Sensing and control interface for precise gap control

Abstract

A one degree-of-freedom precision position control system using an electrostatically actuated and capacitively sensed beam is reported. The beam is allowed to rock on a 10 µm high fulcrum which is fabricated from SU-8 deposited onto a glass substrate. The fulcrum establishes the nominal working gap between the beam and two electrodes located on the substrate. The differential capacitance formed by the beam and electrodes is sensed, however, the electrodes are also simultaneously used for applying controlled electrostatic forces to the beam. The system is unstable so feedback control is necessary to establish a desired stable gap but only after an appropriate feedforward filter that compensates for the forcer-to-pick-off coupling is implemented. The RMS displacement noise from DC to 100 Hz is 7 nm, and the gap can be regulated from DC to 600 Hz.

Identification and compensation of feedthrough in an unstable electrostatic bearing

“…The present paper shows how the identification of a higher fidelity feedthrough model and the implementation of an updated feedforward filter can significantly improve the closedloop performance over what was achieved in [6]. This reference demonstrated that a feedforward filter identified from open-loop measurements can reduce the feedthrough by about an order of magnitude.…”

“…A methodology for generating a frequency response function associated with the linear-time periodic equations of motion is also described. This modeling technique is an extension of a previously reported approach introduced in [6], but it has the benefit of extending the frequency range to the Nyquist frequency associated with the experiments whereas the models in [6] were limited to estimating the frequency response up to half of the carrier frequency ω 0 . This extends the model frequency responses from the high-frequency limit of 12.5 kHz in [6] to a limit of 37.5 kHz in the present work.…”

“…This modeling technique is an extension of a previously reported approach introduced in [6], but it has the benefit of extending the frequency range to the Nyquist frequency associated with the experiments whereas the models in [6] were limited to estimating the frequency response up to half of the carrier frequency ω 0 . This extends the model frequency responses from the high-frequency limit of 12.5 kHz in [6] to a limit of 37.5 kHz in the present work. The approximate frequency responses procured with this technique show very good agreement with experimentally obtained frequency responses and appears to be a reasonable approach for generating a frequency response that is suitable for control design.…”

“…A 10 µm high fulcrum is created by patterning SU-8 onto a glass substrate. Fabrication details are given in [6]. A pair of gold electrodes is deposited on the substrate with one electrode on each side of the fulcrum.…”

“…This level of reduction was adequate for implementing a stabilizing controller, however, the associated stability margins were poor. For example, the magnitudes of the sensitivity and complementary sensitivity functions were reported in [6] to be about 4 from DC to 200 Hz. This high sensitivity is undesirable as it causes amplification of disturbances and noise over a broad frequency band.…”