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Entropy 2014, 16(9), 4937-4959; doi:10.3390/e16094937

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

1
Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62102, Taiwan
2
Department of Mechanical and Computer-Aided Engineering, National Formosa University, Yunlin 63201, Taiwan
3
Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan
4
Department of Vehicle Engineering, National Pingtung University of Science and Technology, Pingtung 91201, Taiwan
*
Author to whom correspondence should be addressed.
Received: 21 May 2014 / Accepted: 29 August 2014 / Published: 15 September 2014
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Abstract

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 control is developed by expansion of the conventional 1D-H 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. View Full-Text
Keywords: distributed control; L2-gain control; nD transfer functions; thermal inertia distributed control; L2-gain control; nD transfer functions; thermal inertia
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MDPI and ACS Style

Chou, C.-Y.; Hong, B.-S.; Chiang, P.-J.; Wang, W.-T.; Chen, L.-K.; Lee, C.-Y. Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism. Entropy 2014, 16, 4937-4959.

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