T. C. Blanken

A model-based, multichannel, real-time capable sawtooth crash detector

Control of the time between sawtooth crashes, necessary for ITER and DEMO, requires real-time detection of the moment of the sawtooth crash. In this paper, estimation of sawtooth crash times is demonstrated using the model-based interacting multiple model (IMM) estimator, based on simplified models for the sawtooth crash. In contrast to previous detectors, this detector uses the spatial extent of the sawtooth crash as detection characteristic. The IMM estimator is tuned and applied to multiple ECE channels at once. A model for the sawtooth crash is introduced, which is used in the IMM algorithm. The IMM algorithm is applied to seven datasets from the ASDEX Upgrade tokamak. Five crash models with different mixing radii are used. All sawtooth crashes that have been identified beforehand by visual inspection of the data, are detected by the algorithm. A few additional detections are made, which upon closer inspection are seen to be sawtooth crashes, which show a partial reconnection. A closer inspection of the detected normal crashes shows that about 42% are not well fitted by any of the full reconnection models and show some characteristics of a partial reconnection. In some case, the measurement time is during the sawtooth crashes, which also results in an incorrect estimate of the mixing radius. For data provided at a sampling rate of 1 kHz, the run time of the IMM estimator is below 1 ms, thereby fulfilling real-time requirements.

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

A 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.