Towards model-based current profile control at DIII-D

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

doi:10.1016/j.fusengdes.2007.04.016

Cited by 82 publications

(79 citation statements)

References 15 publications

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“…From the viewpoint of distributed parameter systems governed by PDEs, several advanced control and optimization approaches have been discussed based on new developments in internal diagnostics and plasma actuation. 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].…”

Section: Magnetohydrodynamic Equilibrmentioning

confidence: 99%

“…In the papers by Witrant [27] and Ou [18], the mathematical formulation for the distributed parameter system framework is discussed, for both the Tore Supra and the DIII-D experimental tokamaks. In these papers, only the magnetic flux PDE is considered and scaling laws are used to account (in an approximate fashion) for the effects of the other PDEs.…”

Section: Magnetohydrodynamic Equilibrmentioning

confidence: 99%

“…In these papers, only the magnetic flux PDE is considered and scaling laws are used to account (in an approximate fashion) for the effects of the other PDEs. In the present work, using the framework proposed by Witrant [27] and Ou [18], we consider the problem of obtaining a specific desired output current profile at the end of the current ramp-up phase, as shown in Figure 2. This problem can be formulated as a finite-time dynamic optimization problem for the magnetic flux diffusion PDE system, which is a type of a bilinear infinite-dimensional system, i.e., the diffusivity control term appears in the second-order elliptic operator.…”

Section: Magnetohydrodynamic Equilibrmentioning

confidence: 99%

See 2 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%

Section: Magnetohydrodynamic Equilibrmentioning

confidence: 99%

Section: Magnetohydrodynamic Equilibrmentioning

confidence: 99%

See 1 more Smart Citation

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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“…This will be particularly crucial for large experiments like ITER where disruptions can have serious consequences. Taking this approach one step further, one can also optimize future actuator inputs by iteratively predicting the plasma state in a model-predictive control scheme as proposed by [16], [17].…”

Section: Tokamakmentioning

confidence: 99%

Real-time physics-model-based simulation of the current density profile in tokamak plasmas

et al. 2011

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Abstract.A new paradigm is presented to reconstruct the plasma current density profile in a tokamak in real-time. The traditional method of basing the reconstruction on real-time diagnostics combined with a real-time GradShafranov solver suffers from the difficulty of obtaining reliable internal current profile measurements with sufficient spatial and temporal accuracy to have a complete picture of the profile evolution at all times. A new methodology is proposed in which the plasma current density profile is simulated in real-time by solving the first-principle physics-based equations determining its evolution. Effectively, an interpretative transport simulation similar to those run today in post-plasma shot analysis is performed in real-time. This provides realtime reconstructions of the current density profile with spatial and temporal resolution constrained only by the capabilities of the computational platform used and not by the available diagnostics or the choice of basis functions. The diagnostic measurements available in real-time are used to constrain and improve the accuracy of the simulated profiles. Estimates of other plasma quantities, related to the current density profile, become available in real-time as well. The implementation of the proposed paradigm in the TCV tokamak is discussed, and its successful use in plasma experiments is demonstrated. This framework opens up the possibility of unifying q profile reconstructions across different tokamaks using a common physics model and will support a wealth of applications in which improved real-time knowledge of the plasma state is used for feedback control, disruption avoidance, scenario monitoring, and external disturbance estimation.

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“…Recent advances in steady steady-state profile control can be found for instance in [7,10,13,14] for JET and DIII-D. Some reviews of Tore Supra feedback control achievements can be found in [4,8].…”

Section: Introductionmentioning

confidence: 99%

Model-based control of the magnetic flux profile in a Tokamak plasma

Argomedo¹,

Witrant²,

Prieur³

et al. 2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-A new model-based controller for the magnetic flux profile in a Tokamak plasma was developed using a simplified model of the magnetic flux dynamics. This simplified model is based on physically relevant dynamics that take into account the distributed nature of the system. Shape constraints on the controlled inputs are introduced, representing the limitations on the shape of the deposed current profiles by non-inductive current sources on the plasma. Some simulation results are presented and discussed.

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Towards model-based current profile control at DIII-D

Cited by 82 publications

References 15 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

Real-time physics-model-based simulation of the current density profile in tokamak plasmas

Model-based control of the magnetic flux profile in a Tokamak plasma

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