Simultaneous estimation of multiple channel faults for two-dimensional linear systems

ABSTRACT

This study focuses on the problem of simultaneous estimation of multiple channel faults for two-dimensional linear systems, which are described by Fornasini–Marchesini second (FM-II) model, and the faults that exist in state equation and measurement equation. By transforming the fault in the measurement equation as augmented state, the FM-II model with faults in the state equation and measurement equation can be rewritten into a singular system. Hence, several observers are proposed for the singular systems, and then the estimation of the faults in the state equation and measurement equation can be obtained. Using Lyapunov stability theory, sufficient conditions for the existence of the asymptotically stable observer and uniformly ultimately bounded observer are derived in the context of time domain. For the bounded observer, the upper bound of estimation error can be provided referring to the fault bound. Numerical and practical examples are given to demonstrate the effectiveness of the proposed method.

KEYWORDS:

• Two-dimensional systems
• singular system
• asymptotically stable observer
• uniformly ultimately bounded observer
• fault estimation

Acknowledgments

The authors extend their sincere gratitude to the anonymous reviewers for their valuable comments and constructive suggestions with regard to this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was supported by the National Natural Science Foundation of China [grant number 61374099]; and Research Fund for the Taishan Scholar Project of Shandong Province of China.

Notes on contributors

Liang Cao

Liang Cao received his BS degree from Beijing University of Chemical Technology, Beijing, China, in 2015, where he is currently working towards his Master's degree in Control Engineering. His research interests include fault-tolerant control, robust control and fault diagnosis.

Dong Zhao

Dong Zhao received his BEng and PhD degrees both from Beijing University of Chemical Technology, Beijing, China, in 2011 and 2016, respectively. His research interests include fault diagnosis and fault-tolerant control, two-dimensional systems and active disturbance rejection control.

Youqing Wang

Youqing Wang received his BS degree from Shandong University, Jinan, Shandong, China, in 2003, and his PhD degree in control science and engineering from Tsinghua University, Beijing, China, in 2008. He worked as a research assistant in the Department of Chemical Engineering, Hong Kong University of Science and Technology, from February 2006 to August 2007. From February 2008 to February 2010, he worked as a senior investigator in the Department of Chemical Engineering, University of California, Santa Barbara, USA. From August 2015 to November 2015, he was a visiting professor at the Department of Chemical and Materials Engineering, University of Alberta, Canada. Currently, he is a professor at Shandong University of Science and Technology and also at Beijing University of Chemical Technology. His research interests include fault-tolerant control, state monitoring, modelling and control of biomedical processes (e.g. artificial pancreas system) and iterative learning control. He is an (associate) editor of Multidimensional Systems and Signal Processing and Canadian Journal of Chemical Engineering. He holds membership of two IFAC Technical Committees (TC6.1 and TC8.2). He is a recipient of several research awards (including Journal of Process Control Survey Paper Prize and ADCHEM2015 Young Author Prize).