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On asymmetric periodic solutions in relay feedback systems
Authors:IM Boiko  NV Kuznetsov  RN Mokaev  ED Akimova
Institution:1. Electrical Engineering, Khalifa University of Science and Technology, Sas Al Nakhl, Abu Dhabi, United Arab Emirates;2. Saint-Petersburg State University, Saint-Petersburg, Russia;3. Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), St.Petersburg, Russia;4. University of Jyväskylä, Jyväskylä, Finland;1. Tsinghua University, Beijing, China;2. Dalian Minzu University, Dalian, China;1. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, 211106 Nanjing, China;2. Nanjing Research Institute of Electronic Technology, 210039 Nanjing, China;1. School of mechanical engineering, Yanshan University, Qinhuangdao 066004, China;2. Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom;3. Nanjing Institute of Technology, Nanjing 211167, China;1. Kuwait University, Faculty of Science, Department of Mathematics, Safat 13060, Kuwait;2. UR Analysis and Control of PDEs, UR13ES64, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir 5019, Tunisia;1. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, Shandong 266520, China;2. School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252059, China;1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, PR China;2. Department of Applied Mathematics, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada
Abstract:Asymmetric self-excited periodic motions or periodic solutions which are produced by relay feedback systems that have symmetric characteristics are studied in the paper. Two different mechanisms of producing an asymmetric oscillation by a system with symmetric properties are noted and analyzed by the locus of a perturbed relay system (LPRS) method. Bifurcation between the ability to excite symmetric and asymmetric oscillation with variation of system parameters is analyzed. An algorithm of finding asymmetric solutions is proposed.
Keywords:
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