Shifted Switching Plane Design for Third-Order Systems with Elastic and Conventional Input Constraints

Abstract

In this paper a new sliding mode control algorithm for a 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 t = t0, this plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the switching 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 is minimised. Two types of input signal constraints are considered. First a conventional constraint expressed by an inequality is analysed, and then an elastic (or stretchable) constraint is taken into account. In the second case, we assume that the threshold value of the system input signal is known and that exceeding this value is undesirable, however not definitely forbidden. Exceeding this value is acceptable if it leads to an essential improvement of the system performance. 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.