State and disturbance observers‐based chattering‐free fixed‐time sliding mode control for a class of high‐order nonlinear systems

Abstract

AbstractIt is essential to consider chattering alleviation of Sliding Mode Control (SMC) design along with providing the system convergence regardless of initial states utilizing the fixed‐time stability notion. Unknown states and disturbance are two major issues in practical applications, which can be effectively solved by using sliding mode observers. This paper deals with state and disturbance Observers‐based Chattering‐Free Fixed‐time SMC (OCFFSMC) design for a class of high‐order nonlinear systems with unknown disturbance, while only the first state is measured physically. A new form of the combined observer‐controller is designed to provide estimated data of unknown disturbance and unmeasured states in the control law. The designed disturbance observer‐based sliding mode controller is not only capable of estimating unknown disturbance but also capable of alleviating the chattering problem in the control signal. Based on defining a new form of the sliding surface, a new control law is designed to alleviate chattering problem and achieve trajectory tracking in a fixed time independently of initial conditions. The fixed‐time stability proof of the closed‐loop system is obtained using Lyapunov stability theory. The validity of the proposed control scheme, OCFFSMC, is verified by applying two examples and simulating in Simulink/MATLAB.