Sliding mode control of a tokamak transformer

Abstract

A novel inductive control system for a tokamak transformer is described. The system uses the flux change provided by the transformer primary coil to control either the electric current or the internal inductance of the transformer's secondary plasma circuit load. The internal inductance control is used to regulate the slow flux penetration due to the skin effect, providing first-order control over the shape of the plasma current density profile in the highly conductive plasma. Inferred loop voltages at specific locations inside the plasma are included in a state feedback structure to improve controller performance. Experimental tests have shown that the plasma internal inductance can be controlled inductively for a whole pulse starting just 30ms after the beginning of plasma breakdown. The details of the control system design are presented, including the transformer model, observer algorithms and controller design.

Internal inductance predictive control for Tokamaks

“…The numerical model under study is the lumped parameter model for the internal inductance of plasma current that was published in [32], which is derived considering energy conservation and flux balance together with a first order approximation for the dynamics of the flux diffusion and has been validated with experimental data from TCV tokamak [34]. Let's recall the equations used to model the plasma current and its internal inductance evolution, and introduce the state space vector , , , with…”

“…From an electrical point of view the tokamaks are modeled as a toroidal transformer primary coupled with the plasma ring by a mutual inductance and the plasma acts as the secondary circuit, where and denote the plasma resistance and inductance respectively [31][32][33][34][35]. The plasma is maintained using poloidal field discharges with the particularity that the total inductance consists of the sum of a constant term (external inductance) due to the inductance of transmission lines and wiring which are geometrical factors, plus a variable term corresponding to the internal inductance of the system.…”

Real Time Hybrid Model Predictive Control for the Current Profile of the Tokamak à Configuration Variable (TCV)

“…The intrinsic minimization of the MPC further reduces the current drive source requirements [31]. Therefore, MPC composes an excellent control option since it not only considers the information related to the system at an operation instant as in other advanced controllers [32,33], but also takes into account the predicted future information so as to obtain an optimal control action. Furthermore, the Ohmic Heating (OH) coil may reduce the power requirements of the non-inductive current drive sources required for current profile control due to its ability to transiently manipulate the low order moments of the current profile.…”

“…Furthermore, the Ohmic Heating (OH) coil may reduce the power requirements of the non-inductive current drive sources required for current profile control due to its ability to transiently manipulate the low order moments of the current profile. Until recently, this line of research [31][32][33] had been carried out with plant models of the type described in [34], which are two orders of magnitude smaller than the RZIp model. These models are excellent for real time control algorithms although the underlying plasma physics are reflected in a limited manner.…”

Contribuciones en sistemas de adquisición de datos inteligentes para entornos de fusión por confinamiento magnético

“…Otro conjunto de 38 "flux loops 2 ", situados también en el perímetro de manera concéntrica con la corriente en el plasma, permiten obtener la componente poloidal perpendicular al perímetro de la vasija de vacío. Por último, se utilizan otros 4 sensores flux loops encargados de medir otras componentes provenientes del plasma como diamagnetismo, componentes de campo toroidal o las corrientes de Eddy, utilizando el desarrollo llevado a cabo en (Romero, Coda et al 2012, Shafranov 1971. Con el fin de realizar dichos cálculos de manera eficiente, se han realizado distintas operaciones que permiten discretizar los pasos más complejos del algoritmo, como es la determinación de la integral de Shafranov.…”