Advanced Plasma Control Systems in Fusion Experiments

現代制御理論を用いた核融合プ
ラズマ制御シミュレーション
三善 悠矢
東京大学大学院新領域創成科学研究科
Introduction
ITER [1]
DEMO [2]
Commercial [2]
Under construction
Construction of 
control system
 is needed.
Construction of control system for 
high performance
plasma with 
limited
 actuators or diagnostics is needed.
Control Logic Construction
 Control 
System
construction
Example of Parameter Categorization
Detailed discussion is needed.
div
load
N
GW
min
p
p
gap
p
eff
D
T
rad
elm
edg
eff
imp
Example of Actuator Categorization
For m
ultiple control, Coupling effect must be taken
into account.
Multiple Control Experiment
qmin
ITG
current profile
pressure gradient
NBI
LHCD
JT-60 experiment
[3]T.Suzuki, J.Plasma Fusion Res. Vol
86
, No9 530-535 (2010) (in Japanese)
1.5D transport code simulation
qmin
ITG
current profile
pressure gradient
NBI
LHCD
JT-60 experiment
Fusion power
 control simulation
Current profile
movie
Density profile
movie
Gas-puff [10^19/sec]
q-minimum control simulation
Current profile
S
imultaneous control simulation
Summary of 1.5D simulation
It is difficult to determine the
appropriate gain matrix from
only the 
response characteristics.
Easy to control
Difficult to control
because of their
interaction
Using modern control theory
JT-60 experiment
Classical
control
Classical and Modern control theory
Control
Physical Model
Model
difference
True system
y
u
e
r
Managed as disturbance
Classical control
Modern control
 
S
tate space model
To determine actuator value, we use this
S
tate space model
actuator vector
state vector
output vector
We can get appropriate actuator value u.
Control requirement
0-D Plasma Physics Model
a=2 (m), R=6.2 (m)
0.7
State Equation
State vector
Actuator vector
Output
 vector
 we get
and
From
Linearized State Equation
P control
Adding the I
ntegrator
Add the integral term to
avoid the disturbance.
PI control
2 degree of freedom control
Feedback
Control
Plasma
y
u
e
r
Δ
u
Feed forward
Control
u
eq
Find the equilibrium point from the
reference and physical model
Find the feed back gain from physical model
Simulink
We use the software ‘MATLAB/Simulink’
to do simulation.
MATLAB/Simulink
Summary
For control logic construction,
categorizing of control parameters,
actuators and diagnostics is necessarily.
In this research, we determine the PI gain
from 0-D plasma physics model, and we
demonstrate the 0-D control simulation.
The simulation using a transport code or
plasma control experiment are future
work.
Reference
[1] http://www.naka.jaea.go.jp/ITER/iter/index.html
[
2] 
http://www.asahi-net.or.jp/~rt6k-okn/subject.htm
[3] 
3]T.Suzuki, J.Plasma Fusion Res. Vol
86
, No9 530-535 (2010) (in Japanese)
[
4
] Y. Miyoshi et.al PFR Vol.
7
  2405135 (2012)
[5] Control system design  (G. C. Goodwin et.al)
Appendix
T
he Effect of Disturbance
Control
Nominal
Model
Model
err
True system
y
u
e
r
d
If controller has integrator (1/s), the
effect of step disturbance will vanish.
Linearize
In this simulation, we assume that equation point 
=
reference point.
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The construction of control systems for high-performance plasma with limited actuators or diagnostics is crucial for ongoing fusion experiments like ITER and DEMO. This involves developing control logic, categorizing various parameters, and understanding actuator systems. Multiple control experiments, simulations, and fusion power control scenarios are explored to achieve efficient plasma stability and shape. The need for detailed discussions and considerations of coupling effects in multiple control setups is highlighted throughout the content.

  • Plasma Control Systems
  • Fusion Experiments
  • Actuator Categorization
  • Control Parameters
  • Simulation

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  1. Introduction Commercial [2] ITER [1] DEMO [2] Under construction Construction of control system is needed. Construction of control system for high performance plasma with limited actuators or diagnostics is needed.

  2. Control Logic Construction Control parameters Control logic actuators and diagnostics Control System construction

  3. Example of Parameter Categorization Control parameter mid parametermeasurable Item parameter Electrical output ne,Z Ti,Te ,f ,f , D T eff Pfus Safety operation qra ,q ,Zeff ,f eff ,n elm imp edg rad q ,W load div Plasma stability Plasma shape, position , n rotation ,qmin, min N GW Ip,ap ,j(r),Bt p R ,ap, , ,d p p Ip,j(r) gap Detailed discussion is needed.

  4. Example of Actuator Categorization gas-puff pellet NBI RF coil ne Zeff fd,fT,fimp Ti Te qrad qelm Ip j(r) Rp,ap , dgap rotation For multiple control, Coupling effect must be taken into account.

  5. Multiple Control Experiment JT-60 experiment current profile LHCD qmin pressure gradient ITG NBI q-minimum real time control Ti real time control Ti Ref Difference in Ti NBI power q-minimum Ref LHCD power Time [3]T.Suzuki, J.Plasma Fusion Res. Vol86, No9 530-535 (2010) (in Japanese)

  6. 1.5D transport code simulation JT-60 experiment current profile LHCD qmin pressure gradient NBI ITG transport code simulation [4] gas-puff Fusion power NBI minimum q-value

  7. Fusion power control simulation Target value Gas-puff [10^19/sec] Fusion power Gas-puff Current profile movie Density profile movie Current profile movie Density profile movie

  8. q-minimum control simulation r/a (q-min) q-min Energy [MW] Current profile Current profile

  9. Simultaneous control simulation Gas-puff [10^19/sec] Energy [MW] r/a (q-min) q-min

  10. Summary of 1.5D simulation Single Control gas-puff Fusion power Easy to control Single Control NBI minimum q-value Simultaneous Control Difficult to control because of their interaction Fusion power gas-puff NBI minimum q-value It is difficult to determine the appropriate gain matrix from only the response characteristics.

  11. Using modern control theory Classical control Modern control 0-D analysis This research Simultaneous control simulation 1.5-D analysis Plasma Experiment JT-60 experiment

  12. Classical and Modern control theory Classical control True system r e u y Black Box Control True system Modern control Model difference r e u y Control Physical Model Managed as disturbance

  13. State space model To determine actuator value, we use this State space model state vector actuator vector Control requirement output vector We can get appropriate actuator value u.

  14. 0-D Plasma Physics Model a=2 (m), R=6.2 (m) 0.7

  15. State Equation State vector From Actuator vector we get Output vector x u and

  16. Linearized State Equation ne P control

  17. Adding the Integrator Add the integral term to avoid the disturbance. PI control

  18. 2 degree of freedom control Find the equilibrium point from the reference and physical model ueq Feed forward Control u u r e y Feedback Control Plasma Find the feed back gain from physical model

  19. Simulink We use the software MATLAB/Simulink to do simulation. MATLAB/Simulink MATLAB/Simulink

  20. Summary For control logic construction, categorizing of control parameters, actuators and diagnostics is necessarily. In this research, we determine the PI gain from 0-D plasma physics model, and we demonstrate the 0-D control simulation. The simulation using a transport code or plasma control experiment are future work.

  21. Reference [1] http://www.naka.jaea.go.jp/ITER/iter/index.html [2] http://www.asahi-net.or.jp/~rt6k-okn/subject.htm [3] 3]T.Suzuki, J.Plasma Fusion Res. Vol86, No9 530-535 (2010) (in Japanese) [4] Y. Miyoshi et.al PFR Vol.7 2405135 (2012) [5] Control system design (G. C. Goodwin et.al)

  22. Appendix

  23. The Effect of Disturbance True system Model err r e u y Nominal Model Control d If controller has integrator (1/s), the effect of step disturbance will vanish.

  24. Linearize In this simulation, we assume that equation point = reference point.

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