타카기-수게노 형태의 비선형 시스템을 위한 H_/H∞ 이상 검출 및 분리

다국어 초록 (Multilingual Abstract)

This thesis addresses sensor fault detection and isolation (FDI) observer design problems subject to H−/H∞ performance. Regarding the maintenance of system stability and reliability, it is regarded as a significant problem to detect and isolate faults in a control system. Since it is generally impossible to predict or prevent any fault, to protect the system from catastrophic failure, fault should be detected and isolated as quickly as possible after it arises.
To design highly reliable diagnostic systems suitable for system characteristics, we propose a model-based observer design technique. The observers are designed to produce a residual from state estimation error between a physical system and an analytic model.

To achieve good FDI performance, the residual should be sensitive to fault (e.g. in H−/H∞ sense) and robust against disturbance (e.g. in H−/H∞ sense) simultaneously. These performances can be quantified and their indices are used for logical basis of fault decision (residual evaluation). As another way to improve the FDI performance, we consider a residual gain in an observer dynamics. To attain the residual gain, an iterative algorithm involving a convex optimization is presented based on the cone complementary linearization technique.

To deal with FDI problem for state-delayed systems, we use delay-dependent observer design criteria. We consider the FDI problem for continuous- and discrete-time linear time-invariant systems containing parametric uncertainties and extend the outcomes to a Takagi--Sugeno fuzzy FDI problem. In a sampled-data FDI problem, the direct discrete-time approach is used. Using an approximate model approach, we explain observer stability and redefine performance indices based on exact-approximate mismatch. Then, an exact discrete-time model approach is applied to a fault detection problem.

In this thesis, we propose the observer bank which consists of the sensor's number of observers. Observer gains and residual gains in each observer are designed such that each residual is as sensitive to a certain partial group of fault but as robust against disturbance as possible. Sufficient design conditions are derived in nonlinear matrix inequality format. The FDI is accomplished by residual evaluation through an FDI decision logic. Numerical examples are provided to verify effectiveness of proposed techniques.

목차 (Table of Contents)

• 1 Introduction 1
• 1.1 Background: Concept of FDI 1
• 1.2 FDI Performance 2
• 1.3 State Delay in Systems 4
• 1.4 Sampled-Data FDI 4
• 1.5 Outline and Objectives 6
• 1.6 Notations 8
• 2 H−/H∞ Sensor FDI of LTI Systems with State Delay 9
• 2.1 Preliminaries 9
• 2.2 Main Results 13
• 2.3 Paralleling to Discrete-time Case 24
• 2.4 Example 34
• 2.5 Conclusions 42
• 3 H−/H∞ FDI for nonlinear systems with state delay in T--S form 44
• 3.1 Preliminaries 44
• 3.2 Main Results 49
• 3.3 Parallelizing to Discrete-time Case 63
• 3.4 Example 74
• 3.5 Conclusions 78
• 4 Sampled-data FDI for Nonlinear Systems in T--S Form: Approximate Model Approach 79
• 4.1 Preliminaries 79
• 4.2 Design 84
• 4.3 Performance and stability analysis 89
• 4.3.1 FDI Performance with Fe 89
• 4.3.2 Stability 95
• 4.4 Example 99
• 4.5 Conclusions 110
• 5 Detecting Sensor Fault in T--S Fuzzy Systems under Sampled-data Measurement: Exact Direct Discrete-time Design Approach 111
• 5.1 T--S Fuzzy System 112
• 5.2 Main Results 117
• 5.3 Example 129
• 5.4 Conclusions 133
• 6 Conclusions 136
• Abstract (in Korean) 146