design method for the sliding mode control of the third order system subject to velocity, acceleration and input signal constraints. Initially, the switching plane passes through the system representative point in the error state space and then, it moves with a constant velocity to the origin of the space. Having reached the origin the plane stops moving and remains fixed. Parameters of the plane are selected to minimize the integral of the time multiplied by the absolute error (ITAE) without violating velocity, acceleration and input signal constraints. Firstly, the ITAE is minimized subject to each of the three constraints separately and next, the minimization task is solved when all of the three constraints are taken into account at the same time. Moreover, the switching plane is designed in such a way that the reaching phase is eliminated, and consequently, the system insensitivity with respect to external disturbance and model uncertainty is guaranteed from the very beginning of the proposed control action. Furthermore, proposed control algorithm ensures monotonic tracking error convergence to zero.