Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions
This paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/6/810 |
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| author | Artem E. Konkov Yuri V. Mitrishkin |
| author_facet | Artem E. Konkov Yuri V. Mitrishkin |
| author_sort | Artem E. Konkov |
| collection | DOAJ |
| description | This paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant model, ensuring the robust stability of the synthesized system. Robustness is further ensured by the small-gain theorem and a novel approach to loop shaping, enabling the use of arbitrary shape functions. As a result, this methodology provides a broad statement of the problem with performance criteria necessary for practical application in control systems. Numerical examples are used to illustrate the methodology, which is implemented using the MATLAB toolbox, freely available for use. |
| first_indexed | 2024-04-24T18:02:29Z |
| format | Article |
| id | doaj.art-52e28a67d04043ac9bae5a0c99e47827 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T18:02:29Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-52e28a67d04043ac9bae5a0c99e478272024-03-27T13:52:58ZengMDPI AGMathematics2227-73902024-03-0112681010.3390/math12060810Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI RestrictionsArtem E. Konkov0Yuri V. Mitrishkin1Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, RussiaFaculty of Physics, Lomonosov Moscow State University, 119991 Moscow, RussiaThis paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant model, ensuring the robust stability of the synthesized system. Robustness is further ensured by the small-gain theorem and a novel approach to loop shaping, enabling the use of arbitrary shape functions. As a result, this methodology provides a broad statement of the problem with performance criteria necessary for practical application in control systems. Numerical examples are used to illustrate the methodology, which is implemented using the MATLAB toolbox, freely available for use.https://www.mdpi.com/2227-7390/12/6/810discrete timeMIMO PIDLTVPLVloop shapingLMI |
| spellingShingle | Artem E. Konkov Yuri V. Mitrishkin Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions Mathematics discrete time MIMO PID LTV PLV loop shaping LMI |
| title | Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions |
| title_full | Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions |
| title_fullStr | Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions |
| title_full_unstemmed | Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions |
| title_short | Synthesis Methodology for Discrete MIMO PID Controller with Loop Shaping on LTV Plant Model via Iterated LMI Restrictions |
| title_sort | synthesis methodology for discrete mimo pid controller with loop shaping on ltv plant model via iterated lmi restrictions |
| topic | discrete time MIMO PID LTV PLV loop shaping LMI |
| url | https://www.mdpi.com/2227-7390/12/6/810 |
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