Disturbance observer based optimal second order sliding mode controller for nonlinear systems with mismatched uncertainty

Abstract

The paper aims to design an optimal second order sliding mode controller for the nonlinear system affected by mismatched uncertainties. Control Lyapunov function (CLF) based methodology is proposed to design an optimal controller for the known part of nonlinear system. The Lyapunov function and the performance index are chosen in such a way that the optimal controller should minimize the control effort. As the optimal controller is highly sensitive to the system uncertainty, a sliding mode controller is integrated with the optimal controller to tackle it. As the conventional sliding mode controller cannot tackle the mismatched disturbance, a disturbance observer is proposed to estimate the disturbance. But the first order sliding mode control is inapplicable to practical system due to the chattering. An optimal second order sliding mode controller proposed in this paper reduces the same. Simulation results ensure that the suggested controller is enable to reduce the control effort as well as chattering phenomenon.