Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems

Abstract In this paper a new integrated observer-based fault estimation and accommodation strategy for discrete-time piecewise linear (PWL) systems subject to actuator faults is proposed. A robust estimator is designed to simultaneously estimate the state of the system and the actuator fault. Then, the estimate of fault is used to compensate for the effect of the fault. By using the estimate of fault and the states, a fault tolerant controller using a PWL state feedback is designed. The observer-based fault-tolerant controller is obtained by the interconnection of the estimator and the state feedback controller. We show that separate design of the state feedback and the estimator results in the stability of the overall closed-loop system. In addition, the input-to-state stability (ISS) gain for the closed-loop system is obtained and a procedure for minimizing it is given. All of the design conditions are formulated in terms of linear matrix inequalities (LMI) which can be solved efficiently. Also, performance of the estimator and the state feedback controller are minimized by solving convex optimization problems. The efficiency of the method is demonstrated by means of a numerical example.

[1]  Nathan van de Wouw,et al.  Reconfigurable control of piecewise affine systems with actuator and sensor faults: Stability and tracking , 2011, Autom..

[2]  Nathan van de Wouw,et al.  Reconfigurable control of PWA systems with actuator and sensor faults: Stability , 2008, 2008 47th IEEE Conference on Decision and Control.

[3]  Thomas Bak,et al.  Reconfigurability of Piecewise Affine Systems Against Actuator Faults , 2011 .

[4]  Vicenç Puig,et al.  Fault‐tolerant model predictive control within the hybrid systems framework: Application to sewer networks , 2009 .

[5]  Youmin Zhang,et al.  Fault detection and identification for bimodal piecewise affine systems , 2009, 2009 American Control Conference.

[6]  Patrizio Colaneri,et al.  Root mean square gain of discrete-time switched linear systems under dwell time constraints , 2011, Autom..

[7]  Mario Vasak,et al.  Identification of a discrete-time piecewise affine model of a pitch-controlled wind turbine , 2011, 2011 Proceedings of the 34th International Convention MIPRO.

[8]  Mogens Blanke,et al.  Fault-tolerant control systems — A holistic view , 1997 .

[9]  O. Diekmann,et al.  On the bounded solutions of a nonlinear convolution equation , 1978 .

[10]  Kazuyuki Aihara,et al.  Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[11]  Bin Jiang,et al.  Fault Tolerant Control Design for Hybrid Systems , 2010 .

[12]  M. V. Iordache,et al.  Diagnosis and Fault-Tolerant Control , 2007, IEEE Transactions on Automatic Control.

[13]  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).

[14]  Bart De Schutter,et al.  Equivalence of hybrid dynamical models , 2001, Autom..

[15]  Karim Salahshoor,et al.  A Clustering-Based Bounded-Error Approach for Identification of PWA Hybrid Systems , 2006, 2006 9th International Conference on Control, Automation, Robotics and Vision.

[16]  Ron J. Patton,et al.  FAULT-TOLERANT CONTROL SYSTEMS: THE 1997 SITUATION , 1997 .

[17]  Andreas Kroll,et al.  On identification of piecewise-affine models for systems with friction and its application to electro-mechanical throttles , 2012 .

[18]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[19]  Anders P. Ravn,et al.  Passive fault-tolerant control of discrete time piecewise affine systems against actuator faults , 2012, Int. J. Syst. Sci..

[20]  Barbara Zitov a.  Journal of the Franklin Institute , 1942, Nature.

[21]  E. A. Woods,et al.  Fault detection, supervision and safety for technical processes , 1993 .

[22]  Manfred Morari,et al.  A clustering technique for the identification of piecewise affine systems , 2001, Autom..

[23]  Mircea Lazar,et al.  Global input-to-state stability and stabilization of discrete-time piecewise affine systems , 2008 .

[24]  Marcel Staroswiecki,et al.  Fault Accommodation for Nonlinear Dynamic Systems , 2006, IEEE Transactions on Automatic Control.

[25]  G.M. Bara,et al.  Switched Output Feedback Stabilization of Discrete-Time Switched Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[26]  Patrizio Colaneri,et al.  A Nonconservative LMI Condition for Stability of Switched Systems With Guaranteed Dwell Time , 2012, IEEE Transactions on Automatic Control.

[27]  Cesare Alippi,et al.  Fault Diagnosis Systems , 2014 .

[28]  Bin Jiang,et al.  A fault tolerant control framework for periodic switched non-linear systems , 2009, Int. J. Control.

[29]  Nathan van de Wouw,et al.  Tracking and synchronisation for a class of PWA systems , 2008, Autom..

[30]  JinJiang.  Fault-tolerant Control Systems--An Introductory Overview , 2005 .

[31]  M. Johansson,et al.  Piecewise Linear Control Systems , 2003 .

[32]  Gouhei Tanaka,et al.  Mathematically modelling and controlling prostate cancer under intermittent hormone therapy. , 2012, Asian journal of andrology.