{"title":"未知时变扰动下刚柔系统的自适应边界反馈控制","authors":"","doi":"10.1016/j.jfranklin.2024.107256","DOIUrl":null,"url":null,"abstract":"<div><p>This paper studies the boundary feedback control of a rotating disk-cable-mass system (DCMS). The system consists of a flexible cable with a rigid disk connected at its upper end and a tip mass at the lower boundary. We assume that the disk and the tip mass are affected by unknown time-varying disturbances, while the cable is influenced by distributed disturbance. We design two boundary controls to suppress the vibration of the flexible cable and simultaneously adjust the system’s rotating speed to a desired value. The first controller is designed assuming the system’s parameters are accurately known. The second controller is conceived under circumstances where some system parameters are unknown, for which an adaptive technique is employed to regulate the DCMS. For these two controls, we choose two Lyapunov functions to prove the stability of the closed-loop system. Theoretical results demonstrate that the states of the closed-loop system are ultimately uniformly bounded. At the end of the paper, we validate two boundary controls through numerical tests.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adaptive boundary feedback control of a rigid–flexible system under unknown time-varying disturbance\",\"authors\":\"\",\"doi\":\"10.1016/j.jfranklin.2024.107256\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper studies the boundary feedback control of a rotating disk-cable-mass system (DCMS). The system consists of a flexible cable with a rigid disk connected at its upper end and a tip mass at the lower boundary. We assume that the disk and the tip mass are affected by unknown time-varying disturbances, while the cable is influenced by distributed disturbance. We design two boundary controls to suppress the vibration of the flexible cable and simultaneously adjust the system’s rotating speed to a desired value. The first controller is designed assuming the system’s parameters are accurately known. The second controller is conceived under circumstances where some system parameters are unknown, for which an adaptive technique is employed to regulate the DCMS. For these two controls, we choose two Lyapunov functions to prove the stability of the closed-loop system. Theoretical results demonstrate that the states of the closed-loop system are ultimately uniformly bounded. At the end of the paper, we validate two boundary controls through numerical tests.</p></div>\",\"PeriodicalId\":17283,\"journal\":{\"name\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S001600322400677X\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S001600322400677X","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Adaptive boundary feedback control of a rigid–flexible system under unknown time-varying disturbance
This paper studies the boundary feedback control of a rotating disk-cable-mass system (DCMS). The system consists of a flexible cable with a rigid disk connected at its upper end and a tip mass at the lower boundary. We assume that the disk and the tip mass are affected by unknown time-varying disturbances, while the cable is influenced by distributed disturbance. We design two boundary controls to suppress the vibration of the flexible cable and simultaneously adjust the system’s rotating speed to a desired value. The first controller is designed assuming the system’s parameters are accurately known. The second controller is conceived under circumstances where some system parameters are unknown, for which an adaptive technique is employed to regulate the DCMS. For these two controls, we choose two Lyapunov functions to prove the stability of the closed-loop system. Theoretical results demonstrate that the states of the closed-loop system are ultimately uniformly bounded. At the end of the paper, we validate two boundary controls through numerical tests.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.