Remediation of Time-Delay Effects in Tokamak Axisymmetric Control Loops by Optimal Tuning and Robust Predictor Augmentation
Symposium on Fusion Technology
Porto, Portugal, September 27-October 1, 2010
| Abstract |
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With the introduction of fully superconducting tokamaks comes the need
to understand how to operate and control plasmas within these devices,
given new constraints imposed by superconducting PF coils. There is a
concern about AC losses triggering coil quench. The minimum distance
of coils from the plasma is increased due to cryogenic insulation
requirements. There is a greater emphasis on minimizing the number of
control coils due to cost. Passive structures are often more conductive,
due to requirements for increased structural strength, multiple
conducting walls, or intentional placement of highly conductive passive
conductors near the plasma to reduce the growth rate of instabilities.
All of these changes from present devices tend to change the plasma
shape control properties, several of them negatively because of
increased delays in responding to plasma disturbances. It is sometimes
assumed that, because superconducting tokamaks already have significant
intrinsic or imposed sources of control delay, introducing extra delays
into the axisymmetric control loops will have negligible detrimental
impact on the plasma control. In fact, introducing extra delays into
the axisymmetric control loops of certain superconducting tokamaks can
have significant detrimental consequences. This study exposes and
quantifies the detrimental effects imposed by time delays in the control
loop in superconducting tokamaks, using as an example the plasma current
control and radial position control in a vertically stable circular
plasma in the KSTAR tokamak [1] (delays in the power supplies, data
acquisition, and vessel structure are taken into account). Two PID
controllers are synthesized based on a decomposition of control action
into ohmic flux and vertical field to control plasma current and radial
position respectively. Extremum seeking [2] is proposed for optimal
tuning of the PID gains in presence of time delays. Extremum seeking,
which is a nonmodel-based method, iteratively modifies the arguments
of a cost function (in this application, the PID parameters) so that
the tracking error is minimized [3] (see references therein for
alternative PID tuning methods). In addition, an augmentation of the
control loop by the introduction of a predictor has been proposed to
improve the performance of the time-delayed closed-loop system. It is
shown that the proposed predictor is robust against uncertainties in
the values of the delays. The stability analysis of closed-loop systems
is carried out using the dual-locus diagram (also called Satche diagram)
method [4]. The dual-locus diagram method is an extension or a variant
of the well-known Nyquist diagram, and is also based on the celebrated
argument principle in complex theory. The dual-locus diagram method is
simple, intuitive and quite effective in assessing stability of
time-delay systems when the time delays appear in only one of the loci.
[1] K. Kim et al., Nuclear Fusion, vol. 45, 2005, pp. 783-789.
[2] K. Ariyur and M. Krstic, Real-Time Optimization by Extremum Seeking Feedback. Wiley, 2003.
[3] N. Killingsworth and M. Krstic, IEEE Control Systems Magazine, vol. 26, 2006, pp. 70-79.
[4] M.Satche, Journal of Applied Mechanics, Transactions of the ASME, vol. 16, 1949, p. 419-420.