Control design for force balance sensors

This paper describes a design methodology for force balance sensors and applies it to the design of a tunneling accelerometer. A controller based on feedback from estimated states is a natural basis for the design. It provides a controller with a rich choice of design methods. The feedback gains can be used to tune the motion of the mass but they do not influence the sensor transfer function that is uniquely given by the filter gains. Since low currents and small distances are measured, noise is an important factor. The main contributions are thermal noise from the air molecules hitting the mass, Johnson-Nyquist noise in the input resistor of the transimpedance amplifier, and tunneling noise. The effects of noise are analyzed giving fundamental limitations for the achievable resolution. The properties of the system are illustrated by simulations and experiments.