Feedback control of torsion balance in measurement of gravitational constant <i>G</i> with angular acceleration method

Abstract

The performance of the feedback control system is of central importance in the measurement of the Newton's gravitational constant G with angular acceleration method. In this paper, a PID (Proportion-Integration-Differentiation) feedback loop is discussed in detail. Experimental results show that, with the feedback control activated, the twist angle of the torsion balance is limited to \documentclass[12pt]{minimal}\begin{document}$7.3\times 10^{-7}\mathrm{rad/ \sqrt{Hz}}$\end{document}7.3×10−7 rad / Hz at the signal frequency of 2 mHz, which contributes a \documentclass[12pt]{minimal}\begin{document}$0.4\,\textrm {ppm}$\end{document}0.4 ppm uncertainty to the G value.