Interface Temperature Control of Czochralski Crystal Furnace Based on Novel Reduced Order PDE Model

Qiran CONG  Peng YAN

doi:10.12034/j.issn.1009-606X.216331

The Chinese Journal of Process Engineering >

2017 , Vol. 17 >Issue 3: 571 - 577

DOI: https://doi.org/10.12034/j.issn.1009-606X.216331

Process & Technology

Interface Temperature Control of Czochralski Crystal Furnace Based on Novel Reduced Order PDE Model

Qiran CONG Peng YAN

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1. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China;
2. School of Mechanical Engineering, Shandong University, Jinan, Shandong 250061, China

Received date: 2016-10-24

Revised date: 2016-12-06

Online published: 2017-06-14

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Abstract

In order to deal with the interface temperature control problem of Czochralski crystal furnace, the associated parabolic partial differential equation (PDE) model is proposed, where the Galerkin method is used for the parabolic PDE order reduction. Furthermore Karhunen-Loève (KL) decomposition method is applied to generate the optimal empirical eigenfunctions, where the irregular domain is mapped to a fixed rectangular domain to facilitate the decomposition process. A method is proposed that decomposes the PDE into a homogeneous part and inhomogeneous parts to improve the computation efficiency. Optimal control method with the proposed model is employed where numerical simulations are provided to verified the effectiveness.

Key words： Crystal remelt; KL-Galerkin method; PDE model decomposition; optimal control

Cite this article

Qiran CONG Peng YAN . Interface Temperature Control of Czochralski Crystal Furnace Based on Novel Reduced Order PDE Model[J]. The Chinese Journal of Process Engineering, 2017 , 17(3) : 571 -577 . DOI: 10.12034/j.issn.1009-606X.216331

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