Zero Assignment for Robust $H_{2}/H_{\infty}$ Fault Detection Filter Design

In practical engineering, it is inevitable that a system is perturbed by noise signals. Unfortunately, H infin /H infin filtering may fail to detect some faults when the noise distribution matrix are the same as the fault distribution matrix. In this paper, it is shown that the dynamic feedback gain of a dynamic filter introduces additional zeros to the filter, and both the filter poles and the additional zeros can be assigned arbitrarily. In order to attenuate band-limited noises, the zero assignment technique is used, and an optimal dynamic fault detection filtering approach is proposed by locating the zeros to the noise frequencies and optimizing the poles. Compared to other dynamic filter design approaches, the zero assignment technique gives a better tradeoff between more design freedom and computation costs. As shown in the simulation, a better noise attenuation and fault detection performance have been obtained. The zero assignment in multivariable fault detection filter design would be the main contribution of this paper.

[1]  C. T. Pi,et al.  Simultaneous disturbance attenuation and fault detection using proportional integral observers , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  R. Nikoukhah,et al.  Fault detection in a mixed H/sub 2//H/sub /spl infin// setting , 2005, IEEE Transactions on Automatic Control.

[3]  D. Henry,et al.  Design and analysis of robust residual generators for systems under feedback control , 2005, Autom..

[4]  H. Marquez,et al.  Design of unknown input observers for Lipschitz nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[5]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[6]  M. Sain,et al.  Research on system zeros: a survey , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[7]  Zidong Wang,et al.  Robust Filtering for Linear Systems with Error Variance Constraints , 2000 .

[8]  R. Nikoukhah,et al.  Fault detection in a mixed H2/H∞ setting , 2005, IEEE Trans. Autom. Control..

[9]  Daniel W. C. Ho,et al.  State/noise estimator for descriptor systems with application to sensor fault diagnosis , 2006, IEEE Transactions on Signal Processing.

[10]  Lei Guo,et al.  Observer-Based Optimal Fault Detection and Diagnosis Using Conditional Probability Distributions , 2006, IEEE Transactions on Signal Processing.

[11]  Keith J. Burnham,et al.  Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation , 2001, IEEE Trans. Signal Process..

[12]  Qing Zhao,et al.  H/sub /spl infin// observer design for lipschitz nonlinear systems , 2006, IEEE Transactions on Automatic Control.

[13]  Qing Zhao,et al.  LMI-based sensor fault diagnosis for nonlinear Lipschitz systems , 2007, Autom..

[14]  Dong Ryeol Shin,et al.  Dynamic observers for linear time-invariant systems , 2002, Autom..

[15]  R. J. Patton,et al.  An LMI approach to H - /H∞ fault detection observers , 2002 .

[16]  W. Wolovich.  State-space and multivariable theory , 1972 .

[17]  Hong Wang,et al.  Robust observer based FDI and its application to the monitoring of a distillation column , 1993 .

[18]  Fuwen Yang,et al.  Robust H-infinity filtering for stochastic time-delay systems with missing measurements , 2006 .

[19]  Ye. Smagina.  Zero Assignment in Multivariable System Using Pole Assignment Method , 2002 .

[20]  P. Frank,et al.  Survey of robust residual generation and evaluation methods in observer-based fault detection systems , 1997 .

[21]  T. Chai,et al.  A robust fault detection filtering for stochastic distribution systems via descriptor estimator and parametric gain design , 2007 .

[22]  Charles A. Desoer,et al.  Zeros and poles of matrix transfer functions and their dynamical interpretation , 1974 .

[23]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[24]  Minyue Fu,et al.  Robust 𝒽∞ filtering for continuous time varying uncertain systems with deterministic input signals , 1995, IEEE Trans. Signal Process..

[25]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

[26]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

[27]  Biao Huang,et al.  Sampled-data filtering with error covariance assignment , 2001, IEEE Trans. Signal Process..

[28]  Yu Yao,et al.  Observer Design for Lipschitz nonlinear Systems , 2009, Control. Intell. Syst..

[29]  Eric Blanco,et al.  Robust Filtering for Linear Time-Invariant Continuous Systems , 2007, IEEE Transactions on Signal Processing.

[30]  Lihua Xie,et al.  New Approach to Mixed Filtering for Polytopic Discrete-Time Systems , 2005 .

[31]  D. Ho,et al.  Proportional multiple-integral observer design for descriptor systems with measurement output disturbances , 2004 .

[32]  Biao Huang,et al.  Robust H2/H∞ filtering for linear systems with error variance constraints , 2000, IEEE Trans. Signal Process..

[33]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .