Marco de Baar

A dynamic state observer for real-time reconstruction of the tokamak plasma profile state and disturbances

A dynamic observer is presented which can reconstruct the internal state of a tokamak fusion plasma, consisting of the spatial distribution of current and temperature, from measurements. Today, the internal plasma state is usually reconstructed by solving an ill-conditioned inversion problem using a large number of measurements at one point in time. Such an approach does not take into account the time evolution of the underlying dynamical system (the plasma) and strongly relies on (technically challenging) internal measurements. The observer-based approach presented here includes the dynamics of the plasma current and temperature, modeled by a set of coupled nonlinear 1-D PDEs which are discretized in space and time to yield a finite-dimensional nonlinear model. The observer, which is based on an Extended Kalman Filter, estimates the state of an augmented model which includes additive state disturbances modeled as a random walk. Simulation results demonstrate the effectiveness of this observer in the case of perturbed models and input disturbances.

Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs

The identification of the spatially dependent parameters in Partial Differential Equations (PDEs) is important in both physics and control problems. A methodology is presented to identify spatially dependent parameters from spatio-temporal measurements. Local non-rational transfer functions are derived based on three local measurements allowing for a local estimate of the parameters. A sample Maximum Likelihood Estimator (SMLE) in the frequency domain is used, because it takes noise properties into account and allows for high accuracy consistent parameter estimation. Confidence bounds on the parameters are estimated based on the noise properties of the measurements. This method is successfully applied to the simulations of a finite difference model of a parabolic PDE with piecewise constant parameters.

Maximum Likelihood Estimation of diffusion and convection in tokamaks using infinite domains

A new method to identify the spatial dependent parameters describing the heat transport, i.e. diffusion and convection, in fusion reactors is presented. These parameters determine the performance of fusion reactors. The method is based on local transfer functions, which are defined between two measurement locations. Estimation of the local transfer functions results in a model of the spatial dependent diffusion and convection. The parameters of the local transfer functions are estimated using Maximum Likelihood Estimation in the frequency domain. This is necessary, because both measurements (input and output of the transfer function) contain noise. Moreover, confidence bounds and validation tests can be used in this framework. Finally, experimental results are presented, which show that the diffusion and convection can be estimated. In this case, the uncertainty bounds are too large on the convection to conclude its presence.

Control-oriented modeling of the Electron Cyclotron Current Drive actuated hybrid mode in ITER

This paper presents a control-oriented model of the magnetic flux in the International Tokamak Experimental Reactor (ITER) actuated with Electron Cyclotron Current Drive (ECCD) at different locations. The main objective of the control-oriented modeling is to derive an input/output representation of the magnetic profile written as a state-space model. The state-space model allows determination of the most suitable actuation strategies using the concept of controllability analysis. To illustrate the controllability analysis of the magnetic flux actuated at different locations, we present numerical results based on space dependent parameters obtained from the integrated modeling code CRONOS.

Tele-Manipulation with Two Asymmetric Slaves: Two Operators Perform Better Than One

Certain tele-manipulation tasks require manipulation by two asymmetric slaves, for example, a crane for hoisting and a dexterous robotic arm for fine manipulation. It is unclear how to best design human-in-the-loop control over two asymmetric slaves. The goal of this paper is to quantitatively compare the standard approach of two co-operating operators that each control a single subtask, to a single operator performing bi-manual control over the two subtasks, and a uni-manual control approach. In a human factors experiment, participants performed a heavy load maneuvering and mounting task using a vertical crane and a robotic arm. We hypothesize that bi-manual control yields worse task performance and control activity compared to co-operation, because of conflicting spatial and temporal constraints. Literature suggests that uni-manual operators should perform better than co-operation, as co-operators critically depend on each others actions. However, other literature provides evidence that individual operators have limited capabilities in controlling asymmetric axes of two dynamic systems. The results show that the two co-operators perform the maneuvering and mounting task faster than either bi- or uni-manual operators. Compared to co-operators, uni-manual operators required more control activity for the vertical crane and less for the robotic arm. In conclusion, this study suggests that when controlling two asymmetric slaves, a co-operating pair of operators performs better than a single operator.

Control of sawteeth and neo-classical tearing modes in tokamaks using electron cyclotron waves

Resistive magneto-hydrodynamic instabilities are expected to limit the performance of nuclear fusion reactors. Prime examples are the sawtooth instability and the neoclassical tearing modes. The sawtooth instability will affect the refueling of the plasma core and the fast particle concentration. In reactor relevant conditions, the sawtooth can also trigger secondary instabilities. These are the neo-classical tearing modes, which can deteriorate the plasma performance or even disrupt the discharge. These modes (sawteeth and tearing modes) appear at specific locations in the tokamak plasma, associated with the distribution of the current density and the toroidal magnetic field. Localized current drive from electron cyclotron waves is foreseen as a possible actuator for the width of the tearing modes and the period of the sawteeth. Magnetic pick-up coils, electron cyclotron emission (ECE) and soft X-ray emission are the most likely sensors. A system approach for real-time detection, localisation and control of resistive magneto-hydrodynamic modes in tokamaks is presented. The system combines an ECE diagnostic for sensing of the instabilities in the same sight-line with a steerable Electron Cyclotron Resonant Heating and Current Drive (ECRH/CD) antenna. A model for the sawtooth is used to derive the linearized input-output relations (transfer functions) from the varying deposition location of high power Electron Cyclotron waves to the sawtooth period. The transfer functions are derived around a large collection of operating points. Proportional-integral-integral (PII) action can be applied to achieve fast and perfect tracking, while satisfying robustness constraints. The launcher dynamics seriously affects the closed loop performance in present-day experiments. Special emphasis is put on the issue of real-time sawtooth period detection. An algorithm based on time-scale wavelet theory and edge detection for accurate real-time sawtooth period estimation has been developed. The period is estimated by detecting subsequent crashes. The realized accuracy of the detection algorithm is well below the uncertainty of the crash period for most crashes. Multi-resolution analysis enables distinction between different sizes of sawtooth crashes due to the different sizes of wavelets (scales), resulting in an algorithm, which is robust and accurate. A methodology for fast detection of q = m/n = 2/1 tearing modes and retrieval of their location, rotation frequency and phase is presented. Set-points to establish alignment of the ECRH/CD deposition location with the centre of the tearing mode are generated in real-time and forwarded in closed-loop to the steerable launcher and as a modulation pulse train to the gyrotron.