Auxiliary Signal Design for Fault Detection in Nonlinear Systems

Abstract

Recently, research has developed in the area of active fault detection and model identification algorithms for linear systems. These algorithms compute an auxiliary input signal which guarantees fault detection, assuming a bounded noise. This dissertation addresses the question of when the previous linear theory can be applied to nonlinear systems. Several case studies are presented to verify that linearizations can in fact produce results in the nonlinear case. Two results are proven about the use of linearizations. The first result gives a parameter which scales the entire problem. Using this parameter, the scaled auxiliary signal, along with a scaled noise bound, will guarantee fault detection in the nonlinear problem. The second result shows how to compute the acceptable noise bound for the nonlinear problem using the exact auxiliary signal from the linearized problem. Also presented is a computational study to verify these two results. Two secondary projects are also presented in this dissertation. The first is a comparison of two different linear algorithms used to compute the optimal auxiliary signal. The second is a port of one of the existing pieces of fault detection software into Matlab. This new software is included, as well as a discuss of the complications of the port.