Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism

Autor: Chia-Yu Chou, Boe-Shong Hong, Pei-Ju Chiang, Wen-Teng Wang, Liang-Kuang Chen, Chia-Yen Lee
Jazyk: angličtina
Rok vydání: 2014
Předmět:
Zdroj: Entropy, Vol 16, Iss 9, Pp 4937-4959 (2014)
Druh dokumentu: article
ISSN: 1099-4300
DOI: 10.3390/e16094937
Popis: 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.
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