Stretchable and Conventional Input Constraints in VSC of the Third Order Systems

In this paper a new sliding mode control algorithm for the third order uncertain, nonlinear 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 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. In order to select the switching plane parameters, the integral of the time multiplied by the absolute error (ITAE) is minimized. Two types of the input signal constraints, i.e. a conventional constraint expressed by an inequality and an elastic constraint which allows the threshold value of the input signal to be slightly exceeded are considered. In both cases 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