The New Second-Order Sliding Mode Control Algorithm

A new class of regulators on the basis of the second-order sliding mode control is proposed. For the second-order system with smooth disturbances, special feedback is chosen with a discontinuous component and a radical function component. The synthesized control law provides a transient oscillatory process with decaying amplitudes, which converge to zero in finite time. In contrast to existing algorithms, the condition of homogeneity of the closed-loop system differential equations is omitted. In comparison to the "twisting"-algorithm, which is well known, designed feedback provides an invariance property with respect to smooth external perturbation with less relay amplitude. With the help of a special Lyapunov function, the convergence proof is considered by using the averaging approach. It is shown that the average oscillation period convergence speed is strictly negative, and the estimation of the convergence time is presented. The simulation results of the designed control law for the one link robot-manipulator are presented, which shows less steady-state oscillations in comparison to existing approaches.