title: Ð¡Ð¸ÑÑÐµÐ¼Ð° Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¿Ð»Ð°Ð·Ð¼Ð¾Ð¹ Ð² Ð¢ÐÐÐÐÐÐÐ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Automatic plasma control system in TOKAMAK
Creators: name: ÐÐ°Ð±Ð¸ÑÐ¾Ð²Ð°, ÐÐ´ÐµÐ»Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: Ð¼Ð¾Ð´ÐµÐ»Ñ
ÑÐ¸ÑÑÐµÐ¼Ð° ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ
ÑÐµÑÐ¼Ð¾ÑÐ´ÐµÑÐ½ÑÐ¹ ÑÐ¸Ð½ÑÐµÐ·
ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð°ÑÐ¸Ñ
Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ðµ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ðµ
ÑÐ¾ÐºÐ°Ð¼Ð°Ðº
Ð¿Ð»Ð°Ð·Ð¼Ð°
Ð¢-15ÐÐ
Ð¿Ð¾Ð»Ð¾Ð¸Ð´Ð°Ð»ÑÐ½Ð¾Ðµ
ÑÐ¾ÑÐ¾Ð¸Ð´Ð°Ð»ÑÐ½Ð¾Ðµ
Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ðµ ÑÐ´ÐµÑÐ¶Ð°Ð½Ð¸Ðµ
model
control system
thermonuclear fusion
stabilization
optimal control
tokamak
plasma
T-15MD
poloidal
toroidal
magnetic holding

description: Ð Ð½Ð°ÑÑÐ¾ÑÑÐµÐµ Ð²ÑÐµÐ¼Ñ Ð¿ÑÐ¾Ð²Ð¾Ð´ÑÑÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð¿Ð¾ Ð¿ÑÑÐºÑ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ð¢-15ÐÐ Ñ Ð²ÑÑÑÐ½ÑÑÑÐ¼ Ð² Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½Ð¾Ð¼ Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ð¸ Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½ÑÐ¼ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼. Ð¡Ð¸ÑÑÐµÐ¼Ð° Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¿Ð»Ð°Ð·Ð¼Ð¾Ð¹ Ð² ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐµ Ð¢-15ÐÐ, Ð² ÑÐ°ÑÑÐ½Ð¾ÑÑÐ¸, ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÐµÐµ Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½ÑÐ¼ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸ÐµÐ¼, Ð½Ð°ÑÐ¾Ð´Ð¸ÑÑÑ Ð½Ð° ÑÑÐ°Ð¿Ðµ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ¸. ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð´Ð»Ñ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐ´ÐµÑÐ¶Ð°Ð½Ð¸Ñ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð¸ ÑÐ¸ÑÑÐµÐ¼ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¿Ð»Ð°Ð·Ð¼Ð¾Ð¹ Ð² ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ°Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¸ ÑÐ¸Ð½ÑÐµÐ·Ñ ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð¸ÑÑÑÑÐµÐ³Ð¾ Ð¸ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¿Ð»Ð°Ð·Ð¼Ð¾Ð¹ Ð² ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐµ Ð¢-15ÐÐ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1) ÐÐ·ÑÑÐµÐ½Ð¸Ðµ ÑÑÑÐ¾ÐµÐ½Ð¸Ñ ÑÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ°, ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ ÑÐ²Ð»ÐµÐ½Ð¸Ð¹ Ð² ÐºÐ°Ð¼ÐµÑÐµ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ°, ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¸Ñ Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ð² Ð² Ð¿Ð»Ð°Ð·Ð¼Ðµ. 2) ÐÐ¿Ð¸ÑÐ°Ð½Ð¸Ðµ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð¸ ÑÐ¿Ð¾ÑÐ¾Ð±Ð¾Ð² ÐµÐµ Ð»Ð¸Ð½ÐµÐ°ÑÐ¸Ð·Ð°ÑÐ¸Ð¸. 3) ÐÐ¾Ð»ÑÑÐµÐ½Ð¸Ðµ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¿Ð»Ð°Ð·Ð¼Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ð¢-15-ÐÐ, ÑÐ¸Ð½ÑÐµÐ· ÑÐ¸ÑÑÐµÐ¼Ñ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ. 4) ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÑÐ±ÑÐ°Ð½Ð½Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ Ð±ÐµÐ· ÑÐµÐ³ÑÐ»ÑÑÐ¾ÑÐ°. 5) Ð¡Ð¸Ð½ÑÐµÐ· ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð¸ÑÑÑÑÐµÐ³Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¿Ð»Ð°Ð·Ð¼Ð¾Ð¹ Ð² ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐµ Ð¢-15-ÐÐ. 6) Ð ÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸. 7) ÐÐ¼Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð². Ð Ð°Ð±Ð¾ÑÐ° Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° Ð½Ð° Ð±Ð°Ð·Ðµ Ð¤Ð¢Ð Ð¸Ð¼. Ð.Ð¤. ÐÐ¾ÑÑÐµ, Ð¾ÑÐºÑÐ´Ð° Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐµ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ ÑÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ Ð¢-15ÐÐ Ð¸ ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¸Ðµ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ñ Ð¿Ð»Ð°Ð·Ð¼Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐ²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¾Ð± ÑÑÐ°Ð¿Ð°Ñ Ð¸ ÑÑÐ°ÑÑÑÐµ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ¾Ðº ÑÑÑÐ¾ÑÑÐµÐ³Ð¾ÑÑ ÑÐµÐ°ÐºÑÐ¾ÑÐ°. ÐÐ¸Ð½ÐµÐ°ÑÐ¸Ð·Ð¾Ð²Ð°Ð½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½Ð¾Ð¹ Ð½ÐµÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð´Ð»Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ð¢-15ÐÐ Ð±ÑÐ»Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð° Ð¿ÑÑÑÐ¼ Ð¸Ð´ÐµÐ½ÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¿Ð»Ð°Ð·Ð¼Ð¾ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÐºÐ¾Ð´Ð° DINA. ÐÐ»Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ð¢-15ÐÐ Ð±ÑÐ»Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° ÑÑÐµÑÐºÐ¾Ð½ÑÑÑÐ½Ð°Ñ ÑÐ¸ÑÑÐµÐ¼Ð° ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð²ÐµÑÑÐ¸ÐºÐ°Ð»ÑÐ½ÑÐ¼ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸ÐµÐ¼ Ð¿Ð»Ð°Ð·Ð¼Ñ ÑÐ¾ ÑÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹ ÑÐ²ÑÐ·ÑÑ. ÐÑÐ¿Ð¾Ð»Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¼ ÑÑÑÑÐ¾Ð¹ÑÑÐ²Ð¾Ð¼ Ð±ÑÐ»Ð° Ð²ÑÐ±ÑÐ°Ð½Ð° Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ°Ð·Ð½Ð¾Ð³Ð¾ ÑÐ¸ÑÐ¸ÑÑÐ¾ÑÐ½Ð¾Ð³Ð¾ Ð²ÑÐ¿ÑÑÐ¼Ð¸ÑÐµÐ»Ñ. Ð¡Ð¸Ð½ÑÐµÐ· ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð¸ÑÑÑÑÐµÐ³Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¾ÑÑÑÐµÑÑÐ²Ð»ÑÐ»ÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹ ÑÐ²ÑÐ·Ð¸ Ð¿Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð¼Ð°ÑÑÐ¸ÑÐ½ÑÑ Ð½ÐµÑÐ°Ð²ÐµÐ½ÑÑÐ². ÐÐ°Ð´Ð°ÑÐ° Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÑÐ°Ð±Ð¸Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐµÑÐ°Ð»Ð°ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÐÐµÐ»Ð»Ð¼Ð°Ð½Ð°.Â  Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐ¹ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½Ñ Ð´Ð»Ñ ÑÐ¾ÐºÐ°Ð¼Ð°ÐºÐ° Ð¢-15ÐÐ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»ÑÑ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÐºÐ¾Ð´Ð° Ð¸Ð¼Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ FRTC Ð² Ð²Ð¸Ð´Ðµ Ð¼Ð¾Ð´ÑÐ»Ñ Ð´Ð»Ñ ÐºÐ¾Ð´Ð° Astra.
description: Currently, work is underway to launch the T-15MD tokamak with a cross section elongated in the vertical direction. The magnetic plasma control system in the T-15MD tokamak, in particular, control of its vertical position, is at the development stage. The given work is devoted to the study of models for magnetic plasma confinement and plasma control systems in tokamaks, as well as the development and synthesis of stabilizing and optimal plasma control in the T-15MD tokamak. The research set the following goals: 1) Study of the structure of the tokamak installation, electromagnetic phenomena in the tokamak chamber, physical processes in the plasma. 2) Description of the nonlinear plasma model and methods of its linearization. 3) Obtaining a mathematical model of the plasma of the T-15-MD tokamak, synthesis of the control system. 4) Study of the selected system without a regulator. 5) Synthesis of stabilizing plasma control in the T-15-MD tokamak. 6) Solution of the optimal stabilization problem. 7) Simulation modeling for the resulting control systems and analysis of the results. For the T-15MD tokamak, it is proposed to synthesize a three-loop system for controlling the vertical position of the plasma with static feedback and a linear model of a multiphase thyristor rectifier as an actuator. The work was carried out based on the Ioffe Institute, from where the main parameters of the T-15MD installation and physical measurements of the plasma were obtained, as well as information about the stages and status of development of the reactor under construction. A linearized model of vertical plasma instability for the T-15MD tokamak was obtained by identifying the DINA plasma physical code. The synthesis of stabilizing control was carried out using state feedback using the method of linear matrix inequalities. The problem of optimal stabilization was solved by the Bellman dynamic programming method. The numerical experiment for the T-15MD tokamak was carried out using the FRTC simulation code as a module for the Astra code.