Using minimal polynomial bases for fault diagnosis

A fundamental part of a fault diagnosis system is the residual generator. Design of residual generators to achieve perfect decoupling in linear systems is considered. A new method, the minimal polynomial basis approach, is presented, where the residual generation problem is transformed into the 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 degree, and the solution has a minimal parameterization.