Non-linear model-based optimization of actuator trajectories for tokamak plasma profile control

F. Felici, O. Sauter

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55 Citations (Scopus)
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Abstract

A computational method is presented to determine the tokamak actuator time evolution (trajectories) required to optimally reach a given point in the tokamak operating space while satisfying a set of constraints. Usually, trajectories of plasma auxiliary heating, current drive and plasma current required during the transient phases of a tokamak shot to reach a desired shape of the plasma temperature and safety factor (q) profiles are determined by trial-and-error by physics operators. In this paper, these trajectories are calculated by solving a non-linear, constrained, finite-time optimal control problem. The optimization problem contains a physics model of the non-linear plasma profile dynamics, a cost function to be minimized, and a set of constraints on the actuators and plasma quantities. The method is tested by optimizing the trajectories of Ip, heating and current drive power to obtain a typical hybrid plasma q profile at the end of the current ramp-up phase, while minimizing both the Ohmic flux swing and the distance from a stationary condition, and requiring q > 1 and edge Vloop > 0 at all times. The optimized trajectories feature an Ip overshoot similar to that used in existing experiments, and are shown to perform significantly better than a set of non-optimized trajectories, allowing stationary profiles to be obtained at the beginning of the flat-top phase. Additional information is obtained, including the parameter sensitivity of the optimal solution, a linear model describing the linearized dynamics of the profiles around the optimal trajectory, as well as a classification of the actuator trajectories based on the critical constraint which limits their value at a given time. This provides a solid basis for subsequent closed-loop feedback controller design. The tools presented in this paper could be useful to improve existing tokamak operational scenarios, to prepare operation of future machines and optimize their design.
Original languageEnglish
Article number025002
Pages (from-to)025002-1/28
Number of pages28
JournalPlasma Physics and Controlled Fusion
Volume54
Issue number2
DOIs
Publication statusPublished - 2012

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Actuators
actuators
Trajectories
trajectories
Plasmas
optimization
profiles
Physics
time optimal control
Heating
safety factors
physics
heating
Safety factor
plasma currents
plasma temperature
Computational methods
ramps
Cost functions
shot

Cite this

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abstract = "A computational method is presented to determine the tokamak actuator time evolution (trajectories) required to optimally reach a given point in the tokamak operating space while satisfying a set of constraints. Usually, trajectories of plasma auxiliary heating, current drive and plasma current required during the transient phases of a tokamak shot to reach a desired shape of the plasma temperature and safety factor (q) profiles are determined by trial-and-error by physics operators. In this paper, these trajectories are calculated by solving a non-linear, constrained, finite-time optimal control problem. The optimization problem contains a physics model of the non-linear plasma profile dynamics, a cost function to be minimized, and a set of constraints on the actuators and plasma quantities. The method is tested by optimizing the trajectories of Ip, heating and current drive power to obtain a typical hybrid plasma q profile at the end of the current ramp-up phase, while minimizing both the Ohmic flux swing and the distance from a stationary condition, and requiring q > 1 and edge Vloop > 0 at all times. The optimized trajectories feature an Ip overshoot similar to that used in existing experiments, and are shown to perform significantly better than a set of non-optimized trajectories, allowing stationary profiles to be obtained at the beginning of the flat-top phase. Additional information is obtained, including the parameter sensitivity of the optimal solution, a linear model describing the linearized dynamics of the profiles around the optimal trajectory, as well as a classification of the actuator trajectories based on the critical constraint which limits their value at a given time. This provides a solid basis for subsequent closed-loop feedback controller design. The tools presented in this paper could be useful to improve existing tokamak operational scenarios, to prepare operation of future machines and optimize their design.",
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Non-linear model-based optimization of actuator trajectories for tokamak plasma profile control. / Felici, F.; Sauter, O.

In: Plasma Physics and Controlled Fusion, Vol. 54, No. 2, 025002, 2012, p. 025002-1/28.

Research output: Contribution to journalArticleAcademicpeer-review

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