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

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.

A new fuzzy decoupled sliding mode control of flexible joint robotic manipulators based on the finite‐time observer in the presence of chaos with experimental validation

“…1. Based on the used coupling variable in the conventional DSMC, it can be seen this method can only guarantee the bounded uniform stability of the closed-loop system because the control input can only make the first sliding surface and its time derivative converge to zero and does not affect the performance of the second sliding surface, whereas all these papers stress the closed-loop system asymptotic stability [21][22][23][24][25][26][27]. Also, the papers have not provided any mathematical proof in this regard.…”

“…5. The use of the sign function in the DSMC structure causes undesirable chattering, which can reduce the drive's lifetime and overall system efficiency [21][22][23][24][25]. 6.…”

“…6. Most of the papers have used this method for regulation objectives in nonlinear systems, while the performance of this method in high-change desired trajectory tracking is problematic [21][22][23][24][25][26][27].…”

Finite-time convergence of perturbed nonlinear systems using adaptive barrier-function nonsingular sliding mode control with experimental validation

“…In (Zhang et al, 2021), an adaptive fuzzy hierarchical SMC approach is designed for the switched nonlinear systems in the existence of actuator faults and parametric uncertainty, where the unknown uncertain functions are estimated via the fuzzy logic system. In (Rajaei et al, 2020), a nonsingular decoupled TSMC technique is recommended for the fourth-order nonlinear dynamical systems in the existence of unknown perturbations, where a finite-time disturbance observer is planned for estimation error. A fuzzy continuous super-twisting SMC stabilizer is provided in (Nguyen et al, 2020) for rotational inverted pendulum in the existence of parametric uncertainty and external perturbation.…”

Adaptive prescribed‐time disturbance observer using nonsingular terminal sliding mode control: Extended Kalman filter and particle swarm optimization

“…Consequently, many studies have been conducted to study the vibration behaviour of micro/nanobeams [31][32][33][34][35]. Furthermore, the analysis of vibration control is used to prevent the micro/nanobeams from damage and improve the performance and resolution of beams [36][37][38][39]. However, the measured dimensions of nanobeams may not be exact; therefore, the estimation analysis and robust controllers are useful to enhance the accuracy.…”