Brief An LMI approach to design robust fault detection filter for uncertain LTI systems

  • Authors:

  • Maiying Zhong;Steven X. Ding;James Lam;Haibo Wang

  • Affiliations:

  • Control Sciences and Engineering School, Shandong University, 73 Jingshi Road, Jinan 250061, China;Institute of Automatic Control and Complex Systems, Gerhard-Mercator-Universität Duisburg, Bismarckstrasse 81 BB, 47048 Duisburg, Germany;Department of Mechanical Engineering, University of Hong Kong, Hong Kong;School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2003

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Abstract

In this paper, the robust fault detection filter design problem for uncertain linear time-invariant (LTI) systems with both unknown inputs and modelling errors is studied. The basic idea of our study is to use an optimal residual generator (assuming no modelling errors) as the reference residual model of the robust fault detection filter design for uncertain LTI systems with modelling errors and, based on it, to formulate the robust fault detection filter design as an H"~ model-matching problem. By using some recent results of H"~ optimization, a solution of the optimization problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the development of an optimal reference residual model, the formulation of robust fault detection filter design problem, the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the LMI solution parameters, the determination of adaptive threshold for fault detection. An illustrative design example is employed to demonstrate the effectiveness of the proposed approach.