External mechanical disturbances compensation with a passive differential measurement principle in nanoforce sensing using diamagnetic levitation

Nanoforce sensors using passive magnetic springs associated to a macroscopic seismic mass are known to be a possible alternative to force sensors based on elastic microstructures like Atomic Force Microscopes if the nanoforces that have to be measured are characterized by a bandwidth limited to a few Hertz. The estimation of the unknown force applied to the seismic mass is based on the deconvolution of the noisy measurement of the mass displacement which has an under-damped dynamic. Despite their high performances in terms of linearity, resolution and measurement range, such force sensors are extremely sensitive to low frequency environmental mechanical disturbances, like the angular variations of the anti-vibration table supporting the device or the residual seismic vibrations that are not filtered by the table. They are also sensitive to the temperature evolution of the ambient air. The evaluation, modeling and compensation of such environmental disturbances have to be specifically studied in the context of magnetic springs associated to a macroscopic seismic mass because of their important negative effects in terms of low frequency drifts and oscillatory disturbances. This article presents an estimation and a passive compensation strategy of the low frequency and non-stationary mechanical disturbances that is based on a differential principle. This approach is applied to a nanoforce sensor based on diamagnetic levitation developed in the last decade. It does not necessitate to add new types of sensors in the measurement chain such as very high resolution and low frequency inclinometers or accelerometers in order to estimate the mechanical disturbances. In term of performances, the force estimation error remains in the nanonewton level over periods of time of several minutes when external temperature remains constant.