Robust fault detection and isolation of nonlinear systems with augmented state models

Abstract

Model-based fault detection and isolation (FDI) is one of the most important fields in system theory and automation. Roughly speaking, FDI aims at finding and backtracking discrepancies between a system's observed behavior (described by its measurements) and its expected behavior (described by its model). Whenever the model used is uncertain, which means that it does not match the real process accurately, the FDI problem becomes particularly challenging. In practical applications, uncertain system representations are not unusual and thus, incorrect fault detection and false diagnosis can only be prevented, if employed FDI algorithms are robust against model uncertainties. This thesis presents novel modeling, analysis, and synthesis concepts for the robust FDI of nonlinear systems in a discrete-time representation. In the modeling section, a new formalism for the representation of nonlinear systems subject to faults is introduced. The presented model allows the description of a particularly wide class of faulty systems and moves the problems of fault diagnosis and state estimation close together, which would otherwise be different. By exploiting this relationship, novel conditions for linear and nonlinear fault-detectability and -isolability analysis are provided. The proposed conditions are based on well-known observability definitions and can thus be verified by means of established methods from the field of observability analysis. On the basis of the proposed model, the nominal and the Gaussian noisy fault diagnosis problem are expressed as an optimal hybrid state estimation problem. The use of sub-optimal solutions is discussed and illustrated by means of a practical example. In order to cope with uncertain problem formulations including plant-model-mismatch and unanticipated faults, the suggested modeling formalism is modified. Disturbances, modeling uncertainties, and measurement noise are characterized using unknown-but-bounded exogenous inputs. The unknown-but-bounded uncertainty representation proves to be exceptionally practicable, since no specific and difficult assumptions about the uncertainties have to be met a priori. On the other hand, unforeseen plant operations that are not captured by the model, e.g. unanticipated faults and unexpectedly large disturbances, are lumped in an unknown mode of operation. Based on the resulting uncertain model, a robust FDI algorithm is developed that is capable of diagnosing permanent and intermittent faults and furthermore is able to detect unknown modes of operation. Robust fault-detection and -isolation conditions are derived, by which the suggested algorithm is guaranteed to determine a meaningful and unique result. The fault diagnosis methods proposed in this thesis are expressed as algorithms that can be directly implemented and processed in a reasonable time. Several detailed examples, including the three-tank benchmark with unknown-but-bounded modeling uncertainties, demonstrate the properties and the applicability of the proposed methods.