Adaptive sliding mode controller for a class of nonlinear system with uncertainty

In this paper, a novel robust nonlinear sliding mode controller for a class of nonlinear system with parameter uncertainty and disturbance is proposed. The controller is designed in a backstepping manner, proportional-integral-derivative(PID) stabilizing signal of the virtual error is introduced in the design procedure. First, according to the backstepping approach, series Lyapunov functions are constructed step by step, the adaptive law of damping coefficient is given in the second step, and finally, a novel sliding surface is designed. The whole control law is obtained by applying the sliding mode control theory, so the disturbance is attenuated. To validate the control law, some simulations were carried on, the results showed that the proposed control method is able to achieve a quite satisfactory control effect.