State–space solution to the ℋ︁₋/ℋ︁_∞ fault‐detection problem

Abstract

In this paper we give an optimal state-space solution to the H − /H ∞ fault-detection (FD) problem for linear time invariant dynamic systems. An optimal H − /H ∞ FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. We provide a state-space realization of the optimal filter in an observer form using the solution of a linear matrix inequalities optimization problem. We also show that, through the use of weighting filters, the detection performance can be enhanced and some assumptions can be removed. Two numerical examples are given to illustrate the algorithm.

Application of model-based LPV actuator fault estimation for an industrial benchmark

“…It follows from the work in Li et al (2012) and Chen et al (2016) that the corresponding solutions of L 1 (ρ) and L 2 are given by…”

“…The purpose of involving the H − index in an H ∞ optimisation is to establish a tradeoff between the fault sensitivity and the robustness of the residual Hou & Patton (1997). This paper extends the work in Li et al (2012) into an LPV framework and proposes a specific H − index which allows the fault estimation to be achieved in the presence of parametric uncertainties. The parameterizable solution of the fault estimator is then used to construct an H ∞ optimisation procedure.…”

“…This approach has been widely developed in the literature (Ding et al, 2000;Wang et al, 2007;Henry & Zolghadri, 2005;Li et al, 2012;Grenaille et al, 2008;Henry, 2012), based on the original work by Hou & Patton (1997).…”

“…There have been a number of application studies on aircraft flight control involving the generation of FDD residuals which are robust against modelling uncertainty, gust and turbulence Yang & Wang, 2010;Wei & Verhaegen, 2011b;Li et al, 2012). The purpose of involving the H − index in an H ∞ optimisation is to establish a tradeoff between the fault sensitivity and the robustness of the residual Hou & Patton (1997).…”

Entwurf robuster modellbasierter Fehlerisolationsfilter

“…Verwandte Problemstellungen sind aus dem Bereich der Fehlerdetektion bekannt, sie werden wie in Abschnitt 2.5 erörtert typischerweise durch den Einsatz von Gewichtungsfiltern gelöst [25,129,135,247]. Dabei wird wobei Λ ∈ R (2n+n f +n d )×χ eine beliebige Matrix mit mindestens n + n f Spalten ist.…”