H-/L_∞ fault detection observer design for uncertain linear systems

ABSTRACT

This paper studies fault detection problem in the finite-frequency domain for linear systems with parameter uncertainties. We design an $H_{-}/L_{\mathrm{\infty }}$ fault detection observer to generate residual that is robust against disturbance and sensitive to a fault. In the design, we use the finite-frequency $H_{-}$ performance index to measure fault sensitivity and introduce $L_{\mathrm{\infty }}$ performance index to measure the effect of disturbance on residual. The obtained fault detection observer exhibits a peak-to-peak disturbance attenuation performance, which provides a time-varying threshold for residual evaluation. Therefore the proposed design method integrates residual generation and threshold calculation together. To facilitate the observer design process, sufficient conditions of the proposed $H_{-}/L_{\mathrm{\infty }}$ fault detection observer are formulated as a set of linear matrix inequalities. Numerical simulations are given to verify the effectiveness of the proposed approach.

Keywords:

• Fault detection
• parameter uncertainty
• finite-frequency domain
• peak-to-peak

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (nos. 61773145, 61622308, 61873206) and the Key Laboratory Opening Funds of Harbin Institute of Technology under grant HIT.KLOF.2018.073.

Notes on contributors

Weixin Han

Weixin Han received his B.S. and Ph.D. degrees from the Harbin Institute of Technology in 2013 and 2018, respectively. From September 2016 to September 2017, he worked as a visiting scholar at University of Groningen, Groningen, The Netherlands. Now he is working in Northwestern Polytechnical University, Xi'an, China. His research interests include observer design and fault diagnosis. E-mail: [email protected]

Zhenhua Wang

Zhenhua Wang received his B.S. degree from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2008 and his M.S. and Ph.D. degree from Harbin Institute of Technology, Harbin, China, in 2010 and 2014, respectively. He is now a Lecturer with the Department of Control Science and Engineering in Harbin Institute of Technology. His main research interests include fault diagnosis and fault-tolerant control. E-mail: [email protected]

Yi Shen

Yi Shen received his B.S., M.S. and Ph.D. degrees from the Harbin Institute of Technology in 1985, 1988 and 1995, respectively. He is a Professor with the Department of Control Science and Engineering, Harbin Institute of Technology. His current research interests include fault diagnosis for control systems, flight vehicle control and ultrasound signal processing. E-mail: [email protected]