Low-risk beginning of the density control on the KSTAR plasmas

摘要

During the early campaigns of the KSTAR project, feedback control of plasma density has been successfully commissioned at the very first attempt by using a transfer function analysis. In order to minimize a chance of any risk happening, a stable and robust Ohmic discharge was chosen as a test-bed of 300 kA (I-p) circular limited plasma in 2.0 T (B-t). Pre-programmed fueling modulation was carried out first by puffing the deuterium gas via a piezoelectric valve. Line-averaged plasma density was measured in real-time by a 280 GHz interferometer system. From those modulations, both the density decay time (tau(i)*) and the external fueling efficiency (f(ex)) were approximated in windows: 3.0-5.0 s and 10-20% respectively. By using the results, a simple plant model has been established based on a global particle balance equation. Then several transient responses such as rising time, settling time and overshoot ratio were estimated in a certain range depending on the windows of tau(i)* and f(ex). It is found that tau(i)* has little effect on those response characteristics while f(ex) plays primary role together with magnitude of the proportional gain G(p). This is due to predominance of valve response whose characteristic time tau(v) was approximately 60 ms, which is much shorter than tau(i)*. Considering the responses, G(p) for closed-loop control were set initially very low i.e. 2.5 being concerned on excessive fueling. It was followed by several stepwise increments to reduce steady-state error instead of using any integral gain G(I) to avoid any chance of instability and uncertainty. Similarly, the target density was also initially low and gradually growing. In this way the very first density feedback control was successfully completed although some of the transient responses were different from the anticipated results while the predicted steady-state error was in good agreement with the experimental undershoot. By investigating an arbitrary time delay tau(alpha), it is found that the digital-low-pass filter embedded in the plasma control system (PCS) of 50 ms also plays crucial role together with the tau(v). In such way, settling time tau(s) and low overshoot case were well agreed but rising time t(r) ring well predicted steady-state error, with settling time t(s), the transfer function analysis with the simple particle balance model is appropriate for relatively slow responses but not applicable for the faster responses and strong overshoot, which may not be linear-time-invariant (LTI) system anymore. More comprehensive physics-basis modeling will be necessary for more accurate prediction including fast responses and strong overshoot of feedback control of the density.