Abstract: This paper presents a mathematical model of the frequency closed-loop control system for an ion microwave clock,constructed using the Simulink platform based on the system architecture and operational principles of the clock.The model simulates the dynamic response of a typical closed-loop control process,with a detailed analysis of key parameters,including the Proportional,Integral,and Derivative (PID) control coefficients,closed-loop response time,ion number decay characteristics,and their impacts on system’s stability and accuracy.Through comprehensive optimization of these parameters,this study elucidates their roles in enhancing system performance and investigates the effects of different parameter configurations on frequency stability.The findings provide a practical simulation and theoretical framework for the design and optimization of ion microwave clocks,contributing to improved long-term stability and precision.The proposed methodology and conclusions are also applicable to other frequency-controlled high-precision time and frequency devices,offering valuable insights for engineering applications in related fields.

Key words: Atomic clock, Closed-loop control, Model simulation