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Finite Element Approximation and Input Parameterization for the Optimal Control of Current Profiles in Tokamak Plasmas

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Open access
Authors
Ren, Z.
Xu, C.
Lin, Qun
Loxton, Ryan
Teo, Kok Lay
Chu, J.
Date
2014
Type
Conference Paper

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Ren, Z. and Xu, C. and Lin, Q. and Loxton, R. and Teo, K.L. and Chu, J. 2014. Finite Element Approximation and Input Parameterization for the Optimal Control of Current Profiles in Tokamak Plasmas, in Boje, E. (ed), Proceedings of the 19th World Congress of the International Federation of Automatic Control, Aug 24-29 2014, pp. 7892-7897. Cape Town, South Africa: International Federation of Automatic Control.
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Proceedings of the 19th IFAC World Congress
Source Conference
19th World Congress of the International Federation of Automatic Control
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Department of Mathematics and Statistics
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NOTICE: This is the author’s version of a work in which changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

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Abstract

In this paper, we consider a simplified dynamic model describing the evolution of the poloidal flux during the ramp-up phase of the tokamak discharge. We first use the Galerkin method to obtain a finite-dimensional model based on the original PDE system. Then, we apply the control parameterization method to obtain an approximate optimal parameter selection problem governed by a lumped parameter system. Computational optimization techniques are subsequently deployed to solve this approximate problem. To validate our approach, we perform numerical simulations using experimental data from the DIII-D tokamak in San Diego,California. The results show that our numerical optimization procedure can generate optimal controls that drive the current profile to within close proximity of the desired profile at the terminal time, thus demonstrating that the Galerkin and control parameterization methods are effective tools for current profile control in tokamak plasmas.