Elastic and Conventional Constraints in Sliding Mode Control of Second Order System

In this paper a new sliding mode control algorithm for second order systems subject to constraints is proposed. The algorithm ensures the reaching phase elimination and guarantees fast and monotonic tracking error convergence to zero without violating input signal and velocity constraints. At the initial time t = t(0) the system representative point belongs to the switching line. Afterwards the line moves with a constant velocity and a constant angle of inclination to the origin of the error state space and having reached the origin it stops moving. By this means insensitivity of the system to external disturbance and model uncertainty from the very beginning of the control action is ensured. The line is designed in such a way that its parameters minimize the integral of the time multiplied by the absolute error (ITAE). Moreover, two types of constraints are considered, i.e. the conventional one expressed by inequality and the elastic (stretchable) constraint which allows the threshold value of the considered signals to be slightly exceeded.