Nonsingular decoupled terminal sliding-mode control for a class of fourth-order under-actuated nonlinear systems with unknown external disturbance

Abstract

Abstract This study is concerned with the design of a nonsingular decoupled terminal sliding mode controller for a class of fourth-order under-actuated uncertain nonlinear systems with unknown external disturbance. For the unmeasured disturbance, a disturbance observer with finite-time convergence of estimation error to zero is proposed. The nonsingular decoupled terminal sliding mode controller is designed by utilizing the output of the proposed disturbance observer. Also, an input saturation constraint and control singularity are considered in the controller design. The finite-time stability and convergence of the disturbance observer are proved for the closed-loop system. In addition, the control of an electrostatically actuated Timoshenko nanobeam subjected to Casimir force is simulated to demonstrate the effectiveness and performance of the proposed control scheme.