Threshold computation for robust fault detection in a class of continuous-time nonlinear systems

This report presents a study on the problem of residual evaluation and threshold computation for detection of faults in continuous time nonlinear systems. A generalized framework for designing norm-based residual evaluation scheme is proposed. The problem of threshold computation is formulated as an optimization problem and its solution is developed using the well known LMI technique. Three commonly used thresholds i.e. Jth,RMS,2, Jth,Peak,Peak and Jth,P eak,2 are computed. A numerical example is given to show the effectiveness of the proposed approach.

[1]  Steven X. Ding,et al.  Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools , 2008 .

[2]  S. Ding,et al.  Threshold calculation using LMI-technique and its integration in the design of fault detection systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[3]  H.J. Marquez,et al.  Robust H Observer Design for a Class of Nonlinear Uncertain Systems via Convex Optimization , 2007, 2007 American Control Conference.

[4]  James Lam,et al.  An LMI approach to design robust fault detection filter for uncertain LTI systems , 2003, Autom..

[5]  R. Martínez-Guerra,et al.  The fault detection problem in nonlinear systems using residual generators , 2005, IMA J. Math. Control. Inf..

[6]  T. Jeinsch,et al.  A New Optimization Approach to the Design of Fault Detection Filters , 2000 .

[7]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..

[8]  Masoud Abbaszadeh,et al.  Robust Hinfinity observer design for sampled-data Lipschitz nonlinear systems with exact and Euler approximate models , 2008, Autom..

[9]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[10]  Min-Shin Chen,et al.  Robust Nonlinear Observer for Lipschitz Nonlinear Systems Subject to Disturbances , 2007, IEEE Transactions on Automatic Control.

[11]  Torsten Jeinsch,et al.  An LMI approach to robust fault detection filter design for discrete-time systems with model uncertainty , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[13]  Janos Gertler,et al.  Fault detection and diagnosis in engineering systems , 1998 .

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

[15]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[16]  M. Abbaszadeh,et al.  Robust H∞ observer design for sampled-data Lipschitz nonlinear systems with exact and Euler approximate models! , 2008 .

[17]  Torsten Jeinsch,et al.  LMI-BASED INTEGRATION OF ROBUST H∞-CONTROL AND RFD FOR LTI SYSTEMS , 2002 .

[18]  Rafael Martínez-Guerra,et al.  The fault detection problem in nonlinear systems using residual generators , 2005 .

[19]  Andreas Johansson,et al.  Dynamic threshold generators for robust fault detection in linear systems with parameter uncertainty , 2006, Autom..

[20]  Long Wang,et al.  Robust fault detection with missing measurements , 2008, Int. J. Control.

[21]  P. Zhang,et al.  A Simple Fault Detection Scheme for Nonlinear Systems , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[22]  Zhenhai Li,et al.  Computation of a reference model for robust fault detection and isolation residual generation , 2008 .

[23]  Mario G. Perhinschi,et al.  An adaptive threshold approach for the design of an actuator failure detection and identification scheme , 2006, IEEE Transactions on Control Systems Technology.

[24]  Marios M. Polycarpou,et al.  A fault detection and isolation scheme for nonlinear uncertain discrete-time sytems , 2007, 2007 46th IEEE Conference on Decision and Control.

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

[26]  Zhengzhi Han,et al.  A note on observers for Lipschitz nonlinear systems , 2002, IEEE Trans. Autom. Control..

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