Fault Detection Filter Design for Dynamical Systems in Finite-Frequency Domain

有限頻域內動態系統的故障檢測濾波器設計

Student thesis: Doctoral Thesis

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Award date18 Aug 2023

Abstract

The ever-increasing sophistication of modern industrial processes and systems necessitates effective fault detection strategies to avoid potential abnormalities, such as performance degradation and safety hazards. In the past decades, a great deal of attention has been devoted to the design of estimation-based fault detection strategies, the key issue of which is concerned with their robustness to disturbances/noises and sensitivity to the faults to be detected. In this context, the robust filtering technique has been well researched under various filtering frameworks, and developing advanced filtering approaches with reduced design conservatism and better filtering performance becomes a significant topic.

It is observed that traditional filtering approaches often fail to make full utilization of available information, such as the frequency information of signals and/or the historical information of the concerned system, which consequently introduces conservatism to a certain extent. In fact, the finite-frequency filtering and the memory filtering are two effective techniques to achieve conservatism reduction and performance improvement. On the one hand, the frequency of disturbances and faults in industrial systems and processes is often restricted to a certain range. Therefore, taking the frequency information of signals into account for the filter design is a sensible method to improve system performance. On the other hand, the rapid development in data-processing capacities of modern systems enables them to store and process more data. Therefore, incorporating more historical system information while designing the filter is a feasible way to reduce design conservatism as the dynamics of the filter can be enriched and the design flexibility can be enhanced.

In this thesis, a number of finite-frequency fault detection filter design approaches are developed for linear systems with polytopic uncertainties and complex nonlinear systems via Takagi–Sugeno (T–S) fuzzy affine models. The main effort is devoted to developing novel finite-frequency fault detection filtering methods for dynamical systems while reducing design conservatism and improving filtering performance. The main results of this thesis consist of four parts. First, the H−/H∞ memory fault detection filter is developed in the finite-frequency domain for discrete-time linear system with polytopic uncertainties. Then, the obtained results are extended to discrete-time nonlinear systems and a novel H−/H∞ memory fault detection filter is designed in the finite-frequency domain for uncertain T–S fuzzy affine models. Next, to make the designed filter suitable for practical situations, the problem of finite-frequency H−/H∞ fault detection filter design is studied for the more challenging continuous-time T–S fuzzy affine systems. Finally, the previous results are further extended and the fault detection problem for networked systems is investigated. In particular, the problem of H−/H∞ fault detection filter design is investigated for T–S fuzzy affine systems with medium access constraints. The merit of the proposed approaches lies in their less design conservatism and better filtering performance, which are realized by making full utilization of the available information, including frequency ranges of signals and/or historical system information. It is also shown that the proposed design approaches are more general in the sense that the traditional full-frequency (FF) and memoryless filtering approaches are included as special cases.

The main results of this thesis can be summarized as follows.

1. The finite-frequency H−/H∞ memory fault detection filtering problem is investigated for discrete-time linear systems with polytopic uncertainties. With the aid of the generalized Kalman–Yakubovič–Popov (GKYP) lemma, Projection lemma, and some matrix inequality convexification techniques, sufficient conditions for analysis and synthesis of the fault detection filter are established. The solution to the filtering problem can be obtained by solving an optimization problem in the form of a set of linear matrix inequalities (LMIs). It is further theoretically proved that the utilization of additional historical system information generally improves the filtering performance. The simulation results show that better filtering performance can be achieved by using the finite-frequency filtering and memory filtering techniques.

2. The finite-frequency H−/H∞ memory fault detection filtering problem is investigated for discrete-time T–S fuzzy affine systems with norm-bounded uncertainties. Based on the GKYP lemma combined with the celebrated S-procedure, new sufficient conditions for the fuzzy affine filtering error system to have the finitefrequency H−/H∞ performance are given at first. By further using piecewise fuzzy quadratic Lyapunov functions (PFQLFs) and Projection lemma, the filter analysis results for the filtering error system to be asymptotically stable with the prescribed finite-frequency H−/H∞ performance are obtained. Then, the filter synthesis is carried out with the aid of matrix inequality convexification techniques, and the synthesis results are described in terms of LMIs. It is also theoretically proven that the utilization of additional historical system information generally improves the filtering performance. The simulation studies are provided to show that better filtering performance can be achieved by using the finite-frequency filtering and memory filtering techniques.

3. The problem of asynchronous finite-frequency fault detection filter design for continuous-time T–S fuzzy affine dynamic systems is investigated. It is assumed that the premise variables of the plant are unmeasurable so that the filter state transition and plant state transition may be asynchronous. By applying the celebrated S-procedure, the GKYP lemma is extended such that the finitefrequency H−/H∞ performance of the fuzzy affine filtering error system is ensured. Furthermore, by utilizing piecewise quadratic Lyapunov functions (PQLFs), Projection lemma, and matrix inequality linearization techniques, the finitefrequency fault detection filter is developed for the concerned T–S fuzzy affine dynamic system. It is shown that sufficient conditions for the existence of the fault detection filter are formulated as feasibility of LMIs. The advantages of the proposed finite-frequency filtering approach is validated by simulation examples.

4. The finite-frequency fault detection filtering problem is investigated for a class of networked nonlinear systems subject to medium access constraints. The nonlinear system is modeled by discrete-time T–S fuzzy affine dynamic models, and only one node that includes partial measured information can gain access to the shared transmission medium according to the allocated access probability. First, by integrating with S-procedure, the GKYP lemma is further developed to obtain sufficient conditions guaranteeing the desired finite-frequency H−/H∞ performance of the filtering error system. Then, by applying PQLFs, Projection lemma, and matrix inequality convexification techniques, the design approach of the fault detection filter is proposed for the constrained networked nonlinear system. It is shown that the filtering problem can be addressed by solving a set of LMIs. The simulation studies are provided to illustrate the advantages of the proposed finite-frequency fault detection filtering approach.