Set-theoretic methods in robust detection and isolation of sensor faults

Abstract

This paper proposes a sensorfault detection and isolation (FDI) approach based on interval observers and invariant sets. In fault detection (FD), both interval observer-based and invariant set-based mechanisms are used to provide real-time fault alarms. In fault isolation (FI), the proposed approach also uses these two different mechanisms. The former, based on interval observers, aims to isolate faults during the transient-state operation induced by faults. If the former does not succeed, the latter, based on both interval observers and invariant sets, is started to guarantee FI after the system enters into steady state. Besides, a collection of invariant set-based FDI conditions are established by using all available system-operating information provided by all interval observers. In order to reduce computational complexity, a method to remove all available but redundant/unnecessary system-operating information is incorporated into this approach. If the considered faults satisfy the proposed FDI conditions, it can be guaranteed that they are detectable and isolable after their occurrences. This paper concludes with a case study based on a subsystem of a wind turbine benchmark, which can illustrate the effectiveness of this FDI technique.

Keywords:

• fault detection and isolation
• interval observers
• positively invariant sets
• linear systems
• zonotopes

Notes

1. The equivalence of (10) and (12(12) $$\begin{array}{ccc}\hfill {\breve{X}}_{k+1}^{ij}& =& (A-L_j{G}_{j}C){\breve{X}}_k^{ij}\oplus L_j(G_j-G_i)CX\oplus L_{j}V\hfill \\ & & \oplus (-W)\oplus (-L_{j}V)\oplus W.\hfill \end{array}$$(12) ) can be verified by applying zonotope operations into (12(12) $$\begin{array}{ccc}\hfill {\breve{X}}_{k+1}^{ij}& =& (A-L_j{G}_{j}C){\breve{X}}_k^{ij}\oplus L_j(G_j-G_i)CX\oplus L_{j}V\hfill \\ & & \oplus (-W)\oplus (-L_{j}V)\oplus W.\hfill \end{array}$$(12) ) to obtain its centre-segment matrix equivalent form, which is the same as (10).

2. Because, in any mode, residual zonotopes are obtainable, without ambiguity, the notation Rⁱ_k corresponding to the ith mode can be generally replaced by the notation R_k.

3. Notice that, for the proposed FDI approach, if it is used for detecting recovery process, then one still uses the terms such as fault detection and isolation and fault occurrence to describe the general mode switching.

4. The form of this feedback signal completely respects the original structure of the second pitch system in the wind turbine benchmark proposed in Odgaard et al. (2009).

5. In this case study, as an example, the reference input u^ref(t) is chosen as a sinusoidal signal.

Additional information

Funding

The work has been partially funded by the DGR of Generalitat de Catalunya [SAC group Ref. 2014/SGR/0375]; European Commission through contract i-Sense [grant number FP7-ICT-2009-6-270428]; China Scholarship Council [Ref. 2011629170]; the Sectoral Operational Programme Human Resources Development 2007–2013 of the Ministry of European Funds through the Financial Agreement [grant number POSDRU/159/1.5/S/132395].

Notes on contributors

Feng Xu

Feng Xu was born on 4 January 1988 (or 15 November 1987 in the lunar calender) in Tianmen, Hubei, P.R. China. He received his BSc degree in measurement and control technology & instruments from the Northwestern Polytechnical University (NWPU), Xi'an, Shaanxi, P.R.China, in July 2010. In November 2014, he received his Ph.D. degree in automatic control from the Institut de Robótica i Informática Industrial (CSIC-UPC), Technical University of Catalonia (UPC), Barcelona, Spain. His research interests are fault diagnosis and fault-tolerant control.

Vicenç Puig

Vicenç Puig was born in Girona, Spain, on 6 November 1969. He received his Ph.D. degree in control engineering in 1999 and his Telecommunications Engineering degree in 1993, both from the Technical University of Catalonia (UPC), Barcelona, Spain. He is currently an associate professor of automatic control and leader of the Advanced Control Systems (SAC) research group of the Research Center for Supervision, Safety and Automatic Control (CS2AC) at UPC. His main research interests are fault detection and isolation of fault-tolerant control of dynamic systems. He has remained involved in several European projects and networks and has published many papers in international conference proceedings and scientific journals.

Carlos Ocampo-Martinez

Carlos Ocampo-Martinez received his Electronic Engineering degree and MSc degree in industrial automation from the National University of Colombia, Campus Manizales, in 2001 and 2003, respectively. In 2007, he received his Ph.D. degree in control engineering from the Technical University of Catalonia (UPC) , Barcelona, Spain. After an year as a research fellow of the ARC Centre of Complex Dynamic Systems and Control (University of Newcastle, Australia), he remained associated with Spanish National Research Council (CSIC) at the Institut de Robòtica i Informàtica Industrial (IRI) in Barcelona as a Juan de la Cierva associate researcher. Since 2011 he has been working as an assistant professor at the Technical University of Catalonia, Automatic Control Department (ESAII). His main research interests are in the areas of constrained MPC, large-scale systems management, nonlinear dynamics, and industrial applications.

Sorin Olaru

Sorin Olaru received his Ph.D. degrees from the University Paris XI, France, and the University Politehnica in Bucharest, Romania, and holds the French Research Habilitation. Since 2001 he has held various positions at INRIA and SUPELEC in France and has been visiting appointments at the University of Newcastle, Australia, and NTNU Trondheim, Norway. Currently he is a professor in SUPELEC and a member of the INRIA Disco team. His research interests include optimization-based control design and set theoretic characterization of constrained dynamical systems.

Florin Stoican

Florin Stoican is an assistant professor at the University Politehnica Bucharest (UPB), Department of Automatic Control and Systems Engineering. He received his BSc degree in electrical in 2008 from the Faculty of Automatic Control and Computers, UPB. He obtained his Ph.D. in control engineering in 2011 from the Department of Automatic Control, SUPELEC, France, and was a postdoctoral research fellow in the Department of Engineering Cybernetics, NTNU, Trondheim, Norway, with an ERCIM Alain Bensoussan Fellowship Programme. His interests are in constrained optimization, fault-tolerant control and mixed integer programming.