Speaker
Description
During the early campaigns of the KSTAR projgect, feedback control of plasma density has been successfully commissioned at the very first attempt by using a transfer function analysis. A stable and robust discharge was chosen as a test-bed i.e. a 300 kA ($I_p$) 2.0 T ($B_t$) ohmic circular limited plasma. Before direct feedback control, pre-programmed fueling modulation was carried out by puffing the deuterium gas. Line-averaged plasma density was measured in real-time by a 280 GHz interferometer system. From the open-loop experiments, both the density decay time ($\tau_i^*$) and the external fueling efficiency ($f_{ex}$) were obtained approximately : 3.0 to 5.0 s and 10 to 20 % respectively. By transfer function analysis, several transient responses such as rising time, settling time and overshoot ratio were estimated in a certain range by the measured ranges of $\tau_i^*$ and $f_{ex}$. It is found that $\tau_i^*$ has little effect on those response characeristics while $f_{ex}$ plays primary role together with magnitude of the proportional gain $K_p$. This is due to predominance of valve response whose characteristic time $\tau_v$ was approximately determined as 60 ms by dusing $D_{\alpha}$ signal, which is much shorter than $\tau_i^*$. Considering these values, $K_p$ for closed-loop control were initially set 2.5 as minimum and followed by stepwise increment to reduce steady-state error without any integral gain $K_i$ to avoid any uncertainty. The small $K_p$ was chosen being concerned on excessive fueling if any unexpected result happens. Similarly the target density waveform was also set low initally liniearly increasing until a flattop period for one second before current ramp-down. In this way the first density feedback control was successfully finished although the transient responses were far different from the experimental result while the predicted steady-state error was in good agreement with the experimental undershoot. By replacing $\tau_v$ with arbitrary characteristic time $\tau_a$ two different settling time in the two subsequent feedback experiments were both matched well with a single $\tau_a\sim120ms$. This is due to a digital low-pass-filter included by a plasma control system (PCS) acting as 50 ms delay of response. Including the filter, transfer function becomes 3-pole system and no more simple analytic expression of response characteristics were avaliable. Instead, they were fully numerically computed. The changed settling times including the digital filter matched well with $\tau_a\sim50ms$ which became much closer to the original $\tau_v$. In summary, response characteristics in longer period (settling time and steady-state error) are evaluated well with the transfer functions in considering simple particle balance model with fixed $\tau_i^*$ and $f_{ex}$ and fueling delay estimated by $D_\alpha$ signal including digital filter. However rising time and overshoot still does not agree with any values of $\tau_a$, which implies the density feedback system is not simply the second or third order or even linear system. For more accurate prediction of response, therefore, nonlinear or time-varying numerical model will be necessary especially in dealing with the recycling coefficient $R$ that underlies in $\tau_i^*\equiv\tau_i/(1-R)$ where $\tau_i$ is particle confinement time.
