Design of a PID Control Scheme for Pound-Drever–Hall Frequency-Tracking System Based on System Identification and Fuzzy Control

We propose a novel PID control scheme for Pound-Drever–Hall (PDH) frequency-tracking system to address the shortcomings of conventional PID schemes, including the instability of theoretical inputs and difficulties in accurately determining transfer functions of controlled modules and actuators. By incorporating the distinctive features of the PDH system and reassessing the choice of modules, which encompasses system inputs, controlled objects, and actuators, the entire control scheme is modified. We set the piezoelectric ceramic transducer (PZT) control voltage that can make the PDH error zero instead of the susceptible resonant frequency as the theoretical input to mitigate the impact of unstable input and using system identification theory to obtain the precise transfer function of the controlled module in the new scheme. Subsequently, optimize PID parameters using fuzzy control theory. Furthermore, we have devised an automatic relocking mechanism tailored to PDH system demands, ensuring seamless operation amidst complex environmental fluctuations. Both simulation and experimental data underscored the superiority of the strategy, which exhibited superior dynamic characteristics. Specifically, it achieved a refined rise time of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.98~\mu $ </tex-math></inline-formula>s and minimized the frequency-tracking error to approximately 419 Hz, ensuring a solid foundation for the development of a highly accurate PDH tracking system, thereby significantly advancing the precision of resonance frequency-tracking for the sensitive resonator.