Ramp-Up-Phase Current-Profile Control of Tokamak Plasmas via Nonlinear Programming

Xu, Chao; Ou, Yongsheng; Dalessio, J.; Schuster, Eugenio; Luce, T. C.; Ferron, J. R.; Walker, M.L.; Humphreys, D.A.

doi:10.1109/tps.2009.2037626

Cited by 47 publications

(64 citation statements)

References 17 publications

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“…Simplified distributed parameter system models have been studied in [18] and [27] toward current profile control at DIII-D and Tore Supra, respectively. In order to achieve an optimal current evolution in the plasma discharges of the ramp-up phase, various dynamic optimization techniques are applied to obtain numerical solutions in an open loop fashion, such as [7], [8], [19], [28]. For online implementations of optimized actuation commands, feedback strategies (e.g., [5,6,20,29]) are necessary to attenuate external perturbations and system uncertainties.…”

Section: Magnetohydrodynamic Equilibrmentioning

confidence: 99%

“…According to (28),θ(t) is approximated by a piecewise-constant function with discontinuities at the internal knot points γ 1 , γ 2 , . .…”

Section: Piecewise-linear Control Parameterizationmentioning

confidence: 99%

“…This section reports computational results from applying the method described in Sections 3 and 4 to the example problem in reference [28]. For this example, the functions D(ρ), ϑ 1 (ρ), and ϑ 2 (ρ) are constructed using experimental data from the DIII-D tokamak in San Diego, California; see and (53)- (54).…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…For this example, the functions D(ρ), ϑ 1 (ρ), and ϑ 2 (ρ) are constructed using experimental data from the DIII-D tokamak in San Diego, California; see and (53)- (54). We considered two target profiles ω d (ρ) in our simulations: the first target profile is generated using the experimental input data in [28]; the second target profile is generated using the experimental output flux data in [19] (see Figure 20(a) in [19]). …”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Our first numerical experiment was designed to validate the finite element scheme by simulating the approximate ODE model under the experimental input data in [28]. For the spatial discretization of the PDE system, we used the first-order basis functions β i (ρ), i = 1, 2, .…”

Section: Model Validationmentioning

confidence: 99%

See 4 more Smart Citations

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

Ren

Lin

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steadystate operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the rampup phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

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Section: Magnetohydrodynamic Equilibrmentioning

confidence: 99%

“…According to (28),θ(t) is approximated by a piecewise-constant function with discontinuities at the internal knot points γ 1 , γ 2 , . .…”

Section: Piecewise-linear Control Parameterizationmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Model Validationmentioning

confidence: 99%

See 3 more Smart Citations

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

Ren

Lin

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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Dynamic optimization of trajectory for ramp‐up current profile in tokamak plasma

Ren

2016

Asia-Pacific J Chem Eng

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In this paper, we consider an open-loop, finite-time, optimal control problem of attaining a specific desired current profile during the ramp-up phase by finding the best open-loop actuator input trajectories. Average density, total power, and plasma current are used as control actuators to manipulate the profile shape in tokamak plasmas. Based on the control parameterization method, we propose a numerical solution procedure directly to solve the original PDE-constrained optimization problem using gradient-based optimization techniques such as sequential quadratic programming (SQP). This paper is aimed at proposing an effective framework for the solution of PDE-constrained optimization problem in tokamak plasmas. A more user-friendly and efficient graphical user interface (GUI) is designed in MATLAB and the numerical simulation results are verified to demonstrate its applicability. In addition, the proposed framework of combining existing PDE and numerical optimization solvers to solve PDEconstrained optimization problem has the prospective to target challenge advanced control problems arising in more general chemical engineering processes.

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Ramp-Up-Phase Current-Profile Control of Tokamak Plasmas via Nonlinear Programming

Cited by 47 publications

References 17 publications

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

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

Dynamic optimization of trajectory for ramp‐up current profile in tokamak plasma

Receding-horizon optimal control of the current profile evolution during the ramp-up phase of a tokamak discharge

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