2022 Fiscal Year Final Research Report
Solution method of matrix equations via a low-dimensional simultaneous equation and an affine mapping, and its application to magnetic levitation systems
| Project/Area Number |
19K04282
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 20010:Mechanics and mechatronics-related
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| Research Institution | Daido University |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | 同伴形式 / 行列方程式 / 連立方程式 / 漸化式 / アフィン写像 / モード切り換え型制御系 |
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| Outline of Final Research Achievements |
Suppressing the vibrations of car bodies generated by weight reduction is necessary to achieve high-speed transportation for magnetically levitated vehicles. In the present study, a controller design algorithm for synthesizing mode switching control systems to attain the desired levitation position is discussed. Because the controller can be synthesized using a certain element of the solution of the matrix equations, a solution method of simultaneous equation with number of unknowns on the same order as the controlled system instead of a direct solution method of matrix equations is proposed.
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| Free Research Field |
制御工学
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| Academic Significance and Societal Importance of the Research Achievements |
様々な制御問題では行列方程式により定式化されることが少なくない。本研究では、行列方程式を制御系の内部変数の数に基づく連立一次方程式とその解を使ったアフィン写像による2段階方式で解く方策を見出した。高次になるほど直接行列方程式を解くよりも次数を減らす効果が高まり、計算にかかる工数が削減できる。また、MSCの制御器は行列方程式を直接解かなくても前述の連立一次方程式の解から求めることができ、設計に係る工数も削減できる。
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