1 MATHEMATICAL MODEL OF THE PLASMA VERTICAL STABILIZATION PROCESS IN...

2.1 Mathematical model of the plasma vertical stabilization process in ITER-FEAT tokamak

−100

The dynamics of plasma control process can be commonly described by the system of ordinary

Magnitude (dB)

differential equations (Misenov, 2000; Ovsyannikov et al., 2006)

−110

dΨ

−120

20

dt

+

RI

=

V, (1)

15

whereΨis the poloidal flux vector,Ris a diagonal resistance matrix,Iis a vector of active and

10

passive currents,Vis a vector of voltages applied to coils. The vectorΨis given by nonlinearrelation

5

Phase (deg)

Ψ

=

Ψ

(

I, I

p

)

, (2)

0

whereI

p

is the plasma current. The vector of output variables is given by

−5

10

⁰

10

²

10

⁴

y

=

y

(

I,I

p

)

. (3)

Frequency (rad/sec)

Fig. 1. Bode diagrams for initial (solid lines) and reduced (dotted lines) models.Linearizing equations (1)–(3) in the vicinity of the operating point, we obtain a linear model ofthe process in the state space form. In particular, the linear model describing plasma verticalcontrol in ITER-FEAT tokamak is presented below.In addition to plant model (5), we must take into account the following limits that are imposedITER-FEAT tokamak (Gribov et al., 2000) has a separate fast feedback loop for plasma verticalon the power supply systemstabilization. The Vertical Stabilization (VS) converter is applied in this loop. Its voltage isevaluated in the feedback controller, which uses the vertical velocity of plasma current cen-V

_max

^VS

=

0.6kV, I

_max

^VS

=

20.7kA, (6)troid as an input. So the linear model can be written as followswhereV

_max

^VS

is the maximum voltage,I

_max

^VS

is the maximum current in the VS converter. So,x˙

=

Ax

+

bu,the linear model (5) together with constraints (6) is considered in the following as the basis fory

=

cx

+

du, (4)controller synthesis.wherex∈E

⁵⁸

is a state space vector,u ∈E

¹

is the voltage of the VS converter,y∈ E

¹

is the