Adaptive Sliding Mode Controller Design for a Class of Nonlinear Systems

An adaptive sliding mode controller is presented for a class of Single Input Single Output (SISO) nonlinear systems with external disturbance. The designed controller, resulting from the combination of the Classical Sliding Mode Control technique (CSMC), the Proportional Integral controller (PI) and the Proportional Derivative controller (PD), can reduce the chattering phenomenon and guarantee the asymptotic convergence to zero of tracking errors and the boundedness of all signals in the closed-loop system. The parameters of the proposed controller, the adaptive laws and the robust control term are derived based on the Lyapunov stability analysis. Finally, an inverted pendulum system and two coupled tanks system are simulated to demonstrate the validity and the effectiveness of the suggested approach.