Adaptive Sliding Mode Fixed-Time Tracking Control Based on Fixed-Time Sliding Mode Disturbance Observer with Dead-Zone Input

Hongbin Wang,Bo Su,Yueling Wang,Jing Gao

doi:10.1155/2019/8951382

Abstract

Aiming at the problem of fixed-time trajectory tracking control for high-order dynamic systems with external time-varying disturbance and input dead-zone, an adaptive fixed-time sliding mode control algorithm is proposed by employing a fixed-time sliding mode disturbance observer (FTSMDO) and high-order fixed-time sliding mode algorithm. Firstly, a FTSMDO is presented for the problem that estimating the compound disturbance is composed of input dead-zone and time-varying external disturbance in the higher-order dynamic system, which cannot be measured accurately. Furthermore, for the case that the total disturbance of the system has an unknown upper bound, the corresponding adaptive law is designed to estimate the unknown upper bound, and the fixed-time controller is designed based on FTSMDO algorithm to make all state variables converge in a fixed-time. Based on Lyapunov technique, the fixed-time convergence performance of the proposed algorithm is proved. The effectiveness of the presented fixed-time control algorithm is verified by simulating the depth tracking control of the underactuated underwater vehicle.

Highlights

Most of the actual physical system models have uncertainties and external disturbances, and some of them have existing dead-zone pheromone in the actuator, which greatly affects the performance of the system
As is known that the convergence time of the finite-time algorithm is related to the initial state of the system, and with the increase of initial state, the convergence time increases, which will greatly affect the transient performance of the system
In the high-order dynamic system subject to deadzone and external disturbance, an adaptive fixed-time sliding mode controller based on fixed-time sliding mode disturbance observer (FTSMDO) is proposed

Summary

Introduction

Most of the actual physical system models have uncertainties and external disturbances, and some of them have existing dead-zone pheromone in the actuator, which greatly affects the performance of the system. The problem of prescribed performance distributed output consensus for higher-order nonaffine nonlinear multiagent systems with unknown dead-zone input was investigated on account of Lyapunov stability theory and the dynamic surface control technique in [17]. The high-order fixed-time sliding mode algorithm combined with the disturbance observer can further improve the robustness. This paper is formulated by the fixed-time sliding mode control of high-order dynamic system subject to external disturbance and input dead-zone. A new fixed-time sliding mode disturbance observer (FTSMDO) is proposed to estimate the complex disturbances, which is composed of external time-varying disturbance and dead-zone nonlinearities in high-order dynamic systems. The control objective is achieved when the proposed comprehensive FTSMDO with fixed-time sliding mode method can track a desired trajectory under the presence of integrated effect of input dead-zone and unknown time-varying external disturbance.

Problem Statement and Preliminaries

Controller Design

Conclusions