Sliding mode control with a linear sliding surface that varies along a smooth trajectory

Sliding Mode Control is a nonlinear control method that has high robustness against uncertainties. The sliding surface is a hyperplane that characterizes the operation of the discontinuous nonlinear control input. The name of the control method comes from the behavior of states that act along sliding surface towards equilibrium point. Where, a gradient of the sliding surface determines convergence characteristics of errors. This paper introduces a sliding mode control with a time varying sliding surface that moves along a smooth trajectory. The smooth trajectory is developed based on a minimum jerk trajectory. Therefore, the error tracking response of the proposed method is smoother than in conventional methods. Moreover, the proposed method can reduce energy consumption and convergence time compared to conventional methods. To verify the advantages of the proposed method, we compare the proposed sliding surface with conventional ellipsoidal and linear sliding surfaces through simulations of a simple second-order uncertain dynamic system.