Fault Isolation for Large Scale Discrete-Time Systems Based on Implicit Set Representation

To detect faults in a system we can adopt an observer, designed for the healthy system, and monitor the discrepancy between actual and expected behaviour of the residual (difference between the system output and its estimate). To isolate faults, we can compute the invariant sets associated with each fault, and their projection in the residual space (limit set): faults can be isolated if the associated limit sets are separated when a (constant) test input is applied. However, the explicit computation of limit sets can be hard even for low-dimensional systems. As a main contribution, we show that, by adopting an implicit representation of limit sets, very efficient procedures can be used to solve the problem, based on convex quadratic programming or linear programming. Simulations show that the approach is effective in solving even large dimensional problems, which makes it suitable for large- scale networked systems.

[1]  Miroslav Simandl,et al.  Constrained Active Fault Detection and Control , 2015, IEEE Transactions on Automatic Control.

[2]  Henrik Niemann,et al.  A Setup for Active Fault Diagnosis , 2006, IEEE Transactions on Automatic Control.

[3]  Sorin Olaru,et al.  Set-theoretic Fault-tolerant Control in Multisensor Systems: Stoican/Set-theoretic Fault-tolerant Control in Multisensor Systems , 2013 .

[4]  Stephen L. Campbell,et al.  Active Robust Fault Detection in Closed-Loop Systems: Quadratic Optimization Approach , 2012, IEEE Transactions on Automatic Control.

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

[6]  Franco Blanchini,et al.  Active Fault Isolation: A Duality-Based Approach via Convex Programming , 2017, SIAM J. Control. Optim..

[7]  José A. De Doná,et al.  Positive invariant sets for fault tolerant multisensor control schemes , 2010, Int. J. Control.

[8]  Vicenç Puig,et al.  Robust fault detection using zonotope‐based set‐membership consistency test , 2009 .

[9]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[10]  B. Krogh,et al.  Hyperplane method for reachable state estimation for linear time-invariant systems , 1991 .

[11]  José A. De Doná,et al.  Multisensor switching control strategy with fault tolerance guarantees , 2008, Autom..

[12]  José A. De Doná,et al.  Reference governor design for tracking problems with fault detection guarantees , 2012 .

[13]  Richard D. Braatz,et al.  Closed-loop input design for guaranteed fault diagnosis using set-valued observers , 2016, Autom..

[14]  Richard D. Braatz,et al.  Optimum input design for fault detection and diagnosis: Model-based prediction and statistical distance measures , 2013, 2013 European Control Conference (ECC).

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

[16]  Daniel Liberzon,et al.  On Invertibility of Switched Linear Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[17]  Ali Zolghadri,et al.  Set Adaptive Observers for Linear Parameter-Varying Systems: Application to Fault Detection , 2014 .

[18]  François Delebecque,et al.  Auxiliary signal design for robust multimodel identification , 2002, IEEE Trans. Autom. Control..

[19]  Ramine Nikoukhah,et al.  Auxiliary Signal Design for Failure Detection , 2004 .

[20]  Richard D. Braatz,et al.  Active fault diagnosis using moving horizon input design , 2013, 2013 European Control Conference (ECC).

[21]  José A. De Doná,et al.  Fault Tolerant Control Allowing Sensor Healthy-to-Faulty and Faulty-to-Healthy Transitions , 2012, IEEE Transactions on Automatic Control.

[22]  Ramine Nikoukhah,et al.  Guaranteed Active Failure Detection and Isolation for Linear Dynamical Systems , 1998, Autom..

[23]  Sorin Olaru,et al.  Controlled invariance-based fault detection for multisensory control systems , 2013 .

[24]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[25]  Richard D. Braatz,et al.  Input design for guaranteed fault diagnosis using zonotopes , 2014, Autom..

[26]  Jakob Stoustrup,et al.  Active fault diagnosis by controller modification , 2010, Int. J. Syst. Sci..

[27]  Ali Zolghadri,et al.  Interval observer design for consistency checks of nonlinear continuous-time systems , 2010, Autom..

[28]  Christophe Combastel,et al.  Fault detection based on robust adaptive thresholds: A dynamic interval approach , 2013, Annu. Rev. Control..

[29]  Konstantinos I. Kouramas,et al.  Invariant approximations of the minimal robust positively invariant set via finite time Aumann Integrals , 2007, 2007 46th IEEE Conference on Decision and Control.

[30]  Vicenç Puig,et al.  Set-membership parity space approach for fault detection in linear uncertain dynamic systems , 2012 .

[31]  Stephen L. Campbell,et al.  Effects of feedback on active fault detection , 2012, Autom..

[32]  Andreas Varga.  Solving Fault Diagnosis Problems: Linear Synthesis Techniques , 2017 .

[33]  Anthony Tzes,et al.  Fault diagnosis based on set membership identification using output‐error models , 2016 .

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

[35]  Vasso Reppa,et al.  Fault detection and diagnosis based on parameter set estimation , 2011 .