The preview control of a class of linear systems and its application in the fault-tolerant control theory

Fucheng LiaoDepartment of Information and Computing Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, People’s Republic of China;Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, People’s Republic of ChinaCorrespondence[email protected]
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Chen JiaDepartment of Information and Computing Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, People’s Republic of China;Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, People’s Republic of ChinaView further author information

Usman MalikDepartment of Information and Computing Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, People’s Republic of ChinaView further author information

Xiao YuDepartment of Information and Computing Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, People’s Republic of China;Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, People’s Republic of ChinaView further author information

Jiamei DengSchool of Computing, Creative Technologies, and Engineering, Leeds Beckett University, Leeds, UKView further author information

ABSTRACT

In the fault-tolerant control theory based on model following control, the desired signal of the control system is the output of a reference system. This paper is concerned with the design of the preview controller for a class of fault systems. A composite vector is introduced by including error vector, fault system state vector and reference system state vector. Then, we derived an augmented system from the known system equation, in which the reference input has equal status with the desired signal in the traditional preview control theory. Therefore, we can use the known theory to design the preview controller for the augmented system, then the preview controller of the original fault system can be obtained by the integration method. This paper strictly discusses the connection between stabilisation and detectability of the augmented system and the corresponding characteristics of the original system. Finally, by applying this theory to a real steam generator water level control system, it is found that the actions of the reference input preview and the fault signal preview can effectively eliminate the effect of the fault signal on the water level of the steam generator. The simulation shows the effectiveness of the controller designed.

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Additional information

Funding

This work was supported by National Key R&D Program of China [grant number 2017YFF0207401] and The oriented Award Foundation for Science and Technological Innovation, Inner Mongolia Autonomous Region, China [grant number 2012].

Notes on contributors

Fucheng Liao

Fucheng Liao received BS degree in Mathematics from Yanan University, Yanan, China, in 1982, MS degree in Mathematics from Northeastern University, Shenyang, China, in 1984, and received his Ph.D. degree in Control Theory and Control Engineering from University of Science and Technology Beijing, Beijing, China, in 2007. Currently, he is a professor in School of Mathematics and Physics, University of Science and Technology Beijing, China. His current research interests are in the area of preview control and robust control.

Chen Jia

Chen Jia was born in 1993. She received the Bachelors’ degree in Mathematics and Applied Mathematics from Yuncheng University, China, in 2014. She is currently a PhD student at the School of Mathematics and Physics, University of Science and Technology Beijing, China. Her current research interests are in the area of preview control and fault-tolerant control.

Usman Malik

Usman Malik received the Masters degree in applied mathematics from international Islamic university Islamabad Pakistan in 2016. He is currently a PhD student at the school of mathematics and physics of the university of science and technology Beijing. His research interests is related to general and fundamental mechanics and preview control.

Xiao Yu

Xiao Yu was born in 1991. She received the Bachelors’ degree in Statistics from Dezhou University, China, in 2014. She is currently a PhD student at the School of Mathematics and Physics, University of Science and Technology Beijing, China. Her current research interest is in the area of preview control.

Jiamei Deng

Jiamei Deng obtained her PhD degree in Reading University on Dec. 2005. She is currently a Professor in Artificial Intelligence and Energy at Leeds Beckett University with a particular interest in control systems design, predictive models, emissions modelling, data-driven power plant safety monitoring.

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