05aD12P
ロバスト制御理論の核融合炉への適用
Application of robust control theory for the fusion plasma
三善悠矢1) 小川雄一1)Yuya MIYOSHI 1), Yuichi OGAWA1)
1) 東大新領域
1) Graduate School of Frontier Sciences, the University of Tokyo
To operate the future reactor, the following threesubjects should be considered. First, many
parameters will have to be controlled at the sametime. For example, in addition to total fusion
power, plasma parameters such as plasma current
and density might be controlled so as to assure astable plasma operation. Second, relationshipbetween actuators and control parameters is not in
one-to-one correspondence, but complexly coupledwith each other. For example, NBI affects not only
on the plasma current, but also on the fusion power.
Finally, the actuators and diagnostics which can beinstalled in a reactor will be limited because of highheat flux or neutron flux. To tackle this MIMO(Multi-Input Multi-Output) system control problem,the modern control theory should be applied. In
modern control theory, the state equation is used.
The state equation is formed as follows,
,
(1)
,
(2)
where, x is state vector, u is actuator vector, y isoutput vector respectively and A, B, C, D are matrix.
This state equation represents the physics model ofthe system. Writing system physics model into thisform, one can deal the control problems as thematrix algebra problems. Of course, the state
equation doesn’t represent the exact system physics
model, and there are model error between the state
equation and the real system. The effect of themodel error, however, can be dealt as thedisturbance.
Considering the fusion plasma, the effect of themodel error will be significant. Thus, the robustcontroller, (i.e. the controller which decreases theeffect of the model error) should be applied to thefusion reactor. In this research, H-infinity control
theory, which is the typical robust control theory, isapplied to the fusion plasma control simulation. In
this simulation, the zero-dimensional plasma model
is solved with the software Matlab/Simulink. In thissimulation, the plasma current, plasma density andthe fusion power are controlled by the induced
current, gas-puff and the NBI. Figure 1 shows thesimulation result. In this simulation, the controller

is designed from the state equation and PID theory.

Fig. 1 The time evaluation of the plasma current
Ip, the fusion power Pf us and the plasma electrondensity < ne >. Ip and < ne > is kept in theconstant target value. Pfus follows the target value
from 400MW to 500MW at 250sec and isrecovered from the disturbance (HH becomes 1.0to 0.95) at 300sec.

In this presentation, the controller, designed with
the H-infinity theory will be demonstrated. InH-infinity theory, the ‘size’ of the transfer function
is evaluated as the H-infinity norm, and thecontroller is designed to minimize the H-infinity
norm. To minimize the model error effect, theH-infinity norm of the transfer function from themodel error to the output (it is called
complementary sensitivity function) should beminimized. In general, however, as the H-infinity
norm of the complementary sensitivity function
decreases, the H-infinity norm of the sensitivity
function, which is the transfer function from thereference value to the deviation, increases. Thus,
generally, the controller is designed with high or
low pass filter. In H-infinity theory, choosing theappropriate transfer functions and the pass filters,
the controller which adapts the various purposes
can be designed.
In this research, using this H-infinity theory, thesethree parameters can be controlled with highaccuracy and high disturbance suppression
performance.