Fault Estimation For Linear Parameter Varying System

As modern system has become more and more complex, there is an increasing demand for dynamic system to become safer and more reliable. As a result, fault diagnosis and fault tolerant control have been receiving more and more attention. Fault diagnosis is the foundation of fault tolerant control. Only if the fault can be detected and recognized, fast and accurately, can suitable methods be designed to deal with the fault. Fault diagnosis is composed of fault detection, fault separation and fault estimation. Fault estimation is the new research hot topics of fault diagnosis methods. It effectively combines functions of fault detection and fault isolation. The main method is to design an estimator to track the fault signal, then by studying the fault signal, the information on the fault can be available. However, in the research field of fault diagnosis, compared to fault detection and fault isolation, there are fewer research papers about fault estimation. The main reason is that the quantitative analysis of the fault is difficult, and the available techniques are rare. In recent years, some research results have been published in this research field, however, there are still more problems that are needed to be in-depth studied. One of them is the robustness issue in fault estimation system. There may be model uncertainty and unknown disturbance in the system. The designed estimator should only be sensitive to the fault, and insensitive to the mode uncertainty and disturbance.This thesis considers robust fault estimator design problem for Linear Parameter Varying(LPV) system. LPV system is a special kind of linear dynamic system, and its main characteristic is that the state space representation of the system depends on the time-varying parameter vector. The parameter vector is made up of time-varying parameters that can be measured or estimated during the system operation. In fact, there are a lot of nonlinear systems which can be modeled as LPV system in real world application, hence, the study on fault estimation for the LPV system has great practical importance.This thesis will propose three fault estimator design algorithms for three different kinds of LPV system. The main work of this thesis is:(1) For a class of continuous LPV systems that can be formulated in an Linear Fractional Transformation(LFT) framework, a gain-scheduled LPV fault estimator design algorithm is proposed. First, the original system is converted to an LFT representation. The time-varying parameters are taken out of the system as the uncertain part of the LFT framework, and the estimator can be also reshaped into an LFT representation, where the uncertain part of it is composed of the time-varying parameters. Put the uncertain parts of the original system and estimator together, the fault estimator design problem can be transformed into a robust control problem for an uncertain system. By using the scaled Small Gain Theorem and scaled Bounded Real Lemma, the existence condition of the estimator can be characterized in terms of linear matrix inequations(LMIs). The fault estimator can be constructed by solving the LMIs. A numerical example is used to prove the effectiveness of the synthesis algorithm.(2) For a class of continuous LPV system whose state space representation depends affinely on time-varying parameter vector, a gain-scheduled LPV fault estimator design algorithm is proposed. The idea is to use the robust control theory to solve the fault estimation problem for LPV system. An adaption of Bounded Real Lemma is used to present the existence condition of the fault estimator in terms of infinite dimensional LMIs, and for convenience of calculations, multi-convexity concept is utilized to convert infinite dimensional LMIs into a finite number of LMIs. The feature of the algorithm is that it use a parameter-dependent Lyapunov function to ensure the stability of the system, and the information on the rates of the parameter variation can be incorporated into the synthesis techniques. The fault estimator design algorithm is proposed, and a numerical example is used to demonstrate the effectiveness of the designed fault estimator.(3) For a class of discrete-time LPV system whose state space representations depend affinely on time-varying parameter vector, a gain-scheduled discrete-time LPV fault estimator design algorithm is proposed. By using discrete-time LPV version of Bounded Real Lemma, the existence condition of the fault estimator is presented in terms of LMIs. The synthesis process of the estimator is presented in detail. The designed fault estimator has the same parameter dependence as the original system, so it has gain scheduling property. A numerical example is used to demonstrate the effectiveness of it.(4) A sensor fault estimation problem for continuous stirred tank reactor(CSTR) system is researched. First, this thesis establishes the LPV model of CSTR system according to the system’s physical characteristics, then the estimator design method proposed for LPV sytem with LFT parameter dependence is utilized to construct a sensor fault estimator. The simulation result shows that the designed fault estimator can detecte and estimate the sensor fault signal, effectively.