Sliding‐mode control of the third‐order system subject to velocity, acceleration and input signal constraints

Abstract

AbstractIn this paper the design of a time‐varying switching plane for the sliding‐mode control of the third‐order system subject to velocity, acceleration and input signal constraints is considered. Initially, the 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. The plane parameters (determining angles of inclination and the velocity of its motion) are selected to ensure the minimum integral absolute error (IAE) without violating velocity, acceleration and input signal constraints. The following cases of the switching plane parameters selection are considered. Firstly, the IAE is minimized subject to each of the three constraints separately. Then, every pair of the constraints is considered, and finally all three constraints are taken into account simultaneously. In all the cases 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 and fast, monotonic error convergence to zero is achieved. Copyright © 2007 John Wiley & Sons, Ltd.