Research on secondary frequency standards control algorithm based on linear quadratic regulator

With the development of Low Earth Orbit (LEO) satellite internet, the number of satellites in LEO constellations has been increasing. To reduce the construction costs of LEO satellites, they are often equipped with secondary frequency standards (primarily crystal oscillators and rubidium atomic clocks) as their time-frequency sources. In order to enhance the performance of these time-frequency sources, many scholars have been investigating methods to optimize secondary frequency standards. Concerning clock control algorithms, classical methods such as PID and Ping-Pong (PP) suffer from slow tuning and uncertainty about optimization. This paper introduces a clock control algorithm based on the Linear Quadratic Regulator (LQR), which determines the optimal adjustment through a designed cost function. The advantages of this algorithm include a clear optimization strategy and ease of parameter tuning. The algorithm proposed in this paper achieves superior performance in terms of both time deviation standard deviation and frequency stability when compared to the PID and Ping-Pong algorithms. After control, for the PID, PP, and LQR algorithms, the standard deviations of the crystal oscillator are 4.2E-9, 2.7E-9 and 1.8E-9, and it’s frequency stability (10000s) has improved to 8.1E-14, 6.1E-14 and 2.8E-14, and the rubidium clock's standard deviations enhanced to 2.6E-9, 5.2E-10 and 3.4E-10, the rubidium clock's frequency stability (10000s) has improved to 6.8E-14, 2.1E-14 and 2.1E-15.