Justin Barton

First-principles-driven model-based current profile control for the DIII-D tokamak via LQI optimal control

In tokamak fusion plasmas, control of the spatial distribution profile of the toroidal plasma current plays an important role in realizing certain advanced operating scenarios. These scenarios, characterized by improved confinement, magnetohydrodynamic stability, and a high fraction of non-inductively driven plasma current, could enable steady-state reactor operation with high fusion gain. Current profile control experiments at the DIII-D tokamak focus on using a combination of feedforward and feedback control to achieve a targeted current profile during the ramp-up and early flat-top phases of the shot and then to actively maintain this profile during the rest of the discharge. The dynamic evolution of the current profile is nonlinearly coupled with several plasma parameters, motivating the design of model-based control algorithms that can exploit knowledge of the system to achieve desired performance. In this work, we use a first-principles-driven, control-oriented model of the current profile evolution in low confinement mode (L-mode) discharges in DIII-D to design a feedback control law for regulating the profile around a desired trajectory. The model combines the magnetic diffusion equations with empirical correlations for the electron temperature, resistivity, and non-inductive current drive. To improve tracking performance of the system, a nonlinear input transformation is combined with a linear-quadratic-integral (LQI) optimal controller designed to minimize a weighted combination of the tracking error and controller effort. The resulting control law utilizes the total plasma current, total external heating power, and line averaged plasma density as actuators. A simulation study was used to test the controllers performance and ensure correct implementation in the DIII-D plasma control system prior to experimental testing. Experimental results are presented that show the first-principles-driven model-based control schemes successful rejection of input disturbances and perturbed initial conditions, as well as target trajectory tracking.

Toroidal current profile control during low confinement mode plasma discharges in DIII-D via first-principles-driven model-based robust control synthesis

In order for ITER to be capable of operating in advanced tokamak operating regimes, characterized by a high fusion gain, good plasma confinement, magnetohydrodynamic stability and a non-inductively driven plasma current, for extended periods of time, several challenging plasma control problems still need to be solved. Setting up a suitable toroidal current density profile in the tokamak is key for one possible advanced operating scenario characterized by non-inductive sustainment of the plasma current. At the DIII-D tokamak, the goal is to create the desired current profile during the ramp-up and early flat-top phases of the plasma discharge and then actively maintain this target profile for the remainder of the discharge. The evolution in time of the toroidal current profile in tokamaks is related to the evolution of the poloidal magnetic flux profile, which is modelled in normalized cylindrical coordinates using a first-principles, nonlinear, dynamic partial differential equation (PDE) referred to as the magnetic diffusion equation. The magnetic diffusion equation is combined with empirical correlations developed from physical observations and experimental data from DIII-D for the electron temperature, the plasma resistivity and the non-inductive current drive to develop a simplified, control-oriented, nonlinear, dynamic PDE model of the poloidal flux profile evolution valid for low confinement mode discharges. In this work, we synthesize a robust feedback controller to reject disturbances and track a desired reference trajectory of the poloidal magnetic flux gradient profile by employing the control-oriented model of the system. A singular value decomposition of the static gain matrix of the plant model is utilized to identify the most relevant control channels and is combined with the dynamic response of system around a given operating trajectory to design the feedback controller. A general framework for real-time feedforward + feedback control of magnetic and kinetic plasma profiles was implemented in the DIII-D Plasma Control System and was used to demonstrate the ability of the feedback controller to control the toroidal current profile evolution in the DIII-D tokamak. These experiments constitute the first time ever a first-principles-driven, model-based, closed-loop magnetic profile controller was successfully implemented and tested in a tokamak device.

Backstepping Control of the Toroidal Plasma Current Profile in the DIII-D Tokamak

One of the most promising devices for realizing power production through nuclear fusion is the tokamak. To maximize performance, it is preferable that tokamak reactors achieve advanced operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic stability, and a largely noninductively driven plasma current. Such scenarios could enable steady-state reactor operation with high fusion gain, the ratio of produced fusion power to the external power provided through the plasma boundary. For certain advanced scenarios, control of the spatial profile of the plasma current will be essential. The complexity of the current profile dynamics, arising due to nonlinearities and couplings with many other plasma parameters, motivates the use of model-based control algorithms that can account for the system dynamics. A first-principles-driven, control-oriented model of the current profile evolution in low-confinement mode (L-mode) discharges in the DIII-D tokamak is employed to address the problem of regulating the current profile evolution around desired trajectories. In the primarily inductive L-mode discharges considered in this paper, the boundary condition, which is dependent on the total plasma current, has the largest influence on the current profile dynamics, motivating the design of a boundary feedback control law to improve the system performance. The backstepping control design technique provides a systematic method to obtain a boundary feedback law through the transformation of a spatially discretized version of the original system into an asymptotically stable target system with desirable properties. Through a nonlinear transformation of the available physical actuators, the resulting control scheme produces references for the total plasma current, total power, and line averaged density, which are tracked by existing dedicated control loops. Adaptiveness is added to the control scheme to improve upon the backstepping controllers disturbance rejection and tracking capability. Prior to experimental testing, a Simserver simulation was carried out to study the controllers performance and ensure proper implementation in the DIII-D Plasma Control System. An experimental test was performed on DIII-D to test the ability of the controller to reject input disturbances and perturbations in initial conditions and to demonstrate the feasibility of the proposed control approach.

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.

Physics-based control-oriented modeling of the safety factor profile dynamics in high performance tokamak plasmas

The tokamak is a device that utilizes magnetic fields to confine a reactant gas to generate energy from nuclear fusion reactions. The next step towards the realization of a tokamak power plant is the ITER project, and extensive research has been conducted to find high performance operating scenarios characterized by a high fusion gain and plasma stability. A key property related to both the stability and performance of the plasma is the safety factor profile (q-profile). In this work, a general control-oriented physics-based modeling approach is developed, with emphasis on high performance scenarios, to convert the first-principles physics model that describes the q-profile evolution in the tokamak into a form suitable for control design, with the goal of developing closed-loop controllers to drive the q-profile to a desired target evolution. The DINA-CH& CRONOS and PTRANSP advanced tokamak simulation codes are used to tailor the first-principles-driven (FPD) model to the ITER and DIII-D tokamak geometries, respectively. The models prediction capabilities are illustrated by comparing the prediction to simulated data from DINA-CH&CRONOS for ITER and to experimental data for DIII-D.

Physics-based control-oriented modeling and robust feedback control of the plasma safety factor profile and stored energy dynamics in ITER

Many challenging plasma control problems still need to be addressed in order for the ITER plasma control system (PCS) to be able to maintain the plasma within a predefined operational space and optimize the plasma state evolution in the tokamak, which will greatly aid in the successful achievement of ITERs goals. Firstly in this work, a general control-oriented, physics-based modeling approach is developed to obtain first-principles-driven (FPD) models of the plasma magnetic profile and stored energy evolutions valid for high performance, high confinement (H-mode) scenarios, with the goal of developing model-based closed-loop algorithms to control the safety factor profile (q profile) and stored energy evolutions in the tokamak. The FPD model is tailored to H-mode burning plasma scenarios in ITER by employing the DINA-CH & CRONOS free-boundary tokamak simulation code, and the FPD models prediction capabilities are demonstrated by comparing the prediction to data obtained from DINA-CH & CRONOS. Secondly, a model-based feedback control algorithm is designed to simultaneously track target q profile and stored energy evolutions in H-mode burning plasma scenarios in ITER by embedding the developed FPD model of the magnetic profile evolution into the control design process. The feedback controller is designed to ensure that the closed-loop system is robust to uncertainties in the electron density, electron temperature and plasma resistivity, and is tested in simulations with the developed FPD model. The effectiveness of the controller is demonstrated by first tracking nominal q profile and stored energy target evolutions, and then modulating the generated fusion power while maintaining the q profile in a stationary condition. In the process, many key practical issues for plasma profile control in ITER are investigated, which will be useful for the development of the ITER PCS that has recently been initiated. Some of the more pertinent investigated issues are the time necessary to drive the q profile and stored energy to a target evolution, and whether plasma control can be achieved through the use of separate individual control algorithms or whether a more fully integrated approach is required.

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.

Robust control of the safety factor profile and stored energy evolutions in high performance burning plasma scenarios in the ITER tokamak

The next step towards the development of a nuclear fusion tokamak power plant is the ITER project. Integrated closed-loop control of the plasma stored energy and safety factor profile (q-profile) is key to maintaining the plasma in a stable state and maximizing its performance. The q-profile evolution in tokamaks is related to the poloidal magnetic flux profile evolution, which is described by a physics model called the magnetic diffusion equation. A first-principles-driven (FPD), nonlinear, control-oriented model of the poloidal magnetic flux profile evolution is obtained by first combining the magnetic diffusion equation with simplified physics-based models of the noninductive current-drives. Secondly, the electron density, electron temperature, and plasma resistivity profiles are modeled as uncertain parameters by defining ranges in which they are expected to be in typical ITER high performance scenarios. This FPD model is then employed to synthesize an H∞ feedback algorithm that utilizes ITERs auxiliary heating/current-drive sources and the total plasma current as actuators to control the q-profile and stored energy in high performance burning plasma scenarios while ensuring the closed-loop system is robust to the uncertainties in the plasma parameters. Finally, the effectiveness of the controller is demonstrated through simulation.

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.

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.