Controlling Clocks with PID Controllers

Demetrios Matsakis

Abstract: The PID approach to controlling clocks determines a frequency steered based upon the dot product of a 3- component gain vector with a vector whose components are optimal estimates of the phase (time, or P for proportional), frequency (derivative D), and integral of the phase (denoted I). Just as with a 2- component “PD” approach [1,2], which ignores the integral I, it is possible to compute the steady-state variances of any linear combination of the controlled clock’s phase, frequency, and steers (hereafter PFS), as well as the time constants(s) for the response to a disturbance. The PD approach assumes unmodeled systematic errors, such as frequency drift, are small. If this is not the case, use of the integral helps allow for them. As with PD controllers, critical PID gains can be computed, which result in a decaying exponential response to a disturbance. The regions of PID stability can be mapped out, and it is found that increasingly higher choices of the integral’s gain coefficient (I_gain) result in stable solutions only if increasingly higher minimum frequency-gain coefficients are selected. Since the minimum values of the three variances occurs with the I_gain set to 0, use of PID can be considered a way to ensure against nonstochastic errors, at the price of greater variance in the PFS.
Published in: Proceedings of the 51st Annual Precise Time and Time Interval Systems and Applications Meeting
January 21 - 24, 2020
Hyatt Regency Mission Bay
San Diego, California
Pages: 320 - 331
Cite this article: Matsakis, Demetrios, "Controlling Clocks with PID Controllers," Proceedings of the 51st Annual Precise Time and Time Interval Systems and Applications Meeting, San Diego, California, January 2020, pp. 320-331.
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