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.
QiuZ.GertlerJ.Robust F.D.I. systems and optimisation. Disturbances and tall fault case. In Proceedings of the 32nd IEEE CDC, San Antonio, Texas, 1993, Vol. 3, pp. 1710–1715.
2.
FrankP. M.DingX.Frequency domain approach to optimally robust residual generation and evaluation for model-based fault diagnosisAutomatica, 1994, 30, 789–804.
3.
EdelmayerA.BokorJ.KeviczkyL.H∞ detection filter design for linear systems: comparison of two approaches. In 13th IFAC World Congress, San Francisco, 1996, pp. 37–42.
4.
FrankP. M.DingX.Survey of robust residual generation and evaluation methods in observer-based fault detection systems. Survey and some new resultsJ. Process Control, 1997, 7 (6), 403–424.
ChenJ.PattonR. J.H∞ formulation and solution for robust fault diagnosis. In 14th World Congress of IFAC, Beijing, PR China, 1999, pp. 127–132.
7.
GertlerJ.Fault detection and diagnosis in engineering systems, 1998 (Marcel Dekker, New York).
8.
NiemannH.SaberiA.StoorvogelA.SannutiP.Exact, almost and delayed fault detection: An observer based approachInt. J. Robust and Nonlinear Control, 1999, 9, 215–238.
9.
SauterD.HamelinF.Frequency-domain optimisation for robust fault detection and isolation in dynamic systemsIEEE Trans. Autom. Control, 1999, 44 (4), 878–883.
10.
SaberiA.StoorvogelA.SannutiP.NiemannH.Fundamental problems in fault detection and identificationInt. J. Robust and Nonlinear Control, 2000, 10, 1209–1236.
11.
StoorvogelA.NiemannH.SaberiA.SannutiP.Optimal fault signal estimationInt. J. Robust and Nonlinear Control, 2002, 12, 697–727.
12.
PattonR. J.FrankP. M.ClarkP. M.Issues of fault diagnosis for dynamic systems, 2000 (Springer-Verlag, Berlin).
13.
IsermannR.Supervision, fault-detection and fault-diagnosis methods - an introductionControl Engng Practice, 1997, 5 (5), 639–652.
14.
GahinetP.ApkarianP.ChilaliM.Affine parameter dependent Lyapunov functions and real parametric uncertaintyIEEE Trans. Autom. Control, 1996, 41, 436–442.
15.
TanakaK.IkedaT.WangH. O.Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designsIEEE Trans. on Fuzzy Systems, 1998, 6, 250–265.
16.
BokorJ.BalasG.Detection filter design within the LPV framework In Digital Avionics Systems Conferences, Philadelphia, Pennsylvania, 2000, pp. 6A3/1-6A3/5.
17.
BaraG. I.DaafouzJ.KratzF.RagotJ.Parameter-dependent state observer design for affine LPV systemsInt. J. Control, 2001, 74 (16), 1601–1611.
18.
BokorJ.BalasG.Detection filter design for LPV systems - a geometric approachAutomatica, 2004, 40, 511–518.
19.
CasavolaA.FamularoD.FranzèG.A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: An LMI approachAutomatica, 2005, 41, 1463–1472.
20.
CasavolaA.FamularoD.FranzèG.Robust fault detection of uncertain linear systems via quasi-LMIs. In 2005 American Control Conference, Portland, Oregon, 2005, pp. 1654–1659.
21.
BoydS.El GhaouiL.FeronE.BalakrishnanV.Linear matrix inequalities in system and control theorySIAM Studies in Appl. Mathematics, 1994, 15.
22.
RambeauxF.HamelinF.SauterD.Optimal thresholding for robust fault detection of uncertain systemsInt. J. Robust and Nonlinear Control, 2000, 10, 1155–1173.
23.
ZhongM.DingS. X.LamJ.HaiboW.An LMI approach to design robust fault detection filter for uncertain LTI systemsAutomatica, 2003, 39, 543–550.
24.
KhosrowjerdiM. J.NikoukhahR.Safari-ShadN.Fault detection in a mixed H2 H∞ settingIEEE Trans. Autom. Control, 2005, 50 (7), 1063–1068.
25.
LiuJ.WangJ. L.YangG. H.An LMI approach to minimum sensitivity analysis with application to fault detectionAutomatica, 2005, 41, 1995–2004.
26.
ApkarianP.GahinetP.BeckerG.Self-scheduled H∞ control of linear parameter-varying systems: a design exampleAutomatica, 1995, 31 (9), 1251–1261.
27.
GauthierJ. P.BornardG.Observability for any u(t) of a class of nonlinear systemsIEEE Trans. Autom. Control, 1981, 26 (4), 875–880.
28.
BeckerG.PackardA.Robust performance of linear parametrically varying systems using para-metrically-dependent linear feedbackSystems and Control Lett., 1994, 23, 205–215.
