Fuzzy Observer-Based Fault Detection Design Approach for Nonlinear Processes

This paper is concerned with the analysis and integrated design of a type of observer-based fault detection (FD) system for general nonlinear processes. To this end, the existence and design condition for this type of nonlinear observer-based FD systems is first introduced. In this context, the integrated design scheme is investigated by dealing with the design condition with the aid of Takagi-Sugeno (T-S) fuzzy dynamic modeling technique. To be specific, the universal T-S fuzzy observer-based residual generator is developed via fuzzy Lyapunov functions. Subsequently, an integrated observer-based FD scheme is proposed with an embedded dynamic threshold, which is generated to meet the real-time FD requirements from industrial processes. In the end, a numerical example and case simulation study on a continuous stirred tank heater process are performed to show the application of the proposed method.

I. Introduction

Thanks to the great efforts over the past two decades in the research and application fields, observer-based fault detection (FD) and isolation (FDI) for linear time-invariant systems has established itself as an attractive research area. Numerous methods have been proposed in the model-based [1]–[3] and data-driven frameworks [4]–[6]. As industrial processes are typically nonlinear, the design issues of observer and further observer-based FDI and fault-tolerant control (FTC) for nonlinear processes have received intensive attention in recent years [7]–[14]. Among involved studies, focuses are on dealing with special types of nonlinear systems, for instance, affine nonlinear systems [15]–[17], Lipschitz nonlinear systems [18], and linear systems with nonlinear uncertainties [19], etc. A thorough literature review on the nonlinear FD works has revealed that, up to now, little attention has been paid to the analysis of general nonlinear systems for FD purpose. Study on FD issues for general nonlinear systems is a theoretically challenging topic, which can help us getting deeper insight into FD systems. Moreover, only few works have been dedicated to the integrated design of observer-based FD systems, which is composed of an observer-based residual generator, an evaluation function, and a decision logic with an embedded threshold [15], [20], [21]. Most studies mainly concentrated on the design schemes of observer-based residual generators, which motivates this paper.