Multiple actuator-fault detectability analysis using invariant sets for discrete-time LPV systems

Abstract

This paper characterises and analyses the minimum detectable fault (MDF) (named generalised MDF here) for multiple multiplicative actuator faults based on set-separation constraints of healthy and faulty residual sets for discrete-time linear parameter varying (LPV) systems with bounded inputs and uncertainties. First, multiple multiplicative actuator faults are equivalently transformed into the form of multiple additive actuator faults for the sake of obtaining the simplified faulty residual set explicitly. Then, two different generalised MDF for different multiple actuator faults are, respectively, defined, which can be computed via solving simple linear programming (LP) problems. Moreover, we propose three detectability conditions to guarantee the detection of multiple multiplicative actuator faults by using the invariant set-based method. Finally, we provide effective selection guidance for the detection of different multiple multiplicative actuator faults by systematically analysing the conservatism and characteristics of these three guaranteed detectability conditions. At the end of this paper, an electrical circuit example is used to illustrate the effectiveness of the proposed method.

Keywords:

• Invariant sets
• linear parameter varying systems
• multiple multiplicative actuator faults
• generalised minimum detectable faults

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number U1813216], the Natural Science Foundation of Guangdong [grant number 2020A1515010334], and the Basic Research Program of Shenzhen [grant numbers JCYJ20170817152701660 and JCYJ20170412171459177].

Notes on contributors

Bo Min

Bo Min received the bachelor's degree from the School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China, in 2018. Currently, he is pursuing the master's degree from the Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China. His research interests include set-theoretic fault diagnosis, linear parameter-varying systems.

Feng Xu

Feng Xu received the bachelor's degree in measurement and control technology and instruments from Northwestern Polytechnical University, Xi'an, China, in July 2010, and the Ph.D. degree in automatic control from the Technical University of Catalonia (UPC), Barcelona, Spain, in December 2014. In 2014, he was a visiting Ph.D. student with the Centrale Supélec, Paris, France. From June 2015 to July 2017, he was a Postdoctoral Researcher with Tsinghua University in control science and engineering, China. Currently, he is an Assistant Professor with Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China. His research interests are fault diagnosis and fault-tolerant control.

Junbo Tan

Junbo Tan received the bachelor's degree from the Department of Management and Engineering, Nanjing University, Nanjing,China, in 2013, and the master's and Ph.D. degrees from the Department of Automation, Tsinghua University, Beijing, China, in 2016 and 2020, respectively. His research interests include fault diagnosis, linear parameter-varying systems, and fault-tolerant control.

Xueqian Wang

Xueqian Wang received the master's and Ph.D. degrees in control science and engineering both from Harbin Institute of Technology (HIT), Harbin, China, in 2005 and 2010, respectively. From June 2010 to February 2014, he was a Postdoctoral Researcher with HIT. Since March 2014, he has been an Associate Researcher and the Leader of the Center for Artificial Intelligence and Robotics, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China. His research interests include dynamics, control and teleoperation.

Bin Liang

Bin Liang received the bachelor's and master's degrees both from the Honors College, Northwestern Polytechnical University, Xi'an, China, in 1989 and 1991, respectively, and the Ph.D. degree from the Department of Precision Instrument, Tsinghua University, Beijing, China, in 1994. From 1994 to 2007, he was a Postdoctoral Researcher, Associate Professor-Level Researcher, Professor-Level Researcher, and Assistant Chief Engineer with the China Aerospace Science and Technology Corporation. Since 2007, he has been a Professor with the Department of Automation, Tsinghua University. His research interests include modeling and control of dynamic systems.