I measured the p-pol PLL fast and slow loop correction signal. We can see from the attached figure. Although at that time fast loop is not stable, it shows very low-frequency drift. But slow loop reads this signal can try to bring the loop back to the original state. Since I calculated the correlation coefficient of these two signal, the slope of these two signal is the same. So the correlation coefficient is -1.

I think this is better than the coherent control loop. It is measured and shown in the entry here.