A minimal polynomial basis solution to residual generation for fault diagnosis in linear systems

A fundamental part of a fault diagnosis system is the residual generator. Here a new method, the minimal polynomial basis approach, for design of residual generators for linear systems, is presented. The residual generation problem is transformed into a problem of finding polynomial bases for null-spaces of polynomial matrices. This is a standard problem in established linear systems theory, which means that numerically efficient computational tools are generally available. It is shown that the minimal polynomial basis approach can find all possible residual generators, including those of minimal McMillan degree, and the solution has a minimal parameterization. It is shown that some other well known design methods, do not have these properties.