control of fusion reactor plasma y. miyoshi frontier science,university of tokyo
TRANSCRIPT
Control of fusion reactor plasma
Y. MiyoshiFrontier Science ,University of Tokyo
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 paramete
rs
①
actuators and
diagnostics
② Control
logic
③
Control System construction
Example of Parameter Categorization
ItemControl parameter
mid parameter
measurable parameter
Electrical output
Pfusne,Z ,f ,f ,Ti,Te
Safety operation
q ,Wqra ,q ,nτ,Zeff ,f
Plasma stability
β , n ,qmin, rotation
Ip,ap ,j(r),Bt
Plasma shape, position
R ,ap,κ,δ,d Ip,j(r)
Detailed discussion is needed.
div
load
N GW min
p p gap
p
eff
D T
rad
elm
edgef
fimp
gas-puffpellet NBI RF coil
ne ○ ○ △ Zeff ○ ○ fd,fT,fimp ○ ○ △
Ti ○ Te ○ ○ qrad ○ ○ qelm ○ ○
Ip ○ ○ ○
j(r) △ ○ △
Rp,ap ○
κ,δ ○
dgap ○
rotation ○
Example of Actuator Categorization
For multiple control, Coupling effect must be taken into account.
Multiple Control Experiment
Ti
Difference in Ti
Ref
NBI power
q-minimu
m
Ref
LHCD power
Time
q-minimum real time control ΔTi real time
control
qminITG
current profilepressure gradient
NBI
LHCD
JT-60 experiment
[3]T.Suzuki, J.Plasma Fusion Res. Vol86, No9 530-535 (2010) (in Japanese)
1.5D transport code simulation
qmin
ITG
current profile
pressure gradient
NBI
LHCD
JT-60 experiment
NBI
gas-puff
Fusion power
minimum q-value
transport code simulation [4]
Fusion power
Gas-puff
Target value
Fusion power control simulation
Current profile movie
Density profile movie
Gas-
puff
[1
0^
19/s
ec]
q-minimum control simulationq-
min
Energ
y
[MW
]
r/a (q
-m
in)
Current profile
Simultaneous control simulation
Energ
y
[MW
]
Gas-
puff
[1
0^
19/s
ec]
q-
min
r/a (q
-m
in)
Summary of 1.5D simulation
gas-puff
Fusion power
Single Control
NBI minimum q-value
Single Control
NBI
gas-puff
Fusion power
minimum q-value
Simultaneous Control
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
0-D analysis
1.5-D analysis
Plasma Experiment
JT-60 experiment
Simultaneous control simulation
Classical control
Modern control
This research
Classical and Modern control theory
Control Physical Model
Model differen
ce
True system
+-
yuer
Managed as disturbance
Control
True system
+-
yuerBlack Box
Classical control
Modern control
State space modelTo determine actuator value, we use this ‘State 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 vectorActuator vector
Output vector x u
we get an
d
From
Linearized State Equation
P control
ne
Adding the Integrator
Add the integral term to avoid the disturbance.
PI control
2 degree of freedom control
Feedback
Control
Plasma
+-
yuer Δu
Feed forward
Control
ueq
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. 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)
Appendix
The Effect of Disturbance
Control Nominal Model
Model err
True system
+-
yuer
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.