Page 281 - Fundamentals of Magnetic Thermonuclear Reactor Design

260 Fundamentals of Magnetic Thermonuclear Reactor Design

l Currents in poloidal field coils (the ‘slow’ loop).
l Plasma current (the ‘slow’ loop).

Plasma shape control parameters and their number differ for limiter-phase
and divertor-phase plasma configurations. It is therefore reasonable to employ
different controllers for the phases with a smooth transition from one configura-
tion control to another.
Programmed values of these parameters are derived from static calcula-
tions, as they enable optimisation of mechanical loads on the poloidal magnetic
system and the tokamak power supply. As a matter of fact, a static scenario
determines the evolution of the plasma shape and poloidal coil currents, which
the control system will have to provide. In addition, a static scenario allows
specifying the programmed values of poloidal coil voltages needed to obtain
given coil currents and a plasma current during a discharge.
At the second stage, we embed a specific CLCS into the simulation code.
This includes a programmed description of control laws (controllers) for limiter
and divertor plasma configurations, a simplified description of coil power sup-
ply and different control algorithms.
Then, we perform the first iteration of discharge simulations and correct
the programmed values of poloidal coil voltages. Where necessary, we adjust
controller coefficients at the same simulation stage. As a rule, simulation
results indicate control parameters that need to be adjusted to improve the
control performance. The improvement is achieved through a linear-mod-
el-based new controller synthesis by selecting weights such that particular
parameters could become better ‘controllable’ or by changing the computa-
tion algorithm for such parameters, if possible. Then, we perform the second
iteration of discharge simulations and adjust the control system additionally,
if necessary.

8.5 ANALYTICAL SYNTHESIS AND CONTROL SYSTEM
OPTIMISATION
8.5.1 Basic Concept

An analytical rationale of the logic of plasma stabilisation in the vicinity of
equilibrium position is based on modern approaches to mathematical modelling
and design of closed-loop control systems [5].
One of the basic features of such approaches is that they are concerned with
mathematical optimisation problems involving different metric spaces. Number
one is the problem of asymptotic stability by Lyapunov. In the vast majority
of cases, Lyapunov stability is achieved in more than one way. So, the second
requirement is that a certain numerical characteristic of the ‘dynamic process
quality’ is optimised.
A formalised approach requires that the desired elements of a designed
system be formed based on the solutions to the mentioned optimisation