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

Entropy

Chia-Yu Chou¹  Boe-Shong Hong¹  Pei-Ju Chiang¹  Wen-Teng Wang²  Liang-Kuang Chen³ 

[1] Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi 62102, Taiwan; E-Mails:;Department of Mechanical and Computer-Aided Engineering, National Formosa University, Yunlin 63201, Taiwan; E-Mail:;Department of Mechanical Engineering, National Taiwan University of Science and Technology, Taipei 10607, Taiwan; E-Mail:

关键词: distributed control;    L₂-gain control;    nD transfer functions;    thermal inertia;   

DOI  :  10.3390/e16094937

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland