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Integrated-control solutions will play a significant role in future tokamaks, in which a variety of coupled control problems will need to be solved simultaneously by means of a limited number of actuators. In this article, the problem of simultaneously regulating the global toroidal rotation, $\Omega _\phi $ , and total plasma energy, $W$ , is tackled. These two 0-D variables, $\Omega _\phi $ and $W$ , depend on the ion toroidal rotation and electron temperature profiles, respectively. Both $\Omega _\phi $ and $W$ also depend on the electron density and safety factor profiles. The actuation methods considered in this article are co-current and counter-current neutral beam injection. A nonlinear, robust controller that makes use of Lyapunov redesign techniques is synthesized based on 0-D, control-oriented models of the $\Omega _\phi $ and $W$ dynamics. In addition, an actuator management scheme is designed to handle variations in the control priorities and availability of the neutral beam injectors. The actuator manager solves an optimization problem in real time in order to find the most appropriate course of action when unexpected changes occur. The integrated control architecture is tested for a DIII-D scenario by means of the 1-D code Control-Oriented Transport Simulator (COTSIM), which predicts the time evolution of the electron temperature, electron density, ion toroidal rotation, and safety factor profiles.

Integrated control of the toroidal current density profile, or alternatively the q-profile, and plasma stored energy is essential to achieve advanced plasma scenarios characterized by high plasma confinement, magnetohydrodynamics stability, and noninductively driven plasma current. The q-profile evolution is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). The MDE prediction depends heavily on the chosen models for the electron temperature, plasma resistivity, and non-inductive current drives. To aid control synthesis, control-oriented models for these plasma quantities are necessary to make the problem tractable. However, a relatively large deviation between the predictions by these control-oriented models and experimental data is not uncommon. For this reason, the electron temperature, plasma resistivity, and non-inductive current drives are modeled for control synthesis in this work as the product of an “uncertain” reference profile and a nonlinear function of the different auxiliary heating and current-drive (H&CD) source powers and the total plasma current. The uncertainties are quantified in such a way that the family of models arising from the modeling process is able to capture the q-profile and plasma stored energy dynamics from a typical EAST shot. A control-oriented nonlinear PDE model is developed by combining the MDE with the “uncertain” models for the electron temperature, plasma resistivity, and non-inductive current drives. This model is then rewritten into a control framework to design a controller that is robust against the modeled uncertainties. The resulting controller utilizes EAST's H&CD powers and total plasma current to regulate the q profile and plasma stored energy even when mismatches between modeled and actual dynamics are present. The effectiveness of the controller is demonstrated through nonlinear simulations.

Active control of the toroidal current density profile is critical for the upgraded National Spherical Torus eXperiment device (NSTX-U) to maintain operation at the desired high-performance, MHD-stable, plasma regime. Initial efforts towards current density profile control have led to the development of a control-oriented, physics-based, plasma-response model, which combines the magnetic diffusion equation with empirical correlations for the kinetic profiles and the non-inductive current sources. The developed control-oriented model has been successfully tailored to the NSTX-U geometry and actuators. Moreover, a series of efforts have been made towards the design of model-based controllers, including a linear-quadratic-integral optimal control strategy that can regulate the current density profile around a prescribed target profile while rejecting disturbances. In this work, the tracking performance of the proposed current-profile optimal controller is tested in numerical simulations based on the physics-oriented code TRANSP. These high-fidelity closed-loop simulations, which are a critical step before experimental implementation and testing, are enabled by a flexible framework recently developed to perform feedback control design and simulation in TRANSP.

There is an increasing need for integrating individual plasma-control algorithms with the ultimate goal of simultaneously regulating more than one plasma property. Some of these integrated-control solutions should have the capability of arbitrating the authority of the individual plasma-control algorithms over the available actuators within the tokamak. Such decision-making process must run in real time since its outcome depends on the plasma state. Therefore, control architectures including supervisory and/or exception-handling algorithms will play an essential role in future fusion reactors like ITER. However, most plasma-control experiments in present devices have focused so far on demonstrating control solutions for isolated objectives. In this work, initial experimental results are reported for simultaneous current-profile control, normalized-beta control, and Neoclassical Tearing Mode (NTM) suppression in DIII-D. Neutral beam injection (NBI), electron-cyclotron (EC) heating & current drive (H&CD), and plasma current modulation are the actuation methods. The NBI power and plasma current are always modulated by the Profile Control category within the DIII-D Plasma Control System (PCS) in order to control both the current profile and the normalized beta. EC H&CD is utilized by either the Profile Control or the Gyrotron categories within the DIII-D PCS as dictated by the Off-Normal and Fault Response (ONFR) system, which monitors the occurrence of an NTM and regulates the authority over the gyrotrons. The total EC power and poloidal mirror angles are the gyrotron-related actuation variables. When no NTM suppression is required, the gyrotrons are used by the Profile Control category, but when NTM suppression is required, the ONFR transfers the authority over the gyrotrons to the NTM stabilization algorithm located in the Gyrotron category. Initial experimental results show that simultaneous control of different aspects of the plasma dynamics may improve the overall control and plasma performances. Also, the potential of the ONFR system to successfully integrate competing control algorithms is demonstrated.

The mission of the low aspect ratio spherical tokamak NSTX-U is to advance the physics basis and technical solutions required for optimizing the configuration of next-step steady-state tokamak fusion devices. NSTX-U will ultimately operate at up to 2 MA of plasma current and 1 T toroidal field on axis for 5 seconds, and has available up to 15 MW of Neutral Beam Injection (NBI) power at different tangency radii and 6 MW of High Harmonic Fast Wave (HHFW) heating. With these capabilities NSTX-U will develop the physics understanding and control tools to ramp-up and sustain high performance fully non-inductive plasmas with large bootstrap fraction and enhanced confinement enabled via the low aspect ratio, high beta configuration. With its unique capabilities, NSTX-U research also supports ITER and other critical fusion development needs. Super-Alfvénic ions in beam-heated NSTX-U plasmas access energetic particle parameter space that is relevant for both -heated conventional and low aspect ratio burning plasmas. NSTX-U can also generate very large target heat fluxes to test conventional and innovative plasma exhaust and plasma facing component (PFC) solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, energetic particle stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control.

ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. If the plasma temperature were to inadvertently rise in this burning regime, the positive correlation between temperature and the fusion reaction rate would establish a destabilizing positive feedback loop. Careful regulation of the plasma’s temperature and density, or burn control, is required to prevent these potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. An adaptive estimator manages destabilizing uncertainties in the plasma confinement properties and the particle recycling conditions (caused by plasma–wall interactions). The controller regulates the plasma density with requests for deuterium and tritium particle injections. In ITER-like plasmas, the fusion-born alpha particles will primarily heat the plasma electrons, resulting in different electron and ion temperatures in the core. By considering separate response models for the electron and ion energies, the proposed controller can independently regulate the electron and ion temperatures by requesting that different amounts of auxiliary power be delivered to the electrons and ions. These two commands for a specific control effort (electron and ion heating) are sent to an actuator allocation module that optimally maps them to the heating actuators available to ITER: an electron cyclotron heating system (20 MW), an ion cyclotron heating system (20 MW), and two neutral beam injectors (16.5 MW each). Two different actuator allocators are presented in this work. The first actuator allocator finds the optimal mapping by solving a convex quadratic program that includes actuator saturation and rate limits. It is nonadaptive and assumes that the mapping between the commanded control efforts and the allocated actuators (i.e. the effector model) contains no uncertainties. The second actuator allocation module has an adaptive estimator to handle uncertainties in the effector model. This uncertainty includes actuator efficiencies, the fractions of neutral beam heating that are deposited into the plasma electrons and ions, and the tritium concentration of the fueling pellets. Furthermore, the adaptive allocator considers actuator dynamics (actuation lag) that contain uncertainty. This adaptive allocation algorithm is more computationally efficient than the aforementioned nonadaptive allocator because it is computed using dynamic update laws so that finding the solution to a static optimization problem is not required at every time step. A simulation study assesses the performance of the proposed adaptive burn controller augmented with each of the actuator allocation modules.

A novel integrated-control architecture has been tested in nonlinear, one-dimensional simulations using the control-oriented transport simulator (COTSIM©) and in DIII-D experiments. Integrated architectures that can perform continuous-mission control while also handling off-normal events will be vital in future reactor-grade tokamaks. Continuous-mission controllers for individual magnetic and kinetic scalars (thermal stored-energy (W), volume-average toroidal rotation (Ω ϕ ), and safety factor profile (q) at different spatial locations) have been integrated in this work with event-triggered neoclassical tearing-mode (NTM) suppression controllers by combining them into an architecture augmented by a supervisory and exception handling (S&EH) system and an actuator management (AM) system. The AM system, which enables the integration of competing controllers, solves in real time a nonlinear optimization problem that takes into account the high-level control priorities dictated by the S&EH system. The resulting architecture offers a high level of integration and some of the functionalities that will be required to fulfill the advanced-control requirements anticipated for ITER. Initial simulations using COTSIM suggest that the plasma performance and its MHD stability may be improved under integrated feedback control. In addition, the integrated-control architecture has been implemented in the DIII-D plasma control system and tested experimentally for the first time ever in DIII-D in a high-q min scenario, which is a candidate for steady-state operation in ITER.

Generating electricity by harnessing the energy released from nuclear fusion reactions is an emerging environmentally-friendly approach. A tokamak is a toroidal device where a hot ionized gas, or plasma, is magnetically confined at temperatures suitable for nuclear fusion. Future commercial tokamaks will require proper control of external actuators, such as particle injection and auxiliary heating, to regulate the density and temperature of burning (fusion producing) plasmas. This is known as burn control, and it is one of the greatest challenges in fusion reactors. Engineering limitations may force upcoming reactors, such as ITER, to operate at conditions where the thermonuclear reaction rate increases as the plasma temperature increases. Plasma operation necessitates active control schemes to precisely regulate the nonlinear burning plasma dynamics. Controllers based on linearized models may fail under large perturbations. Therefore, control designs that consider the nonlinearities of the multivariable plasma dynamics are indeed necessary. In this work, a control algorithm is proposed based on a nonlinear, volume- averaged, two-temperature model. This zero-dimensional (0D) model consists of particle and energy conservation equations. Since plasmas are highly complex systems, any reduced control- oriented model is bound to contain uncertainty. The considered model contains uncertainties in the relationship between the ion and electron temperatures, the plasma confinement scalings, and the particle recycling that results from plasma-wall interactions. Adaptive control laws are employed to stabilize the system despite these numerous uncertainties. A simulation study illustrates the effectiveness of the presented adaptive controller.

Tokamaks are devices with a toroidal shape in which a high-temperature ionized gas (plasma) is confined by means of helical magnetic fields. The final goal of these devices is to obtain energy from thermonuclear fusion reactions within this plasma. A multitude of coupled control problems arise in tokamak-plasma research that need to be solved simultaneously. For tokamaks to be able to operate safely while maximizing plasma performance, integrated control schemes that can handle different aspects of the plasma dynamics must be developed. Moreover, due to the inherent uncertainty that exists in the plasma modeling process, such controllers must be robust against unknown variations of the plasma behavior. In this work, a nonlinear, robust controller is designed for simultaneous regulation of magnetic and kinetic scalar variables, namely the central safety factor, q 0 , the edge safety factor, q edge , the total stored energy, W, and the global toroidal rotation, Ω ϕ . The controller is synthesized from physics-based, zero-dimensional (0D) models of the individual scalars’ dynamics. One-dimensional (1D) simulations using the COTSIM (Control-Oriented Transport Simulator) code are employed to test the proposed controller in a DIII-D scenario.

In future burning tokamaks, active control of the plasma temperature and density will be necessary to produce a determined amount of fusion power. Conventional actuation methods, such as auxiliary power modulation and fueling rate modulation, are usually employed to tackle this so-called burn control problem. Fueling rate modulation can be used not only to directly control the plasma density but also to indirectly control the plasma energy by means of isotopic fuel tailoring. Moreover, based on recent experiments, the in-vessel coil system arises as a possible actuation method to decrease the plasma energy by generating non-axisymmetric fields in the plasma that may reduce the energy confinement time. In this work, a nonlinear burn controller that integrates the three mentioned actuators is proposed. The controller performance is tested via simulations for an ITER-like scenario.

Ongoing work in the fusion community focuses on developing advanced plasma scenarios characterized by high plasma confinement, magnetohydrodynamic (MHD) stability, and noninductively driven plasma current. The toroidal current density profile, or alternatively the q profile, together with the normalized beta, are often used to characterize these advanced scenarios. The development of these advanced scenarios is experimentally carried out by specifying the devices’ actuator trajectory waveforms, such as the total plasma current, the plasma density, and the auxiliary heating and current-drive (H&CD) sources based on trial-and-error basis. In this work, a model-based numerical optimization approach is followed to complement the experimental effort on actuator trajectory planning in the EAST tokamak. The evolution of the q profile is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). In this work, the MDE is combined with physics-based correlations obtained from EAST experimental data for the plasma density, temperature, resistivity and non-inductive current drives to develop a control-oriented nonlinear PDE model. The optimization objective is to design feedforward trajectories for the plasma current, plasma density, electron cyclotron heating power, neutral beam injection power and lower hybrid current drive power that steer the plasma to desired q profile and βN such that the achieved state is stationary in time. The optimization is subject to the plasma dynamics (described by the physics-based PDE model) and plasma state and actuator constraints, such as the maximum available amount of H&CD power and MHD stability limits. This defines a nonlinear, constrained optimization problem that is solved by employing sequential quadratic programming. The optimized actuator trajectories are assessed in nonlinear transport simulations in preparation for experimental tests in EAST.

Active control of the toroidal current density profile is among those plasma control milestones that the National Spherical Torus eXperiment-Upgrade (NSTX-U) program must achieve to realize its next-step operational goals. Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards control design is the development of a physics-based, control-oriented model for the current profile evolution in response to non-inductive current drives and heating systems. The evolution of the toroidal current density profile is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). The proposed control-oriented model predicts the spatial-temporal evolution of the current density profile by combining the nonlinear MDE with physics-based correlations obtained at NSTX-U for the electron density, electron temperature, and non-inductive current drives (neutral beams). The resulting first-principles-driven, control-oriented model is tailored for NSTX-U based on predictions by the time-dependent transport code TRANSP. Main objectives and possible challenges associated with the use of the developed model for the design of both feedforward and feedback controllers are also discussed.

In this work, model-based control techniques are used to obtain target current profiles in low-confinement-mode (L-mode) as well as high-confinement-mode (H-mode) DIII-D discharges. The control problem is formulated as a trajectory optimization problem to search for a feasible path from the expected initial condition to the desired target. The result comprises a sequence of feedforward (open-loop) control requests and a corresponding state evolution from the initial condition to the desired target. On top of this optimal feedforward control sequence a feedback (closed-loop) controller based on a linearized model and optimal control design techniques is added to track the desired state evolution. The effectiveness of the control approach is demonstrated with experiments.

In future tokamaks, the control of burning plasmas will require careful regulation of the plasma density and temperature. Along with the design of effective burn-control systems, understanding how the fusion power varies in the density-temperature space is vital for the operation of fusion power plants. In this work, the steady-state operational space of ITER is studied using a control-oriented core-plasma model coupled to a two-point model of the scrape-off-layer (SOL) and divertor regions. The two models are coupled through the exchange of input-output parameters. The deuterium and tritium recycling from the wall are output parameters of the SOL-divertor model that are used as input parameters in the core-plasma density balance. Furthermore, the separatrix temperature, which is an output parameter of the SOL-divertor model, is incorporated into the radial core-plasma temperature profiles. Therefore, the temperature-dependent power balance of the plasma core is intimately linked to the SOL-divertor model. Both the power entering the SOL from the core, as determined by the core-plasma power balance, and the separatrix density, as dictated by the core-plasma density balance, are input parameters to the SOL-divertor model. They are control knobs in the SOL-divertor model that can be regulated using the core-plasma actuators: auxiliary power and pellet injection. There are various operational limitations, such as the saturation of the aforementioned actuators, that will prevent ITER from accessing certain high-fusion plasma regimes. The achievable tritium concentration in the fueling lines and the maximum sustainable heat load on the divertor will impose further restrictions. By accounting for these limitations, the ITER operational space is computed based on the coupled core-SOL-divertor model and visualized using Plasma Operation Contour (POPCON) plots that map performance metrics, such as the fusion to auxiliary power ratio, over the density-temperature space. Comparisons are drawn between plasmas with different recycling, confinement, and SOL-divertor conditions.

An integrated-control architecture for simultaneous regulation of the plasma internal inductance and normalized beta has been designed and tested in simulations using COTSIM (Control-Oriented Transport SIMulator). As present-day tokamaks evolve into nuclear-fusion reactors capable of producing net energy, a significant control-engineering challenge must be solved: regulating a wide variety of plasma variables, often simultaneously, by employing only a reduced number of actuators. As a contribution towards this objective, the present work tackles the problem of controlling the plasma internal inductance, which is a proxy for the broadness of the current-density profile, simultaneously with the plasma normalized beta. Based on zero-dimensional, control-oriented models of the plasma dynamics, individual Lyapunov-theory-based controllers for the internal inductance and normalized beta have been developed. These controllers are integrated by means of an actuator manager that decides, in real time, how the available actuators are utilized in order to fulfill as many control objectives as possible. In addition, the actuator manager is designed to achieve a particular performance metric defined by the control engineer. This metric could be, for example, prioritizing a particular control task over the others and/or minimizing the use of a particular actuator during certain phases of the plasma discharge. Using COTSIM, which includes one-dimensional models of the plasma current-density and electron-temperature dynamics, the performance of the integrated-control framework has been tested in a steady-state scenario for the DIII-D tokamak. These simulation results yield illustrative insights into the plasma current-density and electron-temperature controllability with the current actuation capabilities in DIII-D. Moreover, these simulations show that the way in which the different actuators are employed during the discharge (based on the choice of the aforementioned actuator-manager performance metric) highly determines the value of internal inductance and normalized beta achieved in steady-state conditions, and therefore, the final current-profile shape.

A control-oriented, two-timescale, linear, dynamic, response model of the rotational transform ι profile and the normalized beta βN is proposed based on experimental data from the DIII-D tokamak. Dedicated system-identification experiments without feedback control have been carried out to generate data for the development of this model. The data-driven dynamic model, which is both device-specific and scenario-specific, represents the response of the ι profile and βN to the electric field due to induction as well as to the heating and current drive (H&CD) systems during the flat-top phase of an H-mode discharge in DIII-D. The control goal is to use both induction and the H&CD systems to locally regulate the plasma ι profile and βN around particular target values close to the reference state used for system identification. 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 robust control design problem is formulated based on the dynamic model to synthesize a stabilizing feedback controller without input constraints 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 controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop system unmodified when no saturation is present. The proposed controller represents one of the first feedback profile controllers integrating magnetic and kinetic variables ever implemented and experimentally tested in DIII-D. The preliminary experimental results presented in this work, although limited in number and constrained by actuator problems and design limitations, as it will be reported, show good progress towards routine current profile control in DIII-D and leave valuable lessons for further advancements in the field.

A neural network model of the effects of neutral beam injection on DIII-D has been developed. The training and testing data used by the model have been generated by the NUBEAM module of TRANSP for experimental discharges from the 2018 DIII-D campaign. Using a principle component analysis to reduce the dimensionality of profile data, the model has been shown to reproduce the results of the Monte Carlo code NUBEAM with a high level of accuracy and an execution time orders of magnitude faster than the execution time of NUBEAM. This makes the neural network model uniquely suited to applications in model-based scenario planning (off-line) and active control (on-line), where a large number of simulation runs are required by the associated optimization tasks that need to be performed before and during the discharge.

Microtearing mode (MTM) real frequency, growth rate, magnetic fluctuation amplitude, and resulting electron thermal transport are studied in systematic NSTX scans of relevant plasma parameters. The dependency of the MTM real frequency and growth rate on plasma parameters, suitable for low and high collision NSTX discharges, is obtained by using the reduced MTM transport model [T. Rafiq et al., Phys. Plasmas 23, 062507 (2016)]. The plasma parameter dependencies are compared and found to be consistent with the results obtained from MTM using the gyrokinetic GYRO code. The scaling trend of collision frequency and plasma beta is found to be consistent with the global energy confinement trend observed in the NSTX experiment. The strength of the magnetic fluctuation is found to be consistent with the gyrokinetic estimate. In earlier studies, it was found that the version of the multi-mode (MM) anomalous transport model, which did not contain the effect of MTMs, provided an appropriate description of the electron temperature profiles in standard tokamak discharges and not in spherical tokamaks. When the MM model, which involves transport associated with MTMs, is incorporated in the TRANSP code and is used in the study of electron thermal transport in NSTX discharges, it is observed that the agreement with the experimental electron temperature profile is substantially improved.

Simultaneous control of the current profile and normalized plasma beta is an essential control problem in the development of advanced tokamak scenarios. However, this control problem is especially challenging due to the nonlinear nature of the current, heat, and particle transport dynamics, as well as the difficulty to understand and accurately model such processes. In this work, a nonlinear, robust, model-based controller for the simultaneous regulation of the current profile and normalized beta has been designed using feedback linearization and Lyapunov redesign techniques. Feedback linearization avoids approximate linearization of the plasma dynamics, retaining the original physics content of the model. Moreover, the use of Lyapunov redesign techniques makes the controller robust against the uncertainties arising during the modeling process. The controller’s performance in the presence of unknown dynamics is tested in nonlinear, one-dimensional simulations using the Control Oriented Transport SIMulator (COTSIM) code, which employs plasma models that are significantly more complex than those employed for control synthesis.

Tokamaks are toroidal devices in which a plasma is confined by means of helical magnetic fields with the purpose of obtaining energy from nuclear fusion reactions. The safety factor, $q$ , measures the pitch of the helical magnetic field lines in a tokamak. Active control of the $q$ profile (i.e., spatial shape) is needed due to its relationship with plasma performance, steady-state operation, and magneto-hydrodynamic stability. However, the responses of some plasma magnitudes, such as the electron temperature, are difficult to model and introduce a high level of uncertainty in the model used for $q$ -profile control design. Control algorithms that are robust against such model uncertainties must be developed in order to ensure successful q-profile regulation. In this work, a nonlinear, robust $q$ -profile controller is designed using feedback linearization and nonlinear damping techniques. The controller makes use of plasma current modulation, neutral beam injection, electron-cyclotron heating & current drive, and electron density modulation as actuation methods. A simulation study is carried out for a DIII-D scenario to test the controller's performance under the presence of electron temperature uncertainties.

Extensive studies have shown that the toroidal current density profile, which is closely related to the poloidal magnetic flux profile, is a key factor to achieving advanced tokamak operating scenarios characterized by improved confinement and possible steady-state operation. In this work, a first-principles-driven, control-oriented model of the poloidal magnetic flux profile evolution is used to design a feedback controller via model predictive control (MPC). The aim of the feedback controller is to track a desired profile for the gradient of the poloidal magnetic flux by solving an optimal control problem in the presence of disturbances, non-modeled dynamics, and arbitrary initial conditions. The simulation results illustrate the capability of the proposed controller in dealing with perturbed initial conditions and disturbances.

The tokamak is a Torus-shaped machine whose final purpose is generating energy from nuclear fusion reactions. In order to achieve this goal, a reactant plasma is confined inside the tokamak by means of magnetic fields. For a tokamak to be commercially competitive, operation for long periods of time at high-performance operating points will be needed. Those high-performance scenarios are characterized by a steady-state, stable plasma operation in which the safety factor, a property of the plasma that measures the pitch of the magnetic field lines, plays a decisive role. In particular, control of the central safety factor, which is the value of the safety factor at the tokamak magnetic axis, is one of the crucial aspects to the success of tokamak devices due to its close relationship to magneto-hydrodynamic stability. Therefore, control algorithms for the central safety factor in tokamaks will be required. In the present work, a linear controller is proposed for the regulation of the central safety factor using neutral beam injection and electron cyclotron launchers. This controller is designed to guarantee a zero input torque delivered by the neutral beam injection system. The controller performance is tested via a simulation study in a DIII-D scenario.

One of the most promising candidates to produce clean nuclear fusion energy is the tokamak, a device magnetically confining an extremely hot plasma (i.e. an ionized gas) where the fusion reactions take place. To produce nuclear fusion energy using tokamak devices, it is crucial that the poloidal magnetic flux (characterized by the so-called q profile) and the plasma internal energy are tightly controlled to avoid magnetohydrodynamic instabilities and to reach the high pressures and temperatures that are needed for high fusion-power density. Simultaneous control of the q profile and the internal energy is challenging for a number of reasons: the system is nonlinear, there are significant parameter uncertainties and large disturbances, the available number of actuators is small, and the actuation authority is limited from a control perspective. Therefore, a variable-structure controller is proposed in this work to tackle this plasma control problem since this type of controllers can typically diminish the impact of serious disturbances and nonlinearities while still leading to good performance. Simulations and recent experiments on the DIII-D tokamak in a challenging high-confinement (H-mode) plasma regime show that this control approach does indeed lead to good and repeatable control of the q profile and the internal energy.

In future burning-plasma tokamaks like ITER, one of the main problems will be controlling the plasma density and temperature during long pulses in order to regulate the fusion power density. Such problem, known as burn control, requires the development of control algorithms in which modulation of the deuterium (D) and tritium (T) fueling rates may play an important role as an actuator. However, unmeasurable variations of the D-T concentration are expected in the fueling lines during such long-pulse operation. Therefore, there will be a need for robust burn controllers that can regulate the plasma density and temperature in spite of the presence of uncertainties in the D-T concentration in the fueling lines. In this work, a nonlinear controller is presented which is able to regulate the burn condition even in the presence of the aforementioned uncertainties. The controller performance is tested in simulations for a burning-plasma ITER-like scenario.

Tokamak plasma rotation is widely recognized for its importance to heat confinement and plasma stability. In this work we consider control of the plasma rotation profile with the aim of building a control strategy suitable for testing various rotation profiles for stability characteristics and reaching desired operating conditions. To obtain a control-oriented model of the toroidal rotation profile evolution, a simplified version of the momentum balance equation is combined with scenario-specific models for the momentum sources. Various momentum sources including on-axis and off-axis neutral beam injection and the non-axisymmetric field coils, which provide rotation damping, allow not only control of the bulk plasma rotation, but also control of the profile shape. A feedback controller is designed in a model predictive control framework to regulate the rotation profile while satisfying constraints associated with the desired plasma stored energy and β (kinetic to magnetic pressure ratio) limits.

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 controller's disturbance rejection and tracking capability. Prior to experimental testing, a Simserver simulation was carried out to study the controller's 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.

Active control of the flow shear, which is related to the radial derivative of the azimuthal flow, is a key factor in reducing the cross-field turbulence-driven particle transport in a magnetically confined plasma column. Once a desired radial azimuthal velocity profile and its associated level of turbulent fluctuations are identified, the challenge of systematically achieving and sustaining it still remains. In this paper, a model-based feedback controller is proposed to overcome this challenge in helicon-cathode (HELCAT). This linear, dual-source, magnetized-plasma, laboratory device employs concentric ring electrodes to mitigate the turbulent plasma transport by generating a sheared radial electric field and modifying the flow profiles by E×B actuation. A linear-quadratic-integral optimal feedback controller is designed to minimize a weighted combination of the tracking error and the control effort with an ultimate goal of regulating the radial azimuthal velocity profile around a prescribed desired profile even with external disturbances and perturbed initial conditions. Numerical simulations show the effectiveness of the proposed controller in shaping the azimuthal flow profile in HELCAT. The proposed control solution has the potential of being used as a systematic tool for physics-oriented studies in laboratory plasmas such as those achieved in HELCAT.

Turbulence and turbulence-driven transport are ubiquitous in magnetically confined plasmas, where there is an intimate relationship between turbulence, transport, destabilizing mechanisms, such as gradients and currents, and stabilizing mechanisms like shear. Active control of fluctuations is investigated in this paper via manipulation of flow profiles in a magnetized laboratory plasma device helicon-cathode (HELCAT). Fluctuations are monitored by electrostatic probes, and E×B flow profiles are controlled via bias ring electrodes. First, a nonmodel-based extremum-seeking optimal control algorithm is implemented in HELCAT to seek the bias ring voltages that minimize a cost function related to the fluctuation amplitude. The experimental results in HELCAT show that the proposed controller is able to not only suppress the fluctuations but also to regulate their average amplitude around a predefined desired level. It is anticipated that this controller can become a valuable tool for physics-oriented studies designed to elucidate the relationship between the shape of the azimuthal flow profile and the amplitude of the fluctuations once the capability of measuring the flow profile in real time becomes available in HELCAT. Second, with the assistance of a HELCAT-tailored transport code capable of predicting the evolution of the azimuthal flow at several radial points within the plasma, the potential of an extremum-seeking controller for directly regulating the azimuthal flow profile around a prescribed target profile is illustrated numerically.

Control of the current profile in tokamak plasmas has been shown to play an important role in achieving advanced scenarios that could enable steady-state operation. The nonlinearity and spatially distributed nature of the current profile dynamics motivate the use of model-based control designs. In this work, we consider a control-oriented model of the current profile evolution in DIII-D high-confinement (H-mode) discharges, and the problem of regulating the current profile around a desired trajectory. The PDE model is discretized in space with a finite difference method and a backstepping design is applied to obtain a transformation from the original system into a particular target system with desirable properties. The resulting boundary condition control law is complemented with control laws for the available distributed actuators. The combined control strategy uses nonlinear combinations of the total plasma current, total power, and line averaged density as actuators. Simulation and experimental results show the ability of the controller to track desired targets and to reject input disturbances.

Extensive research has been conducted to find operating scenarios that optimize the plasma performance in nuclear fusion tokamak devices with the goal of enabling the success of the ITER project. The development, or planning, of these advanced scenarios is traditionally investigated experimentally by modifying the tokamak's actuator trajectories, such as the auxiliary heating/current-drive (H&CD) scheme, and analyzing the resulting plasma evolution. In this work, a numerical optimization algorithm is developed to complement the experimental effort of advanced scenario planning in the DIII-D tokamak. Two properties related to the plasma stability and performance are the safety factor profile ( q -profile) and the normalized plasma beta ( β N ). The optimization algorithm goal is to design actuator trajectories that steer the plasma to a target q -profile and plasma β N , such that the achieved state is stationary in time, subject to the plasma dynamics (described by a physics-based, nonlinear, control-oriented partial differential equation model) and practical plasma state and actuator constraints, such as the maximum available amount of H&CD power. This defines a nonlinear, constrained optimization problem that we solve by employing sequential quadratic programming. The optimized trajectories are then tested through simulation with the physics-based model and experimentally in DIII-D.

The next experimental step in the development of nuclear fusion reactors is the ITER tokamak. It is designed to explore the burning plasma regime in which the plasma temperature is sustained mostly by self-heating from fusion reactions. Burn control, the control of fusion power and other reactor parameters through modulation of fueling and heating, will be essential for achieving and maintaining desired operating points and ensuring stability. Design of burn control strategies is made challenging by the multi-variable, highly nonlinear, uncertain nature of the system. Furthermore, due to the extreme conditions in fusion reactors, diagnostic systems may be limited. To deal with these challenges, we propose the use of a nonlinear, multi-variable output feedback control strategy with a proportional-integral observer. A simulation study is carried out to illustrate the performance of the scheme using a set of diagnostics likely to be available in ITER.

Efficient, high-gain operation of a tokamak device requires the achievement of certain radial shapes for the toroidal current profile. The evolution in time of the toroidal current profile in tokamaks is related to the evolution of the poloidal magnetic flux profile. A model-based control approach for the regulation of the poloidal magnetic flux profile at the DIII-D tokamak is proposed in this work. The model describing the poloidal flux evolution is based on a control-oriented formulation of the magnetic diffusion equation. Auxiliary heating and current drive (H&CD) systems including electron cyclotron (EC) and neutral beam injection (NBI) along with the total plasma current are used as actuators to manipulate the profile shape. Optimal state feedback control with integral action is used to design a controller to regulate the profile around a target while rejecting disturbances. Combining the profile controller with control of the plasma stored energy is found to improve tracking performance. Simulations and experimental results are presented to demonstrate the controller's effectiveness.

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.

The tokamak is a torus-shaped machine in which a reactant ionized gas (plasma) is confined using magnetic fields for the purpose of generating energy from nuclear fusion reactions. In order to be commercially competitive, a tokamak needs to operate for long periods of time at high-performance operating points. Those high-performance scenarios are characterized by a steady-state, stable plasma operation, which is closely related to a property of the plasma that is known as the safety factor, q. Therefore, control of the q profile is one of the crucial aspects to the success of tokamaks. Significant research has been carried out by the fusion community to find control algorithms for the q profile. Most of that previous work makes use of approximate linearization and linear control techniques. In the present work, we propose a nonlinear model-based controller for the regulation of the q profile using feedback linearization. This nonlinear control approach may be applicable to a greater range of operating conditions, and may be able to reject larger perturbations than previous linear controllers. The effectiveness of the controller is demonstrated via a simulation study based on a DIII-D scenario.