{"title":"Synchronization stability of a distributed hysteresis controlled system","authors":"Liang Chen, Dehong Lian, Tingshan Wang","doi":"10.1109/ICIEA.2012.6360984","DOIUrl":null,"url":null,"abstract":"The self-oscillatory system with hysteresis has been widely studied. However, most research deal with one hysteresis element in the system, seldom discuss the multi-hysteresis controllers, not to mention interactions between them. In the paper, we take a simple model with two coupled hysteresis controlled integrators as an example to study a synchronous phenomenon, that is similar to that happened in the large-scale distributed hysteresis controlled system, e.g. the supermarket refrigeration system. In the paper, synchronization is interpreted as a limit cycle in a state space created by switching among piecewise-affine dynamical system. Stability of the resultant limit cycle is examined by a Poincar'e map. We show that the synchronization takes place if the corresponding Poincar'e map is stable.","PeriodicalId":220747,"journal":{"name":"2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICIEA.2012.6360984","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
The self-oscillatory system with hysteresis has been widely studied. However, most research deal with one hysteresis element in the system, seldom discuss the multi-hysteresis controllers, not to mention interactions between them. In the paper, we take a simple model with two coupled hysteresis controlled integrators as an example to study a synchronous phenomenon, that is similar to that happened in the large-scale distributed hysteresis controlled system, e.g. the supermarket refrigeration system. In the paper, synchronization is interpreted as a limit cycle in a state space created by switching among piecewise-affine dynamical system. Stability of the resultant limit cycle is examined by a Poincar'e map. We show that the synchronization takes place if the corresponding Poincar'e map is stable.