LMI-Based Approaches To Fault Detection For Linear Systems

Due to the increasing demand for reliability and safety in industrial processes and aerospace, astronautics areas, fault detection has been the subject of intensive research, the model-based fault detection approach has been accepted as a widely used effective approach in the literature. Recently, H∞and H_ techniques have been introduced in model-based fault detection approach to deal with the disturbance robustness and fault sensitivity problems, respectively. Many approaches have been presented, however, there are still some problems to be developed associated with the existing approaches, eg., the inaccurateness resulted from these frequency weights, the unpracticalness when dealing with stuck faults with arbitrary small stuck value et al. This thesis, based on previous works of others, presents a new approach to deal with the inaccurateness of the frequency weights, where the frequency ranges of faults and disturbances are restricted to certain finite frequency range accurately. A steady-state based approach is also presented to detect these arbitrary small stuck faults including outage cases which cannot be detected using the existing approaches. Moreover, this thesis also presents some approaches to solve the fault detection problem for systems with polytopic uncertainties. Parts of the developed theories are applied to the fault detection filter or observer designs of VTOL aircraft model, F-18 aircraft model by simulations. Simulation examples illustrate the advantages and effectiveness of our approaches.Chapters 1-2 summarize the development and main research methods in fault detection literature, give some preliminaries about the considered problem.Chapters 3-4 investigate the fault detection filter design problem for linear systems with and without uncertainty, respectively. Finite frequency H_ and H∞performance indexes are introduced to increase the fault sensitivity and disturbance robustness, respectively. The recently developed generalized KYP lemma is used to deal with these finite frequency performance indexes which permits a direct treatment of the finite frequency performance indexes, completely avoiding approximations associated with frequency weights. The simulations illustrate the advantages of our approach compared with the existing techniques.Chapters 5-6 focus on the integrated fault detection and control problem for systems with polytopic uncertainty and linear parameter varying systems, respectively. The considered faults are also assumed to be in known frequency ranges, a so-called detector/controller is designed which generates two signals:detection signal and control signal. These two signals are used to detect faults and control the original open-loop systems, respectively. A two-step procedure is adopted to solve the nonconvex problem in Chapter 5. Based on some linearization techniques, these finite frequency performance indexes are finially converted to a set of linear matrix inequalities which can be solved by the MATBAL Control Toolbox. Simulation examples illustrate the effectiveness of the approaches presented in these two chapters.Chapter 7 investigates the fault estimation problem for systems with polytopic uncertainties. Different from the existing approaches, generalize KYP lemma is introduced to deal with the finite frequency characteristics, which gives a direct treatment of the finite frequency performance indexes, completely avoiding approximations associated with frequency weights. The simulation examples illustrate the advantages of our approach compared with the existing approaches.Chapter 8 studies the fault detection problem for a class of uncertain state feedback control systems, where actuator stuck faults are considered. Through satisfying certain performance indexes, a weighting matrix is designed to generate a residual signal, the residual output is minimized when the system is fault-free while maximized when the system gets faulty. An iterative LMI-based approach to the fault detection is proposed to obtain the optimal solution of the weighting matrix. It should be pointed that with the fault detection approach proposed in this paper, actuator stuck faults including outage cases can be detected effectively which is non-trivial in the fault detection literature. A numerical example shows the effectiveness of the proposed design approach by comparing with the existing techniques.Chapters 9-10 are concerned with the simultaneous fault detection and control, simultaneous fault detection and filtering problems, respectively. It should be pointed that a simultaneous design can reduce the complexity greatly compared with the design of fault detection systems and controller or filter separately. Furthermore, using the new methods proposed here, arbitrarily small actuator or sensor stuck faults especially the outages of actuators or sensor can be detected effectively which cannot be detected using the existing techniques. Numerical examples illustrate the advantages of our approach compared with the existing techniques.Finally, the results of the dissertation are summarized and further research topics are pointed out.