A unified theory of fault detection and isolation in dynamic systems.

In this dissertation a unified theory of the fault detection filter is developed to take into account both sensor and actuator faults, as well as deterministic and stochastic system models. The fault detection filter problem is reformulated by means of a series of linear transformations, after the detection filter is re-interpreted through a special eigenstructure which is accomplished by an eigenvalue-eigenvector assignment technique. As a consequence of the novel formulation introduced here, the detection filter is shown to be equivalent to the combination of two decoupled observers, with the advantage that theories already developed for conventional observers can be utilized as design aids. The detection space and detection order are re-defined accordingly, and it is shown that of the two observers which constitute a detection filter, that associated with the detection space is a single-output system. This fact is important since it explains important properties of the fault detection filter in a very uncomplicated fashion, leading to a clear interpretation of the freedom available in designing the filter; in particular, it is shown that the detection filter gains are unique, given the eigenvalues of the detection space. Further, the formulation leads to a closed-form expression for the detection filter, and is therefore well-suited to the development of simple design algorithms. These results are also extended to the detection and identification of sensor faults by formulating sensor faults in a special way permitting them to be treated in the same fashion as actuator faults. Another important consequence of the results described above is that the closed-form expression for the detection filter permits the formulation of the optimal detection filter problem, for optimization with respect to process and measurement noises. The necessary conditions for the existence of the optimal detection filter are obtained, and a numerical solution technique is shown to be feasible by virtue of the uniqueness of the detection filter gains. Finally, the unified theory of detection filters is applied in the simulation of a physical system--a hydraulically controlled active suspension system--to illustrate its application in an engineering context.PhDApplied SciencesAutomotive engineeringElectrical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128769/2/9135669.pd