Disturbance observer‐based tracking control with prescribed performance specifications for a class of nonlinear systems subject to mismatched disturbances

Abstract

This work investigates simultaneous prescribed performance tracking control and mismatched disturbance rejection problems for a class of strict‐feedback nonlinear systems. A novel control scheme combining prescribed performance control, disturbance observer technique, and backstepping method is proposed. The disturbance estimations are introduced into the design of virtual control law design in each step to compensate the mismatched disturbances. To further improve the control performance, a prescribed performance function characterizing the error convergence rate, maximum overshoot, and steady‐state error is used to construct the composite controller. The proposed controller guarantees transient and steady‐state performance specifications of tracking error and provides much better disturbance attenuation ability simultaneously. Rigorous stability analysis for the closed‐loop system is established by direct Lyapunov function method. It is shown that all the states in the resulting closed‐loop system are stable, and the tracking error evolves within the prescribed performance boundaries and asymptotically converges to zero even in the presence of mismatched external disturbances. Finally, theoretical results are illustrated and demonstrated by two simulation examples.

Nested extended state observer design for uncertain nonlinear systems under time‐varying disturbance

“…According to (7), the transfer function between lumped disturbance f and disturbance estimation f can be derived…”

“…[1][2][3] Unknown input observer (UIO), sliding mode observer (SMO), disturbance observer (DO), and extended state observer (ESO) are among the many emergent observer design methods for uncertain nonlinear systems, and many variants have been proposed to deal with different application scenarios. [4][5][6][7] UIO could provide inherent attenuation against unwanted external signal influence via a particular coordination transform. However, the occurrence of coordinate transformation is dependent on observer matching conditions, which is in practice limited.…”

A novel fixed‐time sliding mode control for nonlinear manipulator systems based on adaptive disturbance observer

“…However, since the robotic manipulator is a system with nonlinear and complex perturbations, the actual control is susceptible to modeling errors, friction, and external disturbances, which all increase the difficulty of control. In response to the problems of nonlinear systems, scholars have developed different control methods to improve them, such as neural network control [3,4], fuzzy control methods [5][6][7][8][9], backstepping control methods [10][11][12], and sliding mode control (SMC) methods [13][14][15][16][17][18].…”

Disturbance observer-based fixed-time control for nonlinear systems with multiple disturbances

“…Disturbances widely exist in actual engineering systems, which brings unfavorable effects on system performances; thus, antidisturbance problems have become one of research highlights (Hao et al, 2019;Wei et al, 2016Wei et al, , 2020Yao et al, 2021;Zhang et al, 2017Zhang et al, , 2021. Due to the superiorities of higher accuracy, stronger flexibility, and simpler structure, disturbance observer-based control (DOBC) has been extensively applied to deal with disturbances (Han et al, 2017;Javaid and Dong, 2021;Zhou et al, 2023). Its main principle is to estimate disturbances via the disturbance observer and immediately compensate disturbances in feed-forward path.…”