Robust Fault Estimation And Active Tolerant Control For Linear Parameter Varying Systems

There is an increasing demand for dynamic systems to become safer, more reliable and less polluting to the environment. These requirements extend beyond normally accepted safety-critical systems of nuclear reactors, chemical plants or aircraft, to new systems such as autonomous vehicles or fast rail systems. An effective way to improve the safety and dependability in automated systems is to introduce fault diagnosis and fault-tolerant control. Hence, the study on fault diagnosis and fault-tolerant control technology has both theoretical and practical importance. Due to the existence of modeling uncertainties and unknown disturbance, robust fault diagnosis has received more and more attention in recent years.Linear parameter-varying (LPV) systems are special linear plants whose state-space matrices (i.e., the coefficient matrices of the state-space model) are functions of some vector of varying parameters. An LPV system can be reduced to a linear time-varying (LTV) system for a given parameter trajectory, and it can also be transformed into a linear time-invariant (LTI) system on a constant trajectory. From a practical point of view, a large class of nonlinear systems can be reduced to LPV systems by linearization along the trajectories of the parameters. So it is necessary to study the robust fault diagnosis and fault tolerant control for LPV systems. At present, it has drawn wide attention, and has become one of the main topics in control domain.This dissertation focuses on the robust fault estimation for a class of LPV systems, the robust fault estimation for a class of LPV time-delay systems, the integrated design of robust controller and fault estimator for a class of uncertain LPV systems, and the active fault-tolerant control based on gain-scheduled H∞design strategy. The main contributions of this dissertation can be summarized as follows: (1) For a class of LPV plants which depend affinely on the vector of time-varying parameters, a robust H∞fault estimator design method is proposed. First, the robust fault estimation problem is transformed into a robust H∞control problem. Then, based on gain-scheduled techniques and bounded real lemma for LPV systems, necessary and sufficient conditions for the existence of LPV fault estimators are presented in terms of linear matrix inequalities (LMIs). When these conditions hold, a method for constructing the self-scheduled LPV estimators is proposed, and the resulting LPV estimators have the same parameter dependence as the plants. Finally, the effectiveness of the proposed method is demonstrated through an example.(2) For a class of LPV time-delay plants where the state-space matrices depend affinely on time-varying parameters that can be measured in real-time and the time-delay is unknown but with bounded variation rates, a method for designing the robust fault estimator is presented. Based on H∞control theory and bounded real lemma for LPV time-delay systems, sufficient conditions for the existence of the self-scheduled LPV fault estimators are developed in terms of LMIs that can be solved via efficient interior-point algorithms. As these conditions hold, a robust fault estimator which has the same parameter dependence as the plant is constructed, the resulting estimator can follow the fault swiftly and effectively and with robustness to time-delay and exogenous disturbance.(3) An integrated methd for designing robust controller and fault estimator for a class of uncertain LPV plants which depend affinely on a vector of time-varying parameters is proposed. First, the integrated design problem is reduced to an H∞control problem by introducing the concept of fault estimation error, the resulting robust control problem can be further transformed into a robust stability problem by inserting some fictitious performance blocks. Then, based on scaled H∞theory, a scaled bounded real lemma for LPV systems is proposed. On the basis of this lemma, sufficient conditions for the existence of an LPV integrated"controller/fault estimator"are developed. As these conditions hold, an algorithm for constructing the LPV integrated"controller/fault estimator"is presented. The resulting LPV"controller/fault estimator"has the same parameter dependence as the plants, and can generate both control signals and fault estimations. Finally, to demonstrate the effectiveness of the proposed method, an uncertain system with actuator faults is investigated.(4) Based on the gain-scheduled H∞design strategy, a novel active fault-tolerant control scheme is proposed. An LPV model for systems with all possible sensor, component and actuator faults is presented. Under the assumption that the effects of faults on the state-space matrices of systems can be of affine parameter dependence, a reconfigurable robust LPV controller is developed based on gain-scheduled H∞theory. The resulting controller is a function of the fault effect factors which can be estimated on-line from the residual vector of the fault detection and isolation (FDI) mechanism. To demonstrate the effectiveness of the proposed method, an active fault tolerant controller is designed for a double inverted pendulum system with a fault in the motor tachometer loop.