A Fault Detection filter design method for a class of linear time-varying systems

In this paper we propose a Fault Detection (FD) filter design method for linear parameter varying (LPV) systems. The FD filter is an optimal Hinfin Luenberger observer synthesized by minimizing frequency conditions which ensure guaranteed levels of disturbance rejection and fault detection. Via the Bounded Real Lemma (BRL) and the Separation Principle the design method is formulated as a convex LMI optimization problem. The resulting residual generator is parameter-dependent and uses the plant parameter assumed measurable on-line. Finally, a FD threshold logic is proposed in order to reduce the generation of false alarms. The effectiveness of the design technique is illustrated via a numerical example.

[1]  Gary J. Balas,et al.  Detection filter design for LPV systems - a geometric approach , 2004, Autom..

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

[3]  József Bokor,et al.  H∞ Detection Filter Design for Linear Systems: Comparison of Two Approaches , 1996 .

[4]  Rolf Isermann,et al.  Supervision, fault-detection and fault-diagnosis methods — An introduction , 1997 .

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

[6]  Dominique Sauter,et al.  Frequency-domain optimization for robust fault detection and isolation in dynamic systems , 1999, IEEE Trans. Autom. Control..

[7]  Paul M. Frank,et al.  Issues of Fault Diagnosis for Dynamic Systems , 2010, Springer London.

[8]  Alessandro Casavola,et al.  A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: an LMI approach , 2005, Autom..

[9]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[10]  Andres Marcos,et al.  Linear Parameter Varying Modeling of the Boeing 747-100/200 Longitudinal Motion , 2001 .

[11]  J. Gauthier,et al.  Observability for any of a class of nonlinear systems , 1981 .

[12]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

[13]  József Bokor,et al.  Detection filter design within the LPV framework , 2000, 19th DASC. 19th Digital Avionics Systems Conference. Proceedings (Cat. No.00CH37126).

[14]  A. Packard,et al.  Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback , 1994 .

[15]  Alessandro Casavola,et al.  Robust fault detection of uncertain linear systems via quasi-LMIs , 2005, Proceedings of the 2005, American Control Conference, 2005..

[16]  Steven X. Ding,et al.  Frequency domain approach to optimally robust residual generation and evaluation for model-based fault diagnosis , 1994, Autom..

[17]  Ali Saberi,et al.  Exact, almost and delayed fault detection-an observer based approach , 1999 .

[18]  Ali Saberi,et al.  Fundamental problems in fault detection and identification , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

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

[20]  Ali Saberi,et al.  Optimal fault signal estimation , 2002 .

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

[22]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[23]  Jie Chen,et al.  H∞ Formulation and Solution for Robust Fault Diagnosis , 1999 .

[24]  J. Daafouz,et al.  Parameter-dependent state observer design for affine LPV systems , 2001 .

[25]  Dominique Sauter,et al.  Optimal thresholding for robust fault detection of uncertain systems , 2000 .

[26]  M. Grassi,et al.  AIAA Guidance, Navigation, and Control Conference , 2008 .

[27]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..

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

[29]  Janos Gertler,et al.  Robust FDI systems and H/sub /spl infin//-optimization-disturbances and tall fault case , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[30]  J. Bokor,et al.  DETECTION FILTER DESIGN FOR LPV SYSTEMS – A GEOMETRIC APPROACH , 2002 .

[31]  Jian Liu,et al.  An LMI approach to minimum sensitivity analysis with application to fault detection , 2005, Autom..

[32]  G. Bornard,et al.  Observability for any u(t) of a class of nonlinear systems , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[33]  G. Balas,et al.  Development of linear-parameter-varying models for aircraft , 2004 .