Identifiability of Additive, Time-Varying Actuator and Sensor Faults by State Augmentation

Faults in dynamical systems can have serious safety and reliability implications. For example, actuator and sensor faults have been factors in past incidents and mishaps in many aerospace systems. A large body of research is devoted to developing methods to detect and identify actuator and sensor faults in such systems. One fault detection and identification menthol employs state augmentation, whereby a set of time-varying faults of interest are modeled as outputs of exogenous linear, time-invariant systems and augmented to the state of the nominal system model. The resulting model represents the system dynamics due to a particular actuator-sensor fault configuration. Typically, a filter is associated with each model, and a test matches the model most closely associated with the present system state estimates and measurements. A significant portion of the model-based fault detection and identification literature is concerned with the design of such filters. A basic requirement of these techniques i8 that the modeled fault configuration of interest be identifiable. Recent research has led to a set of necessary and sufficient conditions for identifiability of additive step faults. Such faults manifest themselves as. for example, a stuck control surface or a constant sensor bias. This thesis extends these results by presenting necessary and sufficient conditions for identifiability of additive, time­ varying faults affecting arbitrary combinations of actuators and sensors, either alone or simultaneously. The application of the main theorems is illustrated with two case studies, which provide some insight into how the conditions may be used to check the identifiability of fault configurations of interest for a given system. It is shown that while state augmentation can be used to identify certain fault configurations, other fault configurations cannot be identified. Furthermore. one limitation of model-based methods is that innumerable fault configurations are possible. However, identifiability of known, credible fault configurations can be tested using the theorems presented in this thesis.