Study On Fault Tolerant Control Via Sliding Mode Approach For Uncertain Linear Systems

More and more advanced technological systems rely on sophisticated control sys-tems to increase their reliability and safety. The conventional feedback control designs may result in unsatisfactory performances or even instability once failures occur on ac-tuators, sensors or other system components. This has stimulated enormous research ac-tivities in seeking new design methodologies, for accommodating the component failures and maintaining the acceptable system stability and performances, so that abrupt degra-dation and total system failures can be averted. These types of control methodologies are often well known as fault-tolerant control methodologies. On the other hand, a model of a system or process is an ideal description which ignores model uncertainties and external disturbances, thus the robustness problem of fault tolerant control system (FTCs) is nec-essary to be fully taken into account in the theoretical study. Fortunately, the insensitivity and robustness properties of sliding mode control (SMC) to certain types of disturbance and uncertainty make it very attractive for FTCs, which motivates us to design a fault tol-erant controller for a class of uncertain linear systems in the framework of sliding mode control theory.On the basis of the previous work, this dissertation is concerned on the research of fault tolerant control based on sliding mode theory. For a class of uncertain linear systems, a fault tolerant control strategy using a sliding-mode approach is established by using state feedback and output feedback, respectively. For a class of uncertain linear systems with signal quantization, static quantizers with static adjustment strategies are proposed and the corresponding fault tolerant control law using a sliding-mode approach are given by using state feedback and output feedback, respectively. For a class of uncertain linear systems with actuator saturation, a relationship between fault information and stability area is given. All the main results are verified by simulation and simulation examples illustrate the advantages and effectiveness of our approaches. The main contents are outlined as follows:Chapters 1-2 summarize and analyze the background and the development of fault tolerant control technologies and sliding mode control. Preliminaries about the considered problems are also given.Chapter 3 is concerned with the problem of robust adaptive fault-tolerant compen-sation control via sliding mode state feedback for uncertain linear systems. Based on a matrix full-rank factorization technique, a lower bound of fault information is given and a sufficient condition of sliding mode stability is derived. In terms of the information from adaptive mechanism and without requiring any fault detection and isolation (FDI) mech-anism, a sliding mode controller is designed to guarantee the stability of the closed-loop system despite of actuator faults, especially outage of certain actuators.On basis of the results in Chapter 3, the robust fault tolerant problem via sliding mode output feedback for uncertain linear systems is considered in Chapter 4. Based on the matrix full-rank factorization, it is not required the restrictive assumption that the number of the measurement outputs is larger than that of the inputs. A sufficient condition for the sliding mode stability is given and an adaptive sliding mode controller, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults, is designed to guarantee the asymptotic stability and adaptive H? performance of closed-loop systems.Chapter 5 studies the fault tolerant controller design problem via sliding mode state feedback for uncertain linear systems with signal quantization. In order to compensate for quantization errors, an adjustment range of quantization sensitivity for a dynamic uni-form quantizer is given through the flexible choices of design parameters by taking fault information into account. Comparing with the existing results, the derived inequality con-dition leads to the fault tolerance ability stronger and much wider scope of applicability. Combining with a static adjustment policy of quantization sensitivity, an adaptive sliding mode controller is then designed to maintain the asymptotic stability of the closed-loop system.Chapter 6 extends the idea of state feedback situation developed in Chapter 5 to the output feedback case. By employing the matrix full-rank factorization technique with a design parameter, a sufficient condition for the existence of a linear sliding surface and a compensator in the augmented space is given. By taking fault information into account, an adjustment range and a static adjustment policy of quantization sensitivity is given, which leads to less conservativeness. It is shown that the proposed fault tolerant strategy via sliding mode theory guarantees that the closed-loop system is asymptotically stable in the presence of quantization errors and actuator faults including outage. The effectiveness of the proposed design method is illustrated via an example.In Chapter 7, the fault tolerant control problem via sliding mode state feedback for uncertain chaotic systems with actuator saturation is considered. Under an actuator re-dundancy assumption, an important lemma is first given and proved to find a lower bound of fault information and saturation degree. Then an adaptive sliding mode controller is designed to guarantee locally asymptotical stability of synchronization error. Compared with existing literature, an obvious relationship between actuator fault information and stability region is revealed. An improved strategy is also proposed to reduce conserva-tiveness when estimating stability region. The synchronization problem of a model of Chua's circuit systems is considered to show the effectiveness of proposed method.Finally, the results of the dissertation are summarized and further research topics are pointed out.