A fault-detection, filter-design method for linear parameter-varying systems

Abstract In this paper a fault-detection (FD), filter-design method has been proposed for linear parameter-varying (LPV) systems. The FD filter is an optimal H∞ Luenberger observer synthesized by minimizing frequency conditions that 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 linear matrix inequality (LMI) optimization problem. The resulting residual generator is parameter-dependent and uses the plant parameter assumed measurable online. Finally, an 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]  A. Packard,et al.  Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback , 1994 .

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

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

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

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

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

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

[8]  Ali Saberi,et al.  Fundamental problems in fault detection and identification , 2000 .

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

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

[11]  J. P. Gauteier G. BORNlrRD.  OBSERVABILITY FOR ANY u(t) OF A CLASS OF NONLINEAR SYSTEMS , 1980 .

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

[13]  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.

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

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

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

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

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

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

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

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

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

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

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