Research On Model-based Robust Fault Detection And Estimation Methods For Uncertain Systems

When doing mathematical modeling to uncertain systems, there exist many uncertain characteristics since the system structure, parameters and the disturbance are not fully understood for uncertain systems. The methods of fault diagnosis rely on the accuracy of the mathematical model of the diagnosis object. Therefore, using model-based method for fault diagnosis of uncertain systems and studying how to reduce the effect of uncertainties to the fault diagnosis results and ensure the validity of fault diagnosis is very necessary, and it is also the main problem for model-based fault diagnosis. In this paper, the problems of model-based robust fault detection and estimation for uncertain systems are studied. The methods of robust fault detection and estimation with lower conservatism and universal significance are studied due to the conservatism and limitation of the mathematical models of the robust fault detection and estimation for uncertain systems. The main contents are as follows:Consider the system with unknown input signals and model uncertainties, a method for robust fault detection based on H/H∞observer is presented with multi-objective constraints method. UsingH index and H∞norm theory, the problem of the fault detection observer design is transformed into an optimal problem with multiple LMI constraints. The system matrix and Lyapunov function matrix are decoupled by linearizing the nonlinear part and sufficient conditions for the existence of the observer are presented. On the basis of this, an iterative algorithm is proposed to transform the optimal problem with decoupled matrix inequality group constraints into the optimal problem with LMI constraints to solve the fault detection observer. In the residual evaluation, The model uncertainty system is studied with the adaptive threshold. With further consideration that parts of the noise statistical characteristics are known, the introduction of H2norm, H2norm from noise to residual transfer function indicates the effect to residuals. Then a robust fault detection method based on H/H2/H∞observer is presented and the presented method is used on the fault detection of gyro for satellite attitude control system. Design method of fault detection observer is further extended to Lipschitz nonlinear uncertain systems, the sufficient conditions for the existence of system fault detection observer are presented, and on this basis to study the nonlinear robust fault detection for Lipschitz uncertain systems.Considering the system with model uncertainties, a method for robust fault detection based on H∞filter is presented with H∞filter theory. The problem of fault detection filter design is transformed into the optimal problem with matrix inequality constraints by H∞norm theory. With the nonlinear part linearized, an iterative algorithm is proposed to transform the filter design problem into the optimization problem with linear matrix inequalities constraints. In the residual evaluation stage, the threshold is designed using adaptive threshold method and the robust fault detection for uncertain systems is studied. In order to reduce the amount of calculation, a robust fault detection method based on reduced-order H∞filter is presented. With the residual generator constructed by reduced-order filter and using the relationship between the transfer function from input signals and fault signals to the residual errors and the transfer function from input signals and fault signals to the residuals, the problem of filter design is transformed into the optimal problem with multiple H∞norm. On the basis of this research, robust fault detection for the systems with model uncertainties is studied.Considering the uncertain systems with unknown input signal, a method of robust fault estimation based on adaptive sliding mode observer is presented by adaptive observer and sliding mode observer theory. The sliding mode observer is used for fault reconstruction, the adaptive law is used to compensate the effect by unknown input to error system, and the system fault is estimated by sliding part. Use Lyapunov stability criterion to derive the exist conditions of fault estimation observer, and the characteristics of sliding mode motion to present the expressions of fault estimation, and the presented method is used for the flywheel fault estimation of satellite attitude control system.Considering the model uncertainty, a robust fault estimation method based on H∞adaptive observer with H∞filter design method is presented. Lyapunov stability criterion and H∞performance index are used to derive exist conditions of adaptive observer, and the problem of robust fault estimation for uncertain system is transformed into the optimal problem with LMI constraints. At the same time the fault estimation form of expression is given. The proposed method has good robustness on the uncertainties of the system. In the further consideration of Lipschitz nonlinear uncertain systems, a robust fault estimation method based on LMI adaptive observer is proposed. The fault estimation expressions are given and fault estimation is studied in the case that the existence conditions of the adaptive observer are derived using linear matrix inequality theory and Lyapunov stability criterions.