Qi Mao , Jun Chen , Fei Xie , Liqian Dou , Bailing Tian , Qun Zong
{"title":"利用线性摄动不稳定系统的PI调节器的最优鲁棒性","authors":"Qi Mao , Jun Chen , Fei Xie , Liqian Dou , Bailing Tian , Qun Zong","doi":"10.1016/j.sysconle.2025.106225","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate how a regulator can be implemented for gaining the optimal robustness margin of second-order plants in the presence of uncertain perturbations. We are primarily interested in an intricate system, i.e., the second-order unstable plant with a zero relative degree that is accompanied by at least one unstable pole and non-minimum phase dynamics, both implemented by the proportional and proportional–integral (PI) type regulators. More specifically, we shall examine three scenarios of the system ranging from the worst case of two unstable poles and two minimum phase zeros to the case of one unstable pole and one minimum phase zero. For each class of systems, we furnish the bi-dimensional feasible horizons for the controller parameters of PI regulators. Drawing upon the feasible domains, we derive the explicit expressions of the optimal robustness margin against unknown uncertainties. Beyond that, we determine the regulator parameters for accomplishing the maximum margins, i.e., the optimum proportional and integral gains. At last, we extend to explore the optimum robustness margin achievable with a PI regulator for third-order non-minimum phase systems. Our results illustrate that the optimal robustness margins obtainable are dependent on the locations of the system’s unstable poles and non-minimum phase dynamics while attaining the optimized margin is relevant to the control parameters of the PI regulator, thus casting insight upon the design and adaptation of the regulator parameters.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"205 ","pages":"Article 106225"},"PeriodicalIF":2.5000,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Harnessing optimal robustness towards PI regulators of linear perturbed unstable systems\",\"authors\":\"Qi Mao , Jun Chen , Fei Xie , Liqian Dou , Bailing Tian , Qun Zong\",\"doi\":\"10.1016/j.sysconle.2025.106225\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we investigate how a regulator can be implemented for gaining the optimal robustness margin of second-order plants in the presence of uncertain perturbations. We are primarily interested in an intricate system, i.e., the second-order unstable plant with a zero relative degree that is accompanied by at least one unstable pole and non-minimum phase dynamics, both implemented by the proportional and proportional–integral (PI) type regulators. More specifically, we shall examine three scenarios of the system ranging from the worst case of two unstable poles and two minimum phase zeros to the case of one unstable pole and one minimum phase zero. For each class of systems, we furnish the bi-dimensional feasible horizons for the controller parameters of PI regulators. Drawing upon the feasible domains, we derive the explicit expressions of the optimal robustness margin against unknown uncertainties. Beyond that, we determine the regulator parameters for accomplishing the maximum margins, i.e., the optimum proportional and integral gains. At last, we extend to explore the optimum robustness margin achievable with a PI regulator for third-order non-minimum phase systems. Our results illustrate that the optimal robustness margins obtainable are dependent on the locations of the system’s unstable poles and non-minimum phase dynamics while attaining the optimized margin is relevant to the control parameters of the PI regulator, thus casting insight upon the design and adaptation of the regulator parameters.</div></div>\",\"PeriodicalId\":49450,\"journal\":{\"name\":\"Systems & Control Letters\",\"volume\":\"205 \",\"pages\":\"Article 106225\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2025-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems & Control Letters\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167691125002075\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691125002075","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Harnessing optimal robustness towards PI regulators of linear perturbed unstable systems
In this paper, we investigate how a regulator can be implemented for gaining the optimal robustness margin of second-order plants in the presence of uncertain perturbations. We are primarily interested in an intricate system, i.e., the second-order unstable plant with a zero relative degree that is accompanied by at least one unstable pole and non-minimum phase dynamics, both implemented by the proportional and proportional–integral (PI) type regulators. More specifically, we shall examine three scenarios of the system ranging from the worst case of two unstable poles and two minimum phase zeros to the case of one unstable pole and one minimum phase zero. For each class of systems, we furnish the bi-dimensional feasible horizons for the controller parameters of PI regulators. Drawing upon the feasible domains, we derive the explicit expressions of the optimal robustness margin against unknown uncertainties. Beyond that, we determine the regulator parameters for accomplishing the maximum margins, i.e., the optimum proportional and integral gains. At last, we extend to explore the optimum robustness margin achievable with a PI regulator for third-order non-minimum phase systems. Our results illustrate that the optimal robustness margins obtainable are dependent on the locations of the system’s unstable poles and non-minimum phase dynamics while attaining the optimized margin is relevant to the control parameters of the PI regulator, thus casting insight upon the design and adaptation of the regulator parameters.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.