Robust fault detection of singular LPV systems with multiple time–varying delays

Abstract In this paper, the robust fault detection problem for LPV singular delayed systems in the presence of disturbances and actuator faults is considered. For both disturbance decoupling and actuator fault detection, an unknown input observer (UIO) is proposed. The aim is to compute a residual signal which has minimum sensitivity to disturbances while having maximum sensitivity to faults. Robustness to unknown inputs is formulated in the sense of the ℋ∞-norm by means of the bounded real lemma (BRL) for LPV delayed systems. In order to formulate fault sensitivity conditions, a reference model which characterizes the ideal residual behavior in a faulty situation is considered. The residual error with respect to this reference model is computed. Then, the maximization of the residual fault effect is converted to minimization of its effect on the residual error and is addressed by using the BRL. The compromise between the unknown input effect and the fault effect on the residual is translated into a multi-objective optimization problem with some LMI constraints. In order to show the efficiency and applicability of the proposed method, a part of the Barcelona sewer system is considered.

[1]  Hamid Reza Karimi,et al.  Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay , 2016, Int. J. Syst. Sci..

[2]  H. Karimi,et al.  Discrete‐time H −  ∕ H ∞  sensor fault detection observer design for nonlinear systems with parameter uncertainty , 2015 .

[3]  Qingling Zhang,et al.  Fault detection for singular multiple time-delay systems with application to electrical circuit , 2014, J. Frankl. Inst..

[4]  Hamid Reza Karimi,et al.  Robust Unknown Input Observer Design for Linear Uncertain Time Delay Systems with Application to Fault Detection , 2014 .

[5]  Didier Theilliol,et al.  Robust sensor FDI observer for polytopic descriptor LPV systems with unmeasurable scheduling varying parameter , 2014, 2014 American Control Conference.

[6]  Vicenç Puig,et al.  Linear parameter varying modeling and identification for real-time control of open-flow irrigation canals , 2014, Environ. Model. Softw..

[7]  Hamid Reza Karimi,et al.  Design of unknown inputs proportional integral observers for TS fuzzy models , 2014, Neurocomputing.

[8]  Masoud Shafiee,et al.  Modelling and analysis of quadruped walking robot using singular system theory , 2013, 2013 21st Iranian Conference on Electrical Engineering (ICEE).

[9]  Vicenç Puig,et al.  Limnimeter and rain gauge FDI in sewer networks using an interval parity equations based detection approach and an enhanced isolation scheme , 2013 .

[10]  C. Ocampo‐Martinez,et al.  Application of predictive control strategies to the management of complex networks in the urban water cycle [Applications of Control] , 2013, IEEE Control Systems.

[11]  N. Braiek,et al.  Robust fault detection and estimation for descriptor systems based on multi-models concept , 2012 .

[12]  H. Karimi,et al.  Robust Observer Design for Takagi-Sugeno Fuzzy Systems with Mixed Neutral and Discrete Delays and Unknown Inputs , 2012 .

[13]  Xian Zhang,et al.  Robust Stability and Stabilization Criteria for Discrete Singular Time‐Delay LPV Systems , 2012 .

[14]  Xian Zhang,et al.  A delay‐dependent bounded real lemma for singular LPV systems with time‐variant delay , 2012 .

[15]  N. Braiek,et al.  Fault detection and isolation in linear parameter‐varying descriptor systems via proportional integral observer , 2012 .

[16]  Vicenç Puig,et al.  Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter , 2012, Int. J. Appl. Math. Comput. Sci..

[17]  Vicenç Puig,et al.  Robust fault detection based on adaptive threshold generation using interval LPV observers , 2012 .

[18]  Fotis N. Koumboulis,et al.  Towards fault detection in singular Leontief production models , 2011, ETFA2011.

[19]  Wei Xing Zheng,et al.  Fault Detection Filter Design for Markovian Jump Singular Systems With Intermittent Measurements , 2011, IEEE Transactions on Signal Processing.

[20]  Ming-Yu Zhang,et al.  H∞ fault detection for linear singular systems with time-varying delay , 2011 .

[21]  Ehsan Samiei,et al.  Descriptor modeling and response analysis of two rigid-flexible cooperative arms , 2010, 2010 11th International Conference on Control Automation Robotics & Vision.

[22]  G. Duan.  Analysis and Design of Descriptor Linear Systems , 2010 .

[23]  Mickael Rodrigues,et al.  Robust H∞ fault diagnosis for multi-model descriptor systems: A multi-objective approach , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[24]  Yong He,et al.  Stability Analysis and Robust Control of Time-Delay Systems , 2010 .

[25]  H. D. Taghirad,et al.  Unknown input-proportional integral observer for singular systems: Application to fault detection , 2010, 2010 18th Iranian Conference on Electrical Engineering.

[26]  Khashayar Khorasani,et al.  Robust fault detection and isolation of time-delay systems using a geometric approach , 2009, Autom..

[27]  G Cembrano,et al.  Predictive optimal control of sewer networks using CORAL tool: application to Riera Blanca catchment in Barcelona. , 2009, Water science and technology : a journal of the International Association on Water Pollution Research.

[28]  Alexandre Falcoz,et al.  Structured H∞/H_ LPV filters for fault diagnosis: Some new results , 2009 .

[29]  B. Marx,et al.  Fault diagnosis for Takagi-Sugeno nonlinear systems , 2009 .

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

[31]  Jian Liu,et al.  An LMI approach to H_ index and mixed H_/Hinfinit fault detection observer design , 2007, Autom..

[32]  Jian Liu,et al.  An LMI approach to h_ index and mixed h_ /h∞ fault detection observer design , 2007 .

[33]  J. L. Wang,et al.  An LMI approach to index and mixed fault detection observer design. , 2007 .

[34]  Erik Frisk,et al.  Robust residual generation for diagnosis including a reference model for residual behavior , 2006, Autom..

[35]  D. Koenig,et al.  Unknown Input Observers Design for Time-Delay Systems Application to An Open-Channel , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[36]  Shigeyasu Kawaji,et al.  FAULT DETECTION, ISOLATION AND RECONSTRUCTION FOR DESCRIPTOR SYSTEMS , 2005 .

[37]  Damien Koenig,et al.  Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation , 2005, IEEE Transactions on Automatic Control.

[38]  Mohammed Salah Saadni,et al.  Stability and stabilizability of a class of uncertain dynamical systems with delays , 2005 .

[39]  G. Duan,et al.  Design of Unknown Input Observer for Linear Time-delay Systems , 2004 .

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

[41]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[42]  Guang-Ren Duan,et al.  Robust fault detection in descriptor linear systems via generalized unknown input observers , 2002, Int. J. Syst. Sci..

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

[44]  Olivier Sename,et al.  An unknown input observer design for linear time-delay systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

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

[46]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

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

[48]  M. Boutayeb,et al.  Design of observers for descriptor systems , 1995, IEEE Trans. Autom. Control..

[49]  M. Darouach.  On the novel approach to the design of unknown input observers , 1994, IEEE Trans. Autom. Control..

[50]  Paul M. Frank,et al.  Model-Based Fault Diagnosis , 1992, Concise Encyclopedia of Modelling & Simulation.

[51]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[52]  Jeff S. Shamma,et al.  Analysis and design of gain scheduled control systems , 1988 .

[53]  L. Tiger.  Book Review: Africa: Neo-Colonialism , 1967 .