Disturbance-observer Based Adaptive Control for Second-order Nonlinear Systems Using Chattering-free Reaching Law

In this paper, an adaptive sliding mode control incorporating with a nonlinear disturbance observer is proposed for a class of second-order nonlinear systems with unknown parameters and matched lumped disturbance. A double hyperbolic reaching law with chattering-free characteristic is first constructed, and an adaptive sliding mode controller is designed to guarantee the satisfactory tracking performance and fast error convergence. The chattering problem is eliminated by means of the infinitely approaching equilibrium point instead of crossing it by employing two hyperbolic functions. In order to identify the unknown parameters accurately, an adaptive parametric update law is presented through constructing a set of auxiliary filtered variables. Then, a nonlinear disturbance observer is proposed to improve the tracking performance and compensate for the lumped disturbance including perturbations and uncertainties. The stability analysis is provided by the Lyapunov stability theory, and a numerical simulation on a mass-spring damper system is given to demonstrate the effectiveness of the proposed method.