Model Reference Control for Linear Time-Varying Systems: A Direct Parametric Approach
This paper investigates model reference control for linear time-varying (LTV) systems. It is shown that the problem can be decomposed into two sub-problems: a state feedback stabilization problem of LTV systems and a feed-forward compensation problem. Firstly, the sufficient condition for the existe...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9047889/ |
| _version_ | 1828928141915062272 |
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| author | Yin-Dong Liu Li-Mei Wang Long-Wen Liu |
| author_facet | Yin-Dong Liu Li-Mei Wang Long-Wen Liu |
| author_sort | Yin-Dong Liu |
| collection | DOAJ |
| description | This paper investigates model reference control for linear time-varying (LTV) systems. It is shown that the problem can be decomposed into two sub-problems: a state feedback stabilization problem of LTV systems and a feed-forward compensation problem. Firstly, the sufficient condition for the existence of the model reference control is deduced. The condition concerns two coefficient matrices such that two matrix equations are met simultaneously, and the state feedback gain matrix stabilizes LTV systems according to the unified spectral theory. Secondly, generally complete parametrization of the model reference tracking controller including a state feedback controller and a feed-forward compensator is proposed based on the solution to a type of generalized Sylvester matrix equations. Furthermore, a general procedure for solving the model reference control problem is also provided. Finally, a numerical example shows the feasibility and effectiveness of the parametric design approach to the model reference control in LTV systems. |
| first_indexed | 2024-12-14T00:00:05Z |
| format | Article |
| id | doaj.art-e98e883e889d4dbaa219fa74cc937823 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T00:00:05Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-e98e883e889d4dbaa219fa74cc9378232022-12-21T23:26:23ZengIEEEIEEE Access2169-35362020-01-018612026121210.1109/ACCESS.2020.29836159047889Model Reference Control for Linear Time-Varying Systems: A Direct Parametric ApproachYin-Dong Liu0https://orcid.org/0000-0003-0212-7980Li-Mei Wang1Long-Wen Liu2https://orcid.org/0000-0002-3748-5553School of Electrical Engineering, Shenyang University of Technology, Shenyang, ChinaSchool of Electrical Engineering, Shenyang University of Technology, Shenyang, ChinaCollege of Automation Science and Technology, South China University of Technology, Guangzhou, ChinaThis paper investigates model reference control for linear time-varying (LTV) systems. It is shown that the problem can be decomposed into two sub-problems: a state feedback stabilization problem of LTV systems and a feed-forward compensation problem. Firstly, the sufficient condition for the existence of the model reference control is deduced. The condition concerns two coefficient matrices such that two matrix equations are met simultaneously, and the state feedback gain matrix stabilizes LTV systems according to the unified spectral theory. Secondly, generally complete parametrization of the model reference tracking controller including a state feedback controller and a feed-forward compensator is proposed based on the solution to a type of generalized Sylvester matrix equations. Furthermore, a general procedure for solving the model reference control problem is also provided. Finally, a numerical example shows the feasibility and effectiveness of the parametric design approach to the model reference control in LTV systems.https://ieeexplore.ieee.org/document/9047889/Linear time-varying systemsmodel reference controlparametric approachPD-eigenstructureSylvester equations |
| spellingShingle | Yin-Dong Liu Li-Mei Wang Long-Wen Liu Model Reference Control for Linear Time-Varying Systems: A Direct Parametric Approach IEEE Access Linear time-varying systems model reference control parametric approach PD-eigenstructure Sylvester equations |
| title | Model Reference Control for Linear Time-Varying Systems: A Direct Parametric Approach |
| title_full | Model Reference Control for Linear Time-Varying Systems: A Direct Parametric Approach |
| title_fullStr | Model Reference Control for Linear Time-Varying Systems: A Direct Parametric Approach |
| title_full_unstemmed | Model Reference Control for Linear Time-Varying Systems: A Direct Parametric Approach |
| title_short | Model Reference Control for Linear Time-Varying Systems: A Direct Parametric Approach |
| title_sort | model reference control for linear time varying systems a direct parametric approach |
| topic | Linear time-varying systems model reference control parametric approach PD-eigenstructure Sylvester equations |
| url | https://ieeexplore.ieee.org/document/9047889/ |
| work_keys_str_mv | AT yindongliu modelreferencecontrolforlineartimevaryingsystemsadirectparametricapproach AT limeiwang modelreferencecontrolforlineartimevaryingsystemsadirectparametricapproach AT longwenliu modelreferencecontrolforlineartimevaryingsystemsadirectparametricapproach |