Sliding mode control for systems subjected to unmatched disturbances/unknown control direction and its application

Abstract

This article investigates the control issue for systems subjected to unmatched disturbances and unknown control direction simultaneously. A class of adaptive nonlinear disturbance observer is developed to estimate the unmatched disturbances precisely and then extended to the general high‐order form. The proposed method guarantees the stability of the second‐order and high‐order system under unknown control direction and robustness against the unmatched disturbances with the help of the sliding mode technique. The application in the integrated missile guidance and control (IGC) system design demonstrates the validity of the proposed control method. Herein, the cause of unknown control direction and the influence of the time‐vary control gain on the missile are discussed in detail. Also, the Monte Carlo campaign is run to show the superiority of the developed control strategy compared with the existing IGC method.

A simple approach to estimate unmatched disturbances for nonlinear nonautonomous systems

“…Remark The system considered in Reference 25 is just autonomous with identity matrix $$$ G $$$ and the unmatched disturbance $$$ {d}_i $$$ depends only on $$$ {\overline{x}}_{i-1} $$$ for $$$ i=1,2,\dots, n-1 $$$, where $$$ {\overline{x}}_{i-1}={\left[{x}_1,{x}_2,\dots, {x}_{i-1}\right]}^T $$$. Thus, the system (1) to be studied here is obviously more general than the system given in Reference 25. In addition, it can describe not only a class of nonlinear nonautonomous systems but also nonlinear autonomous systems.…”

“…Moreover, these disturbance observers were mostly designed for nonlinear autonomous (time‐invariant) systems. Finally, the disturbance and its first and higher‐order derivatives must be bounded 25‐27 so that these observers can estimate the disturbances or those controllers are able to cope with it. The boundedness of first and higher‐order derivatives for the disturbance and the required information about first derivative of system states were restrictions of these existing disturbance observers.…”

Discrete‐time design and applications of uncertainty and disturbance estimator

“…To establish comprehensive application-based literature, discrete-time UDE can be applied to more classes of nonlinear systems, including robot manipulators, 50,51 roll, pitch and integrated autopilot designs, [52][53][54] and robust missile guidance. 4,55,56 DATA AVAILABILITY STATEMENT Data sharing is not applicable to this article as no data sets were generated or analyzed during the current study.…”

“…While this characterizes real-world systems more accurately, compensating "unmatched" disturbances is a more complicated problem than compensating "matched" disturbances. Multiple studies propose methods such as higher-order sliding mode observation, [2][3][4] adaptive compensation 5,6 and the use of adaptive neural networks. 7 The focus of this study is on "matched" disturbances only, with compensation of "unmatched" disturbances being a promising avenue for future work.…”

Active fault tolerant control design using switching linear parameter varying controllers with inexact fault‐effect parameters

“…As known, FTC can be divided into two main groups, that is, passive fault-tolerant control (PFTC) 19,20 and active fault-tolerant control (AFTC). [21][22][23] In the PFTC, the fault is usually considered as the appearance of disturbance, and the robust H ∞ control [24][25][26] or other control schemes [27][28][29][30][31][32] are utilized to make the system insensitive to faults. On the other hand, the AFTC frame usually takes the information from fault detection and isolation (FDI) block, 33 and the corresponding control laws are designed to compensate for the effects of the faults, which can achieve better performance in comparison to the PFTC strategy.…”