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.