Design and simulation of extremum-seeking open-loop optimal control of current profile in the DIII-D tokamak

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

doi:10.1088/0741-3335/50/11/115001

Cited by 84 publications

(63 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…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%

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

View full text Add to dashboard Cite

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.

show abstract

Section: Magnetohydrodynamic Equilibrmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…A type of feedback controller, more appropriate for real-time implementation than the hillclimbing numerical algorithm mentioned earlier, is the so-called extremum seeking controller. This is a type of nonlinear adaptive controller which has been used in other applications in the magnetic confinement fusion community: control of the mirror angle for maximum first-pass X3 absorption on TCV [29], control of the sawtooth period by changing the EC deposition location on TCV [30], optimization of Lower Hybrid wave absporption on the FTU tokamak [31], [32], and for simulation studies of optimal plasma profile control on DIII-D [33]. Its attractiveness stems from the relative simplicity of the feedback scheme and the well-established analysis and design methods.…”

Section: Feedback Controller Designmentioning

confidence: 99%

Feedback control of ECRH polarization on LHD

et al. 2010

View full text Add to dashboard Cite

Abstract. The polarization of ECRH waves, set by the orientation of a pair of corrugated mirror polarizers in the transmission line, determines the degree of coupling to O-and X-modes in the plasma and has an important effect on the first-pass absorption. Existing methods for determining the required polarization have been found adequate in most experiments. However, as the pulse length is increased it becomes increasingly important to maximize the first-pass absorption while the plasma or injection conditions change or when there can be significant O-to Xmode power coupling during propagation, particularly in the edge plasma region of a stellarator. This has motivated the development of a dedicated feedback control system which is able to adjust the polarizers' angles settings during the discharge in order to maintain the highest possible absorption. An extremum seeking controller is shown to successfully recover the optimum polarization setting during long-pulse ECRH experiments on LHD.

show abstract

Design and simulation of extremum-seeking open-loop optimal control of current profile in the DIII-D tokamak

Cited by 84 publications

References 25 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

Feedback control of ECRH polarization on LHD

Contact Info

Product

Resources

About