A Parametric Approach for Robust Fault Detection in Linear Systems with Unknown Disturbances *

Robust fault detection in linear systems based on full-order state observers

“…This type of residual generators were widely studied [1,6] because such residual generators have lower dynamical orders than the system dimension and offer more degrees of design freedom by the five coefficient matrices to be designed. Another type of observer-based residual generators with the function of disturbance decoupling is based on full-order observers [5,8,9,15] because such an approach has only one coefficient matrix to be designed and hence is simpler. References [4,8,9,15] employed the technique of eigenstructure assignment.…”

“…In [8,9], some left eigenvectors of the observer system are assigned to be orthogonal to the disturbance distribution direction, while in [4] some of the observer right eigenvectors are assigned to the disturbance distribution direction. Unfortunately, in [5,8,9], only a sufficient condition for full-order state observer design with disturbance decoupling is proposed.…”

“…The same as [5], the design purpose is also to design a residual generator so that the effect of the disturbances is decoupled from the residual signal. Different from [5], this paper gives a sufficient and necessary condition for full-order state observer design with disturbance decoupling.…”

“…The same as [5], the design purpose is also to design a residual generator so that the effect of the disturbances is decoupled from the residual signal. Different from [5], this paper gives a sufficient and necessary condition for full-order state observer design with disturbance decoupling. On the basis of the solution to a type of generalized Sylvester matrix equations, parametric expressions of the observer gain matrix and the left eigenvector matrix of the observer system are established in terms of a group of free parameters s i , g i , i = 1, 2, · · · , n. Based on these parametric expressions and a group of introduced vectors p i , i = 1, 2, · · · , n, the condition for disturbance decoupling is converted into some constraints on these design parameters s i , g i , p i , i = 1, 2, · · · , n. In this case, the parametric expression of the weighting matrix is given.…”

Robust fault detection using Luenberger-type unknown input observers-a parametric approach

“…For the design of residual generators, there have been various kinds of approaches, among which the class of observer-based approaches have been most widely considered (Ge and Fang 1988, Ding and Frank 1990, Frank 1990, 1994, WuÈ ennenberg 1990, Patton and Chen 1991, 1992, 1997, Hou and MuÈ ller 1992, 1994, Duan et al 1997, 1999, Duan and Patton 1998. The basic idea behind the observer-based approaches is to construct a residual by using some types of observer.…”