Computing Open-Loop Optimal Control of the q-Profile in Ramp-Up Tokamak Plasmas Using the Minimal-Surface Theory

XU Chao (许超); OU Yongsheng (欧勇盛); Eugenio SCHUSTER; and YU Xin(于欣)

doi:10.1088/1009-0630/15/5/02

Plasma Science and Technology > 2013 > 15(5): 403-410. > DOI: 10.1088/1009-0630/15/5/02

XU Chao (许超), OU Yongsheng (欧勇盛), Eugenio SCHUSTER, and YU Xin(于欣). Computing Open-Loop Optimal Control of the q-Profile in Ramp-Up Tokamak Plasmas Using the Minimal-Surface Theory[J]. Plasma Science and Technology, 2013, 15(5): 403-410. DOI: 10.1088/1009-0630/15/5/02

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Computing Open-Loop Optimal Control of the q-Profile in Ramp-Up Tokamak Plasmas Using the Minimal-Surface Theory

1 The State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou 310027, China 2 Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China 3 Department of Mechanical Engineering & Mechanics, Lehigh University, Bethlehem, PA 18015, USA 4 Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Funds: supported partially by the US NSF CAREER award program (ECCS-0645086), National Natural Science Foundation of China (No. F030119), Zhejiang Provincial Natural Science Foundation of China (Nos. Y1110354, Y6110751) and the Fundamental Research Funds for the Central Universities of China (No. 1A5000-172210101) and the Natural Science Foundation of Ningbo (No. 2010A610096)

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Received Date: February 23, 2012

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Abstract

Abstract

The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation (PDE) models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op- timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID (proportional-integral-derivative) controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.
- advanced plasma operations,
- current profile dynamics,
- optimal control theory,
- minimal surface equation,
- differential geometry

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