{"title":"输入延迟离散系统的LQG/LTR控制","authors":"D. Horla, A. Królikowski","doi":"10.24425/BPASTS.2019.130895","DOIUrl":null,"url":null,"abstract":"A simple robust cheap LQG control is considered for discrete-time systems with constant input delay. It is well known that the full loop transfer recovery (LTR) effect measured by error function ∆(z) can only be obtained for minimum-phase (MPH) systems without time-delay. Explicit analytical expressions for ∆z) versus delay d are derived for both MPH and NMPH (nonminimum-phase) systems. Obviously, introducing delay deteriorates the LTR effect. In this context the ARMAX system as a simple example of noise-correlated system is examined. The robustness of LQG/LTR control is analyzed and compared with state prediction control whose robust stability is formulated via LMI. Also, the robustness with respect to uncertain time-delay is considered including the control systems which are unstable in open-loop. An analysis of LQG/LTR problem for noise-correlated systems, particularly for ARMAX system, is included and the case of proper systems is analyzed. Computer simulations of second-order systems with constant time-delay are given to illustrate the performance and recovery error for considered systems and controllers.","PeriodicalId":55299,"journal":{"name":"Bulletin of the Polish Academy of Sciences-Technical Sciences","volume":"25 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"LQG/LTR control of input-delayed discrete-time systems\",\"authors\":\"D. Horla, A. Królikowski\",\"doi\":\"10.24425/BPASTS.2019.130895\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A simple robust cheap LQG control is considered for discrete-time systems with constant input delay. It is well known that the full loop transfer recovery (LTR) effect measured by error function ∆(z) can only be obtained for minimum-phase (MPH) systems without time-delay. Explicit analytical expressions for ∆z) versus delay d are derived for both MPH and NMPH (nonminimum-phase) systems. Obviously, introducing delay deteriorates the LTR effect. In this context the ARMAX system as a simple example of noise-correlated system is examined. The robustness of LQG/LTR control is analyzed and compared with state prediction control whose robust stability is formulated via LMI. Also, the robustness with respect to uncertain time-delay is considered including the control systems which are unstable in open-loop. An analysis of LQG/LTR problem for noise-correlated systems, particularly for ARMAX system, is included and the case of proper systems is analyzed. Computer simulations of second-order systems with constant time-delay are given to illustrate the performance and recovery error for considered systems and controllers.\",\"PeriodicalId\":55299,\"journal\":{\"name\":\"Bulletin of the Polish Academy of Sciences-Technical Sciences\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Polish Academy of Sciences-Technical Sciences\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.24425/BPASTS.2019.130895\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Polish Academy of Sciences-Technical Sciences","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.24425/BPASTS.2019.130895","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
LQG/LTR control of input-delayed discrete-time systems
A simple robust cheap LQG control is considered for discrete-time systems with constant input delay. It is well known that the full loop transfer recovery (LTR) effect measured by error function ∆(z) can only be obtained for minimum-phase (MPH) systems without time-delay. Explicit analytical expressions for ∆z) versus delay d are derived for both MPH and NMPH (nonminimum-phase) systems. Obviously, introducing delay deteriorates the LTR effect. In this context the ARMAX system as a simple example of noise-correlated system is examined. The robustness of LQG/LTR control is analyzed and compared with state prediction control whose robust stability is formulated via LMI. Also, the robustness with respect to uncertain time-delay is considered including the control systems which are unstable in open-loop. An analysis of LQG/LTR problem for noise-correlated systems, particularly for ARMAX system, is included and the case of proper systems is analyzed. Computer simulations of second-order systems with constant time-delay are given to illustrate the performance and recovery error for considered systems and controllers.
期刊介绍:
The Bulletin of the Polish Academy of Sciences: Technical Sciences is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred:
Artificial and Computational Intelligence,
Biomedical Engineering and Biotechnology,
Civil Engineering,
Control, Informatics and Robotics,
Electronics, Telecommunication and Optoelectronics,
Mechanical and Aeronautical Engineering, Thermodynamics,
Material Science and Nanotechnology,
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