New fixed-time sliding mode control for a mismatched second-order system

Abstract

A fixed-time sliding mode control (FTSMC) method is proposed for a second-order system with mismatched uncertainties in this paper. A new sliding mode, which is insensitive to the mismatched disturbance, is present to eliminate the effect of mismatched uncertainties by adopting the differentiable nonlinear function, and to obtain the fixed time stability independent of initial conditions by using the fraction-order function. In order to improve the performance of control system, the extended disturbance-observer-based fixed-time sliding mode control (EDO-FTSMC) approach is investigated to obtain the fixed-time stability subject to the mismatched uncertainties. Finally, the performance of the proposed control method is illustrated to compare other control approaches with numerical simulation results and application examples.

Robust steering control for a steer-by-wire automated guided vehicle via fixed-time adaptive recursive sliding mode

“…Unfortunately, the TSM controllers can only ensure the system finite-time convergence (Liu et al, 2020;Wang et al, 2018;Zhu et al, 2020), where the setting time will increase unboundedly with the variation of initial states. Therefore, the fixed-time sliding mode (FTSM) control has attracted the attention of researchers recently for its faster convergence rate and fixed settling time independent of initial conditions (Guo and Yang 2020;Zuo, 2015aZuo, , 2015b. In Cao et al (2020) and Hu et al (2022), the improved fixed-time stable systems (FTSSs) are developed to ensure a faster convergence rate.…”

Predefined-time stabilization of brushed direct current motor system affected by matched and unmatched disturbances and stochastic noises

“…Under these circumstances, some works have overcome this problem by designing a disturbance observer and couple its output to the SMC. The purpose for the disturbance observer is to estimate the magnitude of the unmatched disturbance and feed the values to the SMC (see, for example, Durmaz et al (2012); Wei et al (2016); Guo et al (2020); Hou et al (2017); Guo and Yang (2021); Rauf et al (2020); Nasiri et al (2020); and Sun et al (2021)).…”

Fixed-Time Tracking Control for Flexible Joint Manipulator With Prescribed Performance Constraint

“…In [15], a fractional-order nonsingular terminal sliding mode control (FONTSMC) was proposed, which has better control performance, can ensure limited time convergence, enhance the robustness of the closed-loop system and the ability to suppress mismatched disturbance, and reduce chattering problem. Recently, a more optimal fixed-time theory was proposed and the convergence decision theorem was given in [17,38]. The convergence time does not depend on the initial value and the convergence time can be designed through parameters.…”

“…In [27], a novel fixed-time sliding mode disturbance observer (FTSMDO) based second-order fixed-time sliding mode control (FTSMC) was proposed for small scale unmanned helicopter to extend the conventional local assumption to a new global assumption. In [17], the extended disturbance-observer-based fixed-time sliding mode control approach, by adopting a new sliding mode, is designed for a second-order system with mismatched uncertainties. Fixed-time of higherorder sliding mode (HOSM) and its observer is realized in [28,29].…”