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Fault detectability analysis for linear systems within a set-based framework |
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| Institution: | 1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China;2. Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;1. School of Mathematics and Statistics, Guizhou University,Guiyang 550025, China;2. CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University,Changsha 410081, China;1. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China;2. Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg 47057, Germany |
| Abstract: | This paper investigates the fault detectability issue for linear systems within a set-based framework. A set-based fault detectability analysis method is developed based on the geometric approach-based fault detection observer and zonotopes. Three concepts of fault detectability are established according to the relationship between the observer output sets in the presence and absence of faults. Necessary and sufficient conditions are derived corresponding to different detectability concepts. It can be found that the obtained conditions are related to system inputs in open-loop systems and system controllers in closed-loop systems. The impact of both system inputs and system controllers on fault detectability is analyzed. A numerical simulation is presented to illustrate the validity of the conclusions. |
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