Continuous, saturation, and discontinuous tokamak plasma vertical position control systems

A lumped parameter, state space model for a tokamak transformer including the slow flux penetration in the plasma (skin effect transformer model) is presented. The model does not require detailed or explicit information about plasma profiles or geometry. Instead, this information is lumped in system variables, parameters and inputs. The model has an exact mathematical structure built from energy and flux conservation theorems, predicting the evolution and non-linear interaction of plasma current and internal inductance as functions of the primary coil currents, plasma resistance, non-inductive current drive and the loop voltage at a specific location inside the plasma (equilibrium loop voltage). Loop voltage profile in the plasma is substituted by a three-point discretization, and ordinary differential equations are used to predict the equilibrium loop voltage as a function of the boundary and resistive loop voltages. This provides a model for equilibrium loop voltage evolution, which is reminiscent of the skin effect. The order and parameters of this differential equation are determined empirically using system identification techniques. Fast plasma current modulation experiments with random binary signals have been conducted in the TCV tokamak to generate the required data for the analysis. Plasma current was modulated under ohmic conditions between 200 and 300 kA with 30 ms rise time, several times faster than its time constant L/R approximate to 200 ms. A second-order linear differential equation for equilibrium loop voltage is sufficient to describe the plasma current and internal inductance modulation with 70% and 38% fit parameters, respectively. The model explains the most salient features of the plasma current transients, such as the inverse correlation between plasma current ramp rates and internal inductance changes, without requiring detailed or explicit information about resistivity profiles. This proves that a lumped parameter modelling approach can be used to predict the time evolution of bulk plasma properties such as plasma inductance or current with reasonable accuracy; at least under ohmic conditions without external heating and current drive sources.

Development and validation of a tokamak skin effect transformer model

This paper reports the results of the design and modeling of a hierarchical control system for ITER plasma shape, position and current. The system contains three hierarchy levels. The first level is a model correcting loop with a feedback constant matrix. The second level consists of two loops: a fast SISO plasma vertical position stabilization loop and a slow MIMO plasma current and shape control loop. Both loops have the controllers which were designed by an H ∞ loop shaping approach in the framework of the disturbance rejection configuration. The third level is a structure with a Model Predictive Controller for improving the plasma shape control process by a vertical position reference adjustment during a plasma discharge. The main idea of our proposal is to solve a tokamak plasma vertical position instability problem in cooperation with the plasma shape and current MIMO control loop. The plasma vertical position stabilization technique provides a more reliable control system in whole when compared with the known system approach when a plasma vertical speed is stabilized at about zero. The simulation results of the plasma magnetic hierarchical control system obtained on plasma-physics nonlinear DINA code for ITER are presented. The system was modeled on DINA code on the divertor phase of the plasma current ramp-up stage and on a DINA linearized model on the flat-top phase when a minor disruption occurs.

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Hierarchical plasma shape, position, and current control system for ITER

Synthesis and simulation of a hierarchical (two-level) magnetic system for controlling a tokamakreactor plasma throughout the entire divertor discharge stage, including the plasma current ramp-up phase, are carried out. The plasma vertical velocity is stabilized about zero by using a proportional controller in a scalar control loop. The gain of the controller—the coefficient that ensures the required stability margins—is found by using a second-order linear model constructed by solving the identification problem on the basis of numerical experiments carried out with the DINA plasmophysical computer code. The internal cascade (the lower level of the system) for tracking the scenario currents in the poloidal magnetic field coils is synthesized by using the complete dynamic channel decoupling method. The external cascade (the upper level of the system) for tracking the plasma current and shape is synthesized by using the method of pseudoseparation of the control channels and the multidimensional diagonal proportional-integral controller, with proportional, integrating, and double integrating units connected in parallel in each channel. In the hierarchical control system, the lower level (the internal cascade) is subordinated to the upper level (the external cascade). The external cascade acts on the internal one by the signals that set the required currents in the coils of the central solenoid and of the poloidal magnetic field in order to ensure the required plasma current and shape in accordance with the output signals from the plant, which are transmitted through the vector feedback channel. The lower level is aimed exclusively at tracking the reference inputs by tracking the currents in the control coils. An operating mode of the system under the conditions of current saturation in the control coils is proposed and implemented. Results are presented from numerical simulations of the two-level (cascade) control system for reference scenario no. 2 of the ITER database (www.iter.org) with the DINA nonlinear code.

Synthesis and simulation of a two-level magnetic control system for tokamak-reactor plasma

The paper is devoted to the development of two-loop plasma position, current and shape control system in tokamak-reactor. The Hinfin approach is used for the design of SISO and MIMO feedback controllers. In the procedure of controllers design the MIMO linear plant model (plasma in tokamak) DINA-L was used. The linear model was obtained from non-linear plant model realized by plasma-physics DINA code for ITER conditions. The set of simulations of closed-loop magnetic system was done on linear (DINA-L) and nonlinear (DINA) plant models when minor disruptions occurred. Simulations results for both models were superimposed and showed good coincidence at acceptable control system performance

Plasma magnetic robust control in tokamak-reactor

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Reconstruction of Equilibrium Distribution of Tokamak Plasma Parameters by External Magnetic Measurements and Construction of Linear Plasma Models

The article deals with the development of a two-contour system of magnetic control of the position, current, and shape of the plasma in the tokamak-reactor. The H∞-theory of control is used for the synthesis of a scalar and a multidimensional feedback controller. The controllers are synthesized on the basis of the multidimensional linear model DINA-L of an object (plasma in the tokamak). The linear model DINA-L is obtained from the nonlinear model implemented by the plasmophysical DINA code for conditions of the international thermonuclear experimental reactor (ITER). The numerical modeling of a closed control system is carried out on the linear DINA-L model and the nonlinear DINA model of an object at disturbances of the type of small disruptions. The modeling results for both of the cases were superimposed on each other, which showed their good coincidence at the acceptable quality of control of the synthesized system.

Synthesis and modeling of the H ∞ -system of magnetic control of the plasma in the tokamak-reactor

Consideration was given to the design and mathematical modeling of the stabilization system for unstable vertical position of plasma in the T-15 tokamak (Institute of Tokamak Physics, National Research Centre "Kurchatov Institute"). For suppression of vertical instability of plasma, the poloidal systems of vertically elongated tokamaks were analyzed with the aim of detecting the most efficient positioning of the winding of the horizontal magnetic field (fast winding) in the T-15 tokamak. The controllability domains of vertical shift of the plasma magnetic axis were estimated for various arrangements of the fast winding (i) outside the toroidal winding, (ii) between the toroidal winding and the vacuum chamber, (iii) inside the tokamak vacuum chamber. Part I considered the linear control system for vertical plasma position where the fast winding is located outside the tokamak toroidal winding. For the given configuration of the poloidal system, the control system of the T-15 tokamak was shown to be inherently unstable. Inherent system stability is attained by using a multidimensional control system where all windings of the central solenoid and the windings of the poloidal field are used to control the vertical plasma position and the current in the fast winding.

Stabilization of unstable vertical position of plasma in T-15 tokamak. II

The problem of parameter estimation of a plasma column motion model in a tokamak by the method of the adaptive state identifier is considered In the suggested algorithm, the variation rate of the vector of the identifier parameters to be adjusted is determined by the antigradient of the mismatch function between the output values of the subject and its model For the vertically moving plasma model in the T-14 tokamak we estimated simultaneously two parameters and an additive perturbation, in which case the model can be unstable The results of control coil parameters evaluation by the experimental data are also given for the case of the vertical plasma stabilization in the TVD tokamak

Yu. V. Mitrishkin

Papers

Synthesis and simulation of a two-level magnetic control system for tokamak-reactor plasma

Reconstruction of Equilibrium Distribution of Tokamak Plasma Parameters by External Magnetic Measurements and Construction of Linear Plasma Models

Synthesis and modeling of the H ∞ -system of magnetic control of the plasma in the tokamak-reactor

Stabilization of unstable vertical position of plasma in T-15 tokamak. II

Estimation of parameters of stabilized plasma