Modeling, observer design and robust control of the particle density profile in tokamak plasmas

\u3cp\u3eA new approach to real-time estimation and feedback control of the particle density profile in tokamak plasmas is presented, based on ideas from Kalman filtering and H∞ robust control synthesis. Traditionally, the density profile is reconstructed in real-time by solving an inversion problem using a measurement from a single time instant. Such an approach is sensitive to sensor errors and does not account for the dynamical evolution and spatial continuity of the density. The observer-based approach we presented here includes the system dynamics, which is realized by careful modeling of the particle density behaviour using a 1D PDE with a nonlinear source term and two ODEs, which are discretized in space and time to yield a finite-dimensional nonlinear model. The influence of other plasma quantities and operational modes on the transport dynamics are included in the control-oriented model as time-varying parameters. An extended Kalman filter estimates the density, additive random-walk state disturbances as well as fringe jumps (a specific type of sensor error) from measurements, for which special measures are needed. Offline reconstruction using tokamak measurements show accurate estimation of the density profile and show the quality of fringe jump detection. Moreover, a robust state feedback controller with anti-windup is designed based on the model to track a reference signal for the average density, with the estimate obtained from the observer. Closed-loop simulations show that the controller is able to track representative reference signals, with the performance mostly limited by the nonnegativity constraint of the control input.\u3c/p\u3

Density control in ITER:an iterative learning control and robust control approach

\u3cp\u3ePlasma density control for next generation tokamaks, such as ITER, is challenging because of multiple reasons. The response of the usual gas valve actuators in future, larger fusion devices, might be too slow for feedback control. Both pellet fuelling and the use of feedforward-based control may help to solve this problem. Also, tight density limits arise during ramp-up, due to operational limits related to divertor detachment and radiative collapses. As the number of shots available for controller tuning will be limited in ITER, in this paper, iterative learning control (ILC) is proposed to determine optimal feedforward actuator inputs based on tracking errors, obtained in previous shots. This control method can take the actuator and density limits into account and can deal with large actuator delays. However, a purely feedforward-based density control may not be sufficient due to the presence of disturbances and shot-to-shot differences. Therefore, robust control synthesis is used to construct a robustly stabilizing feedback controller. In simulations, it is shown that this combined controller strategy is able to achieve good tracking performance in the presence of shot-to-shot differences, tight constraints, and model mismatches.\u3c/p\u3

Control-oriented modeling of the plasma particle density in tokamaks and application to real-time density profile reconstruction

\u3cp\u3eA model-based approach to real-time reconstruction of the particle density profile in tokamak plasmas is presented, based on a dynamic state estimator. Traditionally, the density profile is reconstructed in real-time by solving an ill-conditioned inversion problem using a measurement at a single point in time. This approach is sensitive to diagnostics errors and failure. The inclusion of a dynamic model in a real-time estimation algorithm allows for reliable reconstruction despite diagnostic errors. Predictive simulations show that the model can reproduce the density evolution of discharges on TCV and ASDEX-Upgrade after tuning of a few parameters. Offline reconstructions using experimental data from TCV show accurate estimation of the density profile and show examples of fault detection of interferometry signals.\u3c/p\u3

Tokamak-agnostic actuator management for multi-task integrated control with application to TCV and ITER

\u3cp\u3eThe plasma control system (PCS) of a long-pulse tokamak must be able to handle multiple control tasks simultaneously, and must be capable of robust event handling with a limited set of actuators. For ITER, this is particularly challenging given the large number of actuator-conflicting control requirements. To deal with these issues, this work develops a task-based approach, where a plasma supervisory controller and an actuator manager make high-level decisions on how to handle the considered control tasks, using generic actuator resources and controllers. This simplifies the interface for operators and physicists since the generic control tasks (instead of controllers) can be directly defined from the general physics goals. This approach also allows one to decompose the PCS into a tokamak-dependent layer and a tokamak-agnostic layer. The developed scheme is first implemented and tested on TCV for simultaneous β control, neoclassical tearing mode (NTM) control, central co-current drive, and H-mode control tasks. It is then applied to an ITER test scenario to prove its flexibility and applicability to systematically handle a large number of tasks and actuators.\u3c/p\u3

Real-time plasma state monitoring and supervisory control on TCV

In ITER and DEMO, various control objectives related to plasma control must be simultaneously achieved by the plasma control system (PCS), in both normal operation as well as off-normal conditions. The PCS must act on off-normal events and deviations from the target scenario, since certain sequences (chains) of events can precede disruptions. It is important that these decisions are made while maintaining a coherent prioritization between the real-time control tasks to ensure high-performance operation.\u3cbr/\u3e\u3cbr/\u3eIn this paper, a generic architecture for task-based integrated plasma control is proposed. The architecture is characterized by the separation of state estimation, event detection, decisions and task execution among different algorithms, with standardized signal interfaces. Central to the architecture are a plasma state monitor and supervisory controller. In the plasma state monitor, discrete events in the continuous-valued plasma state are modeled using finite state machines. This provides a high-level representation of the plasma state. The supervisory controller coordinates the execution of multiple plasma control tasks by assigning task priorities, based on the finite states of the plasma and the pulse schedule.\u3cbr/\u3e\u3cbr/\u3eThese algorithms were implemented on the TCV digital control system and integrated with actuator resource management and existing state estimation algorithms and controllers. The plasma state monitor on TCV can track a multitude of plasma events, related to plasma current, rotating and locked neoclassical tearing modes, and position displacements.\u3cbr/\u3e\u3cbr/\u3eIn TCV experiments on simultaneous control of plasma pressure, safety factor profile and NTMs using electron cyclotron heating (ECH) and current drive (ECCD), the supervisory controller assigns priorities to the relevant control tasks. The tasks are then executed by feedback controllers and actuator allocation management. This work forms a significant step forward in the ongoing integration of control capabilities in experiments on TCV, in support of tokamak reactor operation

Real-time control of neoclassical tearing modes and its integration with multiple controllers in the TCV Tokamak

\u3cp\u3ePreliminary integrated control of NTMs, beta and model-estimated q profiles has been demonstrated experimentally in TCV for the first time. An upgrade of the supervision layer is foreseen. Dedicated NTM tests show that density affects the triggering of NTMs through global q profile modifications with central co-ECCD - too low or too high density will hinder the triggering. More detailed simulations are ongoing to further clarify these effects.\u3c/p\u3

Feedback controlled, reactor relevant, high-density, high-confinement scenarios at ASDEX Upgrade

\u3cp\u3eOne main programme topic at the ASDEX Upgrade all-metal-wall tokamak is development of a high-density regime with central densities at reactor grade level while retaining high-confinement properties. This required development of appropriate control techniques capable of coping with the pellet tool, a powerful means of fuelling but one which presented challenges to the control system for handling of related perturbations. Real-time density profile control was demonstrated, raising the core density well above the Greenwald density while retaining the edge density in order to avoid confinement losses. Recently, a new model-based approach was implemented that allows direct control of the central density. Investigations focussed first on the N-seeding scenario owing to its proven potential to yield confinement enhancements. Combining pellets and N seeding was found to improve the divertor buffering further and enhance the operational range accessible. For core densities up to about the Greenwald density, a clear improvement with respect to the non-seeding reference was achieved; however, at higher densities this benefit is reduced. This behaviour is attributed to recurrence of an outward shift of the edge density profile, resulting in a reduced peeling-ballooning stability. This is similar to the shift seen during strong gas puffing, which is required to prevent impurity influx in ASDEX Upgrade. First tests indicate that highly-shaped plasma configurations like the ITER base-line scenario, respond very well to pellet injection, showing efficient fuelling with no measurable impact on the edge density profile.\u3c/p\u3

Profile control simulations and experiments on TCV:A controller test environment and results using a model-based predictive controller

\u3cp\u3eThe successful performance of a model predictive profile controller is demonstrated in simulations and experiments on the TCV tokamak, employing a profile controller test environment. Stable high-performance tokamak operation in hybrid and advanced plasma scenarios requires control over the safety factor profile (q-profile) and kinetic plasma parameters such as the plasma beta. This demands to establish reliable profile control routines in presently operational tokamaks. We present a model predictive profile controller that controls the q-profile and plasma beta using power requests to two clusters of gyrotrons and the plasma current request. The performance of the controller is analyzed in both simulation and TCV L-mode discharges where successful tracking of the estimated inverse q-profile as well as plasma beta is demonstrated under uncertain plasma conditions and the presence of disturbances. The controller exploits the knowledge of the time-varying actuator limits in the actuator input calculation itself such that fast transitions between targets are achieved without overshoot. A software environment is employed to prepare and test this and three other profile controllers in parallel in simulations and experiments on TCV. This set of tools includes the rapid plasma transport simulator RAPTOR and various algorithms to reconstruct the plasma equilibrium and plasma profiles by merging the available measurements with model-based predictions. In this work the estimated q-profile is merely based on RAPTOR model predictions due to the absence of internal current density measurements in TCV. These results encourage to further exploit model predictive profile control in experiments on TCV and other (future) tokamaks.\u3c/p\u3