Performance-Based Fault Detection and Fault-Tolerant Control for Nonlinear Systems With T–S Fuzzy Implementation

This article addresses the performance-based fault detection (FD) and fault-tolerant control (FTC) issues for nonlinear systems. For this purpose, in the first part of this article, the performance-based FD and FTC scheme is investigated with the aid of the nonlinear factorization technique. To be specific, the controller parameterization for nonlinear systems is first discussed. The so-called fault-tolerant margin is introduced as an indicator of the system fault-tolerant ability. Then, the FD scheme aiming at estimating and detecting the stability performance degradation of the closed-loop system caused by the system faults is developed. Furthermore, to recover the system performance, the performance-based FTC strategy is presented. In the second part of this article, the design approach of the performance-based FD and FTC scheme is studied by applying the Takagi-Sugeno fuzzy dynamic modeling technique. The achieved results are demonstrated in the end by a case study on the three-tank system.

I. Introduction

During the past few decades, the fault detection (FD) and fault-tolerant control (FTC) issues for linear systems have been considerably investigated to meet the requirements for system performance and reliability [1]–[5]. Because of the inevitable existence of nonlinearities in real industrial processes, intensive attention has also been drawn to nonlinear systems. As a result, significant progress has been made in dealing with the nonlinear FD and FTC problems. Among the published results on nonlinear FD and FTC, special types of nonlinear systems, such as networked control systems [6], affine nonlinear systems [7], and Lipschitz nonlinear systems [8], have been widely studied. In recent years, the ever-increasing demands in processes for enhancing system performance call for intensive study on the FD and FTC problems. Hence, the research concerning the control performance, such as the stability performance [9], performance [10], tracking control performance [11], and the robustness [12], for nonlinear FTC design has been conducted. However, very limited attention has been paid to characterizing and detecting the changes in stability performance expressed in terms of stability margin. In fact, it is a natural and reasonable way to trigger an FTC algorithm by means of control performance degradation monitoring. In nonlinear systems, all types of faults will cause changes in the system dynamics and may affect system stability. Directly monitoring and recovering the stability performance degradation are of considerable practical importance. Lately, the control performance-based FD and FTC issues have been investigated for faulty linear systems and singular systems in [13] and [14], respectively, by using the Youla parameterization via the coprime factorization techniques. Nevertheless, to the best of our knowledge, studies on FD and FTC for a general class of nonlinear systems in the context of the stability performance degradation have not been made. This motivates our work in this article.