Nanometer positional control using magnetic suspension for vacuum-to-air mass metrology

This paper explains the control scheme that is to be used in the magnetic suspension mass comparator (MSMC), an instrument designed to directly compare mass artifacts in air to those in vacuum, at the United States National Institute of Standards and Technology. More specifically, the control system is used to apply a magnetic force between two chambers to magnetically suspend the mass artifacts, which allows for a direct comparison (i.e., a calibration) between the mass held in air and a mass held in vacuum. Previous control efforts that have been demonstrated on a proof-of-concept (POC) of this system utilized proportional-integral-derivative (PID)-based control with measurements of the magnetic field as the control signal. Here, we implement state-feedback control using a laser interferometric displacement measurement with a noise floor of approximately 5 nm (rootmean-square). One of the unique features and main challenges in this system is that, in order to achieve the necessary accuracy (relative uncertainty of 20 × 10^-9 in the MSMC), the magnetic suspension must not impose appreciable lateral forces or moments. Therefore, in this design, a single magnetic actuator is used to generate a suspension force in the vertical direction, while gravity and the symmetry of the magnetic field provide the lateral restoring forces. The combined optical measurement and state-feedback control strategy presented here demonstrate an improvement over the previously reported results with magnetic field measurements and a PID-based control scheme.