%0 Journal Article
%T Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism
%A Chia-Yu Chou
%A Boe-Shong Hong
%A Pei-Ju Chiang
%A Wen-Teng Wang
%A Liang-Kuang Chen
%A Chia-Yen Lee
%J Entropy
%P 4937-4959
%D 2014
%I MDPI AG
%R 10.3390/e16094937
%X 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 ¡Þ /¦Ì control is developed by expansion of the conventional 1D- H ¡Þ /¦Ì 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.
%K distributed control
%K L2-gain control
%K nD transfer functions
%K thermal inertia
%U http://www.mdpi.com/1099-4300/16/9/4937