Observer synthesis for a class of Takagi–Sugeno descriptor system with unmeasurable premise variable. Application to fault diagnosis

ABSTRACT

This paper proposes a methodology to design a Takagi–Sugeno (TS) descriptor observer for a class of TS descriptor systems. Unlike the popular approach that considers measurable premise variables, this paper considers the premise variables depending on unmeasurable vectors, e.g. the system states. This consideration covers a large class of nonlinear systems and represents a real challenge for the observer synthesis. Sufficient conditions to guarantee robustness against the unmeasurable premise variables and asymptotic convergence of the TS descriptor observer are obtained based on the H_∞ approach together with the Lyapunov method. As a result, the designing conditions are given in terms of linear matrix inequalities (LMIs). In addition, sensor fault detection and isolation are performed by means of a generalised observer bank. Two numerical experiments, an electrical circuit and a rolling disc system, are presented in order to illustrate the effectiveness of the proposed method.

KEYWORDS:

• Descriptor systems
• Takagi–Sugeno systems
• observer design
• fault isolation
• fault diagnosis

Acknowledgments

The authors would like to thank four anonymous reviewers and the editor for their constructive and valuable comments that have improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the Tecnológico Nacional de México (TecNM) under the program Apoyo a la Investigación Científica y Tecnológica, project 6358.17-P.

Notes on contributors

F. R. López-Estrada

Francisco-Ronay Lopez-Estrada received his Ph.D. in automatic control from the University of Lorraine, France, in 2014. He has been with Instituto Tecnologico de Tuxtla Gutierrez, Mexico, as an assistant professor since 2008. He received his M.Sc. degree in electronic engineering in 2008 from Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET), Mexico. His research interests are in descriptor systems, TS systems, fault detection, fault tolerant control, and its applications to Unmmaned Vehicles, and pipeline leak detection systems.

C. M. Astorga-Zaragoza

Carlos Manuel Astorga-Zaragoza was born in Minatitl´an, Veracruz, Mexico, in 1967. He received the M.Sc. degree in electronic engineering from Centro Nacional de Investigaci´on y Desarrollo Tecnol´ogico (CENIDET), Cuernavaca, Morelos, Mexico, in 1993, and the Ph.D. in process engineering from Universit´e Claude Bernard Lyon 1, France, in 2001. Since 1993, he has held teaching and research positions at CENIDET, where he mainly works on automatic control of energy conversion processes. His research interests include the nonlinear observers, fault diagnosis, and control systems with applications, in particular to process engineering.

D. Theilliol

Didier Theilliol received the Ph.D. degree in Control Engineering from UNIVERSITY OF LORRAINE (France) in 1993. Since September 2004, he is a full Professor in Research Centre for Automatic Control of Nancy (CRAN) at University of Lorraine where he co-ordinates and leads national, European and International R&D projects in steel industries, wastewater treatment plant and aerospace domains. His current research interests include sensor and actuator modelbased fault diagnosis (FDI) method synthesis and active faulttolerant control (FTC) system design for LTI, LPV, Multilinear systems and also reliability analysis of components. Prof. Theilliol published over 200 journal/conference papers and is a co-author of a book entitled ‘Fault-tolerant Control Systems: Design and Practical Applications’ (2009). He was during two years Visiting Professorship for Senior International Scientists for Chinese Academy of Sciences. He is one of European Advanced Control and Diagnosis (EACD) steering committee members and is also a member of IFAC Technical Committee 6.2. Mining, Mineral and Metal Processing.

J. C. Ponsart

Jean-Christophe Ponsart received his Ph.D. in 1996 from the UNIVERSITY OF SAVOIE in Annecy, France, in nonlinear control of magnetic suspensions and its digital implementation aspects. In 1997, he participated in design and implementation of real time controllers with digital signal processor architecture for an industrial company. He has been with the Research Center for Automatic Control of Nancy (CRAN) at the UNIVERSITY OF LORRAINE since 1998 as an Assistant Professor. In 2011, he obtained the Habilitation a Diriger des Recherches` (HDR) from the UNIVERSITY OF LORRAINE. His current interests include fault diagnosis and accommodation, and fault-tolerant control applied to LPV and nonlinear systems. Currently, he develops these topics on UAV applications among others.

G. Valencia-Palomo

Guillermo Valencia-Palomo was born in Merida, Mexico, in 1980. He received the Engineering degree in Electronics from the Instituto Tecnologico de Merida, Mexico, in 2003, and the M.Sc. and the Ph.D. degree in Automatic Control from the National Center of Research and Technological Development (CENIDET) in 2006 and The University of Sheffield in 2010, respectively. Since 2010, Dr. Guillermo Valencia-Palomo is a full-time professor at the Instituto Tecnológico de Hermosillo. His research interests include: predictive control, descriptor systems, linear parameter varying systems, fault detection, fault tolerant control systems and its applications.

L. Torres

Lizeth Torres earned her bachelor's degree from Instituto Tecnológico de Veracruz and her master's degree from Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET), both in electronic engineering. She received a Ph.D. in Automatic Control from Université de Grenoble in 2011 and worked as a temporary assistant professor and researcher (ATER) at ENSE3, INP Grenoble in France. She is currently a full time research staff member (CONACyT Research Fellow) at Instituto de Ingeniería, UNAM in Mexico City. Her research interests include the modeling, state estimation and diagnosis systems of transmission lines, pipeline networks and marine structures.