Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System
The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system...
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MDPI AG
2021-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/7/3252 |
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| author | Akihiro Takeshita Tomohiro Yamashita Natsuki Kawaguchi Masaharu Kuroda |
| author_facet | Akihiro Takeshita Tomohiro Yamashita Natsuki Kawaguchi Masaharu Kuroda |
| author_sort | Akihiro Takeshita |
| collection | DOAJ |
| description | The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order to estimate the states originating from the fractional-order derivative term. Fourth, numerical simulations are presented using a numerical calculation method corresponding to a fractional-order state equation. Finally, the numerical simulation results demonstrate that the fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping. |
| first_indexed | 2024-03-10T12:35:37Z |
| format | Article |
| id | doaj.art-435589da348241b89ad0504368545e0b |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T12:35:37Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-435589da348241b89ad0504368545e0b2023-11-21T14:15:43ZengMDPI AGApplied Sciences2076-34172021-04-01117325210.3390/app11073252Fractional-Order LQR and State Observer for a Fractional-Order Vibratory SystemAkihiro Takeshita0Tomohiro Yamashita1Natsuki Kawaguchi2Masaharu Kuroda3Department of Mechanical Engineering, Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, JapanDepartment of Mechanical Engineering, Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, JapanDepartment of Mechanical Engineering, Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, JapanDepartment of Mechanical Engineering, Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, JapanThe present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order to estimate the states originating from the fractional-order derivative term. Fourth, numerical simulations are presented using a numerical calculation method corresponding to a fractional-order state equation. Finally, the numerical simulation results demonstrate that the fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping.https://www.mdpi.com/2076-3417/11/7/3252vibrationcontrolfractional calculuslinear quadratic regulator (LQR)algebraic Riccati equationiteration |
| spellingShingle | Akihiro Takeshita Tomohiro Yamashita Natsuki Kawaguchi Masaharu Kuroda Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System Applied Sciences vibration control fractional calculus linear quadratic regulator (LQR) algebraic Riccati equation iteration |
| title | Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System |
| title_full | Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System |
| title_fullStr | Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System |
| title_full_unstemmed | Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System |
| title_short | Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System |
| title_sort | fractional order lqr and state observer for a fractional order vibratory system |
| topic | vibration control fractional calculus linear quadratic regulator (LQR) algebraic Riccati equation iteration |
| url | https://www.mdpi.com/2076-3417/11/7/3252 |
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