Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas》.pdf

Commun Nonlinear Sci Numer Simulat 32 (2016) 31–48 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: /locate/cnsns Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas✩ a a,∗ b b b Zhigang Ren , Chao Xu , Qun Lin , Ryan Loxton , Kok Lay Teo a State Key Laboratory of Industrial Control Technology and Institute of Cyber-Systems Control, Zhejiang University, Hangzhou, Zhejiang, China b Department of Mathematics Statistics, Curtin University, Perth, Western Australia, Australia a r t i c l e i n f o a b s t r a c t Article history: Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective Received 2 December 2014 steady-state operation. The evolution of the current spatial profile is related to the evolu- Revised 31 July 2015 tion of the poloidal magnetic flux, which can be modeled in the normalized cylindrical co- Accepted 4 August 2015 ordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion Available online 18 August 2015 equation. In this paper, we consider the dynamic optimization problem of attaining the best Keywords: possible current spatial profile during the ramp-up phase of the tokamak. We first use the Nuclear fusion Galerki