Robust fault diagnosis in linear and nonlinear systems based on unknown input, and sliding mode functional observer methodologies

The field of observer based fault diagnosis for complex control systems has become an important topic of research in the control community over the last three decades. Recently, special attention has been paid to the problem of robust fault diagnosis for linear and nonlinear uncertain systems. Many proposed fault diagnosis approaches are based on robust state observer techniques, which can provide the right estimation of system states under the existence of a large class of model uncertainties and disturbances, known as unknown inputs. It is noted that robust state estimation requires strong restrictive existence conditions, which confines its practical application. On the other hand, it is unnecessary to estimate all states for the objective of fault diagnosis. This thesis is an attempt to accomplish robust fault diagnosis under weaker existence conditions through the development of the unknown input and sliding mode functional observer theory. The proposed functional observers can estimate a function of system states by decoupling the effect of the unknown inputs.; The necessary and sufficient conditions for the existence of unknown input functional observer (UIFO) for linear systems are obtained with the aid of Loop Transfer Recovery (LTR) technique. A constructive design procedure is given. The problem of estimating the unknown input is also addressed. Two kinds of reduced-order unknown input estimators using only measured outputs are presented. They extend full-order input estimators design in the existing literature and have advantage of working for certain class of non minimum phase systems.; Under a UIFO framework, the unknown input decoupled residual generator is developed, and the remaining freedom for fault diagnosis observer design, after unknown input decoupling, is completely revealed. A fault diagnosis algorithm is proposed, which combines unknown input decoupling theory and the Beard-Jones detection filter, or input estimator. This algorithm offers maximum residual dimension and is therefore more applicable than existing robust fault diagnosis schemes which are based on unknown input observer. Representation of a sensor fault, as a mathematical equivalent of an actuator fault, is further developed. The structured properties of the augmented system for sensor fault detection are provided.; The results for linear systems are extended to bilinear systems with unknown inputs. For bilinear systems, a robust fault diagnosis observer with linear estimation error dynamic can be derived under special structured conditions. A robust fault diagnosis observer with bilinear estimation error dynamic which improves the fault isolation capability of the system is proposed under less conservative conditions. For a class of bilinear systems with bounded control inputs, the existence conditions for a robust fault diagnosis observer are relaxed further.; A robust functional observer design, using the sliding mode principle, is studied in depth for linear systems and for a class of nonlinear systems, which are subject to bounded unknown inputs. The connections between the unknown input observer and the sliding mode observer methodology are investigated. It is shown that a sliding mode functional observer (SMFO) can be designed under weaker conditions than those for UIFO. Finally, the potential advantages and disadvantages of fault diagnosis using, SMFO are discussed extensively.; Numerical examples are presented throughout the thesis to illustrate the applicability of the proposed estimation and fault diagnosis methods. Many of these cannot be handled by the existing methods in the literature.