  Feedback control plays a crucial role in improving system accuracy and
stability for a variety of scientific and engineering applications. Here, we
theoretically and experimentally investigate the implementation of feedback
control in microwave photonic (MWP) transversal filter systems based on optical
microcomb sources, which offer advantages in achieving highly reconfigurable
processing functions without requiring changes to hardware. We propose four
different feedback control methods including (1) one stage spectral power
reshaping, (2) one stage impulse response reshaping, (3) two stage spectral
power reshaping, and (4) two stage synergic spectral power reshaping and
impulse response reshaping. We experimentally implement these feedback control
methods and compare their performance. The results show that the feedback
control can significantly improve not only the accuracy of comb line shaping as
well as temporal signal processing and spectral filtering, but also the systems
long term stability. Finally, we discuss the current limitations and future
prospects for optimizing feedback control in microcomb based MWP transversal
filter systems implemented by both discrete components and integrated chips.
Our results provide a comprehensive guide for the implementation of feedback
control in microcomb based MWP filter systems in order to improve their
performance for practical applications.
