Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism
In a previous study we provided analytical and experimental evidence that some materials are able to store entropy-flow, of which the heat-conduction behaves as standing waves in a bounded region small enough in practice. In this paper we continue to develop distributed control of heat conduction in...
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MDPI AG
2014-09-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/16/9/4937 |
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| author | Chia-Yu Chou Boe-Shong Hong Pei-Ju Chiang Wen-Teng Wang Liang-Kuang Chen Chia-Yen Lee |
| author_facet | Chia-Yu Chou Boe-Shong Hong Pei-Ju Chiang Wen-Teng Wang Liang-Kuang Chen Chia-Yen Lee |
| author_sort | Chia-Yu Chou |
| collection | DOAJ |
| description | In a previous study we provided analytical and experimental evidence that some materials are able to store entropy-flow, of which the heat-conduction behaves as standing waves in a bounded region small enough in practice. In this paper we continue to develop distributed control of heat conduction in these thermal-inductive materials. The control objective is to achieve subtle temperature distribution in space and simultaneously to suppress its transient overshoots in time. This technology concerns safe and accurate heating/cooling treatments in medical operations, polymer processing, and other prevailing modern day practices. Serving for distributed feedback, spatiotemporal H ∞ /μ control is developed by expansion of the conventional 1D-H ∞ /μ control to a 2D version. Therein 2D geometrical isomorphism is constructed with the Laplace-Galerkin transform, which extends the small-gain theorem into the mode-frequency domain, wherein 2D transfer-function controllers are synthesized with graphical methods. Finally, 2D digital-signal processing is programmed to implement 2D transfer-function controllers, possibly of spatial fraction-orders, into DSP-engine embedded microcontrollers. |
| first_indexed | 2024-04-11T22:27:05Z |
| format | Article |
| id | doaj.art-0701d1dd8abb41189de60c164baf4655 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:27:05Z |
| publishDate | 2014-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0701d1dd8abb41189de60c164baf46552022-12-22T03:59:37ZengMDPI AGEntropy1099-43002014-09-011694937495910.3390/e16094937e16094937Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical IsomorphismChia-Yu Chou0Boe-Shong Hong1Pei-Ju Chiang2Wen-Teng Wang3Liang-Kuang Chen4Chia-Yen Lee5Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62102, TaiwanDepartment of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62102, TaiwanDepartment of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62102, TaiwanDepartment of Mechanical and Computer-Aided Engineering, National Formosa University, Yunlin 63201, TaiwanDepartment of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10607, TaiwanDepartment of Vehicle Engineering, National Pingtung University of Science and Technology, Pingtung 91201, TaiwanIn a previous study we provided analytical and experimental evidence that some materials are able to store entropy-flow, of which the heat-conduction behaves as standing waves in a bounded region small enough in practice. In this paper we continue to develop distributed control of heat conduction in these thermal-inductive materials. The control objective is to achieve subtle temperature distribution in space and simultaneously to suppress its transient overshoots in time. This technology concerns safe and accurate heating/cooling treatments in medical operations, polymer processing, and other prevailing modern day practices. Serving for distributed feedback, spatiotemporal H ∞ /μ control is developed by expansion of the conventional 1D-H ∞ /μ control to a 2D version. Therein 2D geometrical isomorphism is constructed with the Laplace-Galerkin transform, which extends the small-gain theorem into the mode-frequency domain, wherein 2D transfer-function controllers are synthesized with graphical methods. Finally, 2D digital-signal processing is programmed to implement 2D transfer-function controllers, possibly of spatial fraction-orders, into DSP-engine embedded microcontrollers.http://www.mdpi.com/1099-4300/16/9/4937distributed control L2-gain controlnD transfer functionsthermal inertia |
| spellingShingle | Chia-Yu Chou Boe-Shong Hong Pei-Ju Chiang Wen-Teng Wang Liang-Kuang Chen Chia-Yen Lee Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism Entropy distributed control L2-gain control nD transfer functions thermal inertia |
| title | Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism |
| title_full | Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism |
| title_fullStr | Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism |
| title_full_unstemmed | Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism |
| title_short | Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism |
| title_sort | distributed control of heat conduction in thermal inductive materials with 2d geometrical isomorphism |
| topic | distributed control L2-gain control nD transfer functions thermal inertia |
| url | http://www.mdpi.com/1099-4300/16/9/4937 |
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