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2017 | OriginalPaper | Chapter

2. Modelling Systems with Faults

Author : Andreas Varga

Published in: Solving Fault Diagnosis Problems

Publisher: Springer International Publishing

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Abstract

In this chapter, the main types of faults are first reviewed and linear time-invariant plant models with additive faults are introduced. These models represent the basis of the synthesis approaches of fault detection filters presented in this book. Models with fictive noise inputs can be used to account for the effects of parametric variations. Two approaches are presented to arrive at such models starting from linear parameter-varying models and multiple linear time-invariant models. Physical fault modelling leads naturally to multiple-model representations, which form the basis of the synthesis methods of model detection filters.

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Footnotes
1
An upper LFT for a partitioned matrix \(M = \left[ \begin{array}{cc} M_{11} &{} M_{12} \\ M_{21} &{} M_{22} \end{array} \right] \) and a compatible \(\varDelta \) is defined as \(LFT_u(M,\varDelta ) := M_{22} + M_{21}\varDelta (I-\varDelta M_{11})^{-1}M_{12}\).
 
Metadata
Title
Modelling Systems with Faults
Author
Andreas Varga
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-51559-5_2