The sliding mode controller with an additional proportional controller for fast tracking control of second order systems

In this paper, we propose a sliding mode controller with an additional proportional controller (SMC with APC) for fast tracking control of second order systems. Using the additional proportional controller, fast tracking control is achieved. The control input of the sliding mode control law is modified accordingly by applying the Lyapunov stability condition and adding a proportional controller. To show the validation of the proposed method, the stability is proved by using two Lyapunov functions. And the PHANToM™ haptic device of a nonlinear second-order system is considered. The results of performance are compared with conventional sliding mode controllers which have an additional proportional controller or not.