The figure schematically illustrates part of an accelerometer in which a feedback control subsystem applies voltages to generate electrostatic forces to minimize the displacement of a proof mass suspended on a spring. Older systems of this type provide active control of the displacements of proof masses but do not provide any compensation for spring stiffnesses; as a result, low-frequency responses are characterized by displacement errors proportional to mechanical resonance frequencies. The present system differs from older systems in that it operates with a combination of voltages chosen to produce not only active control of the displacement of the proof mass but also passive compensation for the stiffness of the spring. Consequently, in the present system, the effective spring stiffness and resonance frequency are reduced to near zero, and the low-frequency position error is greatly reduced.

The proximity-sensor circuit measures the displacement of the proof mass relative to a nominal position along a direction between the fixed electrodes. The proximity sensor in this system is a quantum-mechanical-tunneling tip, but a capacitor electrode or other suitable device could also be used. The output of the proximity-sensor circuit is processed through feedback control electronic circuitry, which generates electrostatic deflection voltages to drive the displacement toward zero. One of the electrostatic deflection voltages is taken as a measure of the force tending to displace the proof mass, and thus as a measure of acceleration.

The electrodes on the proof mass are grounded. The voltages applied to the upper and lower fixed electrodes are U0+ U and U0 - U, respectively, where U is the output voltage generated by the feedback control subsystem and U0 is a fixed offset voltage that can be chosen to compensate for the spring stiffness. More specifically, one can choose U0 so that the net component of electrostatic force associated with U0and favoring a small displacement is equal in magnitude to the spring force that opposes the displacement.

One can calculate the required value of U0 with the help of some simplifying assumptions that include linearity of the spring response; coincidence of the nominal, equilibrium, and middle positions; smallness of displacement relative to the equilibrium electrode separation d0; absence of irreversible processes; absence of slow drifts in mechanical and electronic responses; absence of parasitic feedback loops associated with stray capacitances; and attribution of all errors to noise sources only. In the special case in which the accelerometer is oriented with its sensory (displacement) vertical in a gravitational field and U = Ug is needed to keep the proof mass at the nominal position, the value of U0 needed to compensate for the spring stiffness is given by

U0 = Ug d0ω02 / g,

where w0 is the resonance frequency and g is the gravitational acceleration. In tests, the accelerometer was used to measure small vertical accelerations. Although designed for use aboard a spacecraft, the accelerometer also performed well in normal Earth gravitation: it was demonstrated to respond to accelerations as small as 10¯6g, at frequencies from 0.01 to 20 Hz.

This Accelerometer Is Similar to previously reported micromachined spring-and-mass accelerometers with feedback electrostatic displacement control, except that the offset voltage U0 can be chosen to compensate for the spring stiffness, yielding nearly zero effective spring stiffness and correspondingly increased low-frequency response.

This work was done by Benjamin Dolgin, Boris Lurie, and Paul Zavracky of Caltech for NASA's Jet Propulsion Laboratory. In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to

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Refer to NPO-20292

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Eletrostatic displacement control compensates for spring

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Motion Control Tech Briefs Magazine

This article first appeared in the September, 1998 issue of Motion Control Tech Briefs Magazine.

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