Design of electrostatic feedback for an experiment to measure $G$

TL;DR

This paper presents the design and implementation of an electrostatic feedback servo for a torsion pendulum used to measure the gravitational constant, achieving high measurement precision through a digital Kalman filter-based control system.

Contribution

It introduces a novel electrostatic servo design with a digital Kalman filter for precise gravitational measurements, demonstrating improved measurement accuracy.

Findings

Achieved measurement uncertainty comparable to open-loop methods.

Demonstrated effective feedback control using three electrodes.

Validated the servo design for high-precision gravitational experiments.

Abstract

The torsion pendulum at the heart of the apparatus to measure the gravitational constant, $G$ at the Bureau International des Poids et Mesures (BIPM) is used to measure the gravitational torque between source and test-mass assemblies with two methods. In the Cavendish method, the pendulum moves freely. In the electrostatic-servo method, the pendulum is maintained at a constant angle by applying an electrostatic torque equal and opposite to any gravitational torque on the pendulum. The electrostatic torque is generated by a servo. This article describes the design and implementation of this servo at the National Institute of Standards and Technology. We use a digital servo loop with a Kalman filter to achieve measurement performance comparable to the one in an open loop. We show that it is possible to achieve small measurement uncertainty with an experiment that uses three electrodes for feedback control.