William Wehner

Integrated magnetic and kinetic control of advanced tokamak plasmas on DIII-D based on data-driven models

The first real-time profile control experiments integrating magnetic and kinetic variables were performed on DIII-D in view of regulating and extrapolating advanced tokamak scenarios to steady-state devices and burning plasma experiments. Device-specific, control-oriented models were obtained from experimental data using a generic two-time-scale method that was validated on JET, JT-60U and DIII-D under the framework of the International Tokamak Physics Activity for Integrated Operation Scenarios (Moreau et al 2011 Nucl. Fusion 51 063009). On DIII-D, these data-driven models were used to synthesize integrated magnetic and kinetic profile controllers. The neutral beam injection (NBI), electron cyclotron current drive (ECCD) systems and ohmic coil provided the heating and current drive (H&CD) sources. The first control actuator was the plasma surface loop voltage (i.e. the ohmic coil), and the available beamlines and gyrotrons were grouped to form five additional H&CD actuators: co-current on-axis NBI, co-current off-axis NBI, counter-current NBI, balanced NBI and total ECCD power from all gyrotrons (with off-axis current deposition). Successful closed-loop experiments showing the control of (a) the poloidal flux profile, Ψ(x), (b) the poloidal flux profile together with the normalized pressure parameter, βN, and (c) the inverse of the safety factor profile, , are described.

Control-oriented modelling for neoclassical tearing mode stabilization via minimum-seeking techniques

Suppression of magnetic islands driven by the neoclassical tearing mode (NTM) is necessary for efficient and sustained operation of tokamak fusion reactors. Compensating for the lack of bootstrap current, due to the pressure profile flattening in the magnetic island, by a localized electron cyclotron current drive (ECCD) has been proved experimentally as an effective method to stabilize NTMs. The effectiveness of this method is limited in practice by the uncertainties in the width of the island, the relative position between the island and the beam, and the ECCD power threshold for NTM stabilization. Heuristic search and suppress algorithms have been proposed and shown effective in improving the alignment of the ECCD beam with the island, using only an estimate of the island width. Making use of this estimate, real-time, non-model-based, extremum-seeking optimization algorithms have also been proposed not only for beam steering but also for power modulation in order to minimize the island-beam misalignment and the time required for NTM stabilization. A control-oriented dynamic model for the effect of ECCD on the magnetic island is proposed in this work to enable both control design and performance analysis of these minimum-seeking type of controllers. The model expands previous work by including the impact of beam modulation parameters such as the island-beam phase mismatch and the beam duty-cycle on the island width dynamics.

Stabilization of Neoclassical Tearing Modes in tokamak fusion plasmas via extremum seeking

The neoclassical tearing mode (NTM) instability produces magnetic islands in tokamak plasmas that can degrade confinement and lead to plasma disruptions. NTMs are driven by a lack of bootstrap current inside the magnetic island where the pressure profile is flattened. Suppression of these islands is necessary for sustained energy confinement and efficient operation in tokamak magnetic-fusion reactors. Compensating for the lack of bootstrap current by an Electron Cyclotron Current Drive (ECCD) has been proved experimentally as an effective method to stabilize NTMs. The effectiveness of this method is limited in practice by the uncertainties in the width of the island, the relative position between the island and the EC beam, and the EC power threshold for NTM stabilization. Heuristic search and suppress algorithms have been proposed and shown effective to improve the alignment of the EC beam with the island by just using an estimate of the island width. Making use of this estimate, a real-time, non-model-based, extremum-seeking optimization algorithm is proposed in this work for EC beam steering and modulation in order to minimize the island-beam misalignment and the time (control energy) required for NTM stabilization. The efficiency of the proposed method is compared with traditional search and suppress algorithms.

Multivariable robust control of the plasma rotational transform profile for advanced tokamak scenarios in DIII-D

The tokamak is a high order, distributed parameter, nonlinear system with a large number of instabilities. Therefore, accurate theoretical plasma models are difficult to develop. However, linear plasma response models around a particular equilibrium can be developed by using data-driven modeling techniques. This paper introduces a linear model of the rotational transform ι profile evolution based on experimental data from the DIII-D tokamak. The model represents the response of the ι profile to the electric field due to induction as well as to heating and current drive (H&CD) systems. The control goal is to use both induction and H&CD systems to regulate the plasma ι profile around a particular target profile. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed sensitivity H∞ control design problem is formulated to synthesize a stabilizing feedback controller without input constraint that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is then augmented with an anti-windup compensator, which keeps the given profile controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop unmodified when no saturation is present. Finally, computer simulations and experimental results illustrate the performance of the model-based profile controller.

Data-driven modeling and feedback tracking control of the toroidal rotation profile for advanced tokamak scenarios in DIII-D

First-principle predictive tokamak plasma models based on flux averaged transport equations often yield complex expressions not suitable for real time control implementations. Addition of turbulent transport phenomena further encumbers these models with transport coefficients that must be determined experimentally and the interdependences between parameters must be accounted for with ad hoc assumptions. As an alternative to first principle modeling, data-driven modeling techniques involving system identification have the potential to obtain practical, low complexity, dynamic models without the need for ad hoc assumptions. This paper considers the evolution of the toroidal rotation profile in response to the heating and current drive (H&CD) systems. Experiments are conducted during plasma current flattop, in which the actuators are modulated in open-loop to obtain data for the model identification. The rotation profile is discretized in the spatial coordinate by Galerkin projection. Then a linear state space model is generated by the prediction error method (PEM) to relate the rotation profile to the actuators according to a least squares fit. An optimal tracking controller is proposed to regulate the rotation profile to a desired reference trajectory.

A two-time-scale model-based combined magnetic and kinetic control system for advanced tokamak scenarios on DIII-D

System identification techniques have been successfully used to obtain linear dynamic plasma response models around a particular equilibrium in different tokamaks. This paper identifies a two-time-scale dynamic model of the rotational transform ι profile and βN in response to the electric field due to induction as well as to heating and current drive (H&CD) systems based on experimental data from DIII-D. The control goal is to regulate the plasma ι profile and βN around a particular target value. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed sensitivity H∞ control design problem is solved to determine a stabilizing feedback controller that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is augmented with an anti-windup compensator, which keeps the given controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop unmodified when no saturation is present. Experimental results illustrate the performance of the proposed controller, which is one of the first profile controllers integrating magnetic and kinetic variables ever implemented in DIII-D.

Optimal feedback control of the poloidal magnetic flux profile in the DIII-D tokamak based on identified plasma response models

First-principles predictive models based on flux-averaged transport equations often yield complex expressions not suitable for real-time control implementations. It is however always possible to reduce these models to forms suitable for control design while preserving the dominant physics of the system. If further model simplification is desired at the expense of less model accuracy and controller capability, data-driven modeling emerges as an alternative to first-principles modeling. System identification techniques have the potential of producing low-complexity, linear models that can capture the system dynamics around an equilibrium point. This paper focuses on the control of the poloidal magnetic flux profile evolution in response to the heating and current drive (H&CD) systems and the total plasma current. Open-loop data for model identification is collected during the plasma current flattop in a high-confinement scenario (H-mode). Using this data a linear state-space plasma response model for the poloidal magnetic flux profile dynamics around a reference profile is identified. The control goal is to use the H&CD systems and the plasma current to regulate the magnetic profile around a desired target profile in the presence of disturbances. The target profile is defined close enough to the reference profile used for system identification in order to stay within the range of validity of the identified model. An optimal state feedback controller with integral action is designed for this purpose. Experimental results showing the performance of the proposed controller implemented in the DIII-D tokamak are presented.

Physics-model-based nonlinear actuator trajectory optimization and safety factor profile feedback control for advanced scenario development in DIII-D

DIII-D experimental results are reported to demonstrate the potential of physics-model-based safety factor profile control for robust and reproducible sustainment of advanced scenarios. In the absence of feedback control, variability in wall conditions and plasma impurities, as well as drifts due to external disturbances, can limit the reproducibility of discharges with simple pre-programmed scenario trajectories. The control architecture utilized is a feedforward + feedback scheme where the feedforward commands are computed off-line and the feedback commands are computed on-line. In this work, a first-principles-driven (FPD), physics-based model of the q profile and normalized beta () dynamics is first embedded into a numerical optimization algorithm to design feedforward actuator trajectories that steer the plasma through the tokamak operating space to reach a desired stationary target state that is characterized by the achieved q profile and . Good agreement between experimental results and simulations demonstrates the accuracy of the models employed for physics-model-based control design. Second, a feedback algorithm for q profile control is designed following an FPD approach, and the ability of the controller to achieve and maintain a target q profile evolution is tested in DIII-D high confinement (H-mode) experiments. The controller is shown to be able to effectively control the q profile when is relatively close to the target, indicating the need for integrated q profile and control to further enhance the ability to achieve robust scenario execution. The ability of an integrated q profile + feedback controller to track a desired target is demonstrated through simulation.

Experimental and Simulation Testing of Physics-model-based Safety Factor Profile and Internal Energy Feedback Controllers in DIII-D Advanced Tokamak Scenarios

Abstract Active closed-loop control of the plasma safety factor profile ( q -profile) and internal energy dynamics in nuclear fusion tokamak devices has the potential to significantly impact the success of the ITER project. These plasma properties are related to both the stability and performance of a given plasma operating scenario. In this work, we develop integrated feedback control algorithms to control the q -profile and internal energy dynamics in DIII-D advanced tokamak (high performance) scenarios. The feedback controllers are synthesized by embedding a nonlinear, physics-based, control-oriented partial differential equation model of the plasma dynamics into the control design and to be robust to uncertainties in the plasma electron density, electron temperature, and plasma resistivity profiles. The auxiliary heating and current-drive system and the total plasma current are the actuators utilized by the feedback controllers to control the plasma dynamics. Finally, the feedback controllers are tested both through simulations based on the physics-based model and experimentally in the DIII-D tokamak.

Model predictive control with integral action for the rotational transform profile tracking in NSTX-U

Active control of the toroidal current density profile is among those plasma control milestones that the National Spherical Tokamak eXperiment - Upgrade (NSTX-U) program must achieve to realize its next-step operational goals, which are characterized by high-performance, long-pulse, MHD-stable plasma operation with neutral beam heating. In this work, a previously developed physics-based control-oriented model is embedded in a feedback control scheme based on a model predictive control (MPC) strategy to track a desired current density profile evolution specified indirectly by a desired rotational transform profile. An integrator is embedded into the standard MPC formulation to account for various modeling uncertainties and external disturbances. The neutral beam powers, electron density, and total plasma current are used as actuators. The effectiveness of the proposed MPC strategy in regulating the current density profile in NSTX-U is demonstrated in closed-loop nonlinear simulations.