A Simple Force Feedback
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Transcript of A Simple Force Feedback
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A Simple Force Feedback Accelerometer Based on a Tuning
Fork Displacement Sensor
by David Stuart-Watson
Thesis Presented for the Degree of
DOCTOR OF PHILOSOPHY in the Department of Electrical Engineering
UNIVERSITY OF CAPE TOWN April 2006
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Declaration
This thesis is being presented for the degree of Doctor of Philosophy in the Department of
Electrical Engineering at the University of Cape Town. It has not been submitted before for any
degree or examination at this or any other university. This author confirms that it is his own
original work. Portions of the work have been published in condensed form in the journal Review
of Scientific Instruments and in the conference proceedings at the First African Control
Conference (2003): the author confirms in accordance with University rule GP7 that he was the
primary researcher in all instances where work described in this thesis was published under joint
authorship.
David Stuart-Watson
3 April 2006.
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Acknowledgments
I would like to thank my supervisor, Prof. J. Tapson, for all his help and support throughout the
project. I would also like to thank B. Prenzlow for all the technical and non-technical discussions
shared in the office. My family, friends and especially Sarah Makin also deserve my thanks, not
so much for the technical stuff, but all the important bits in between.
The author received financial support from the National Research Foundation (NRF) and the
University of Cape Town.
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Abstract
This thesis describes research into the use of a piezoelectric tuning fork as the displacement
sensor in a simple force feedback accelerometer. The research also includes the use of a second
piezoelectric transducer as both the suspension system and the force transducer for the
accelerometer.
A simple inertial accelerometer model, based on a damped mass-spring system, was
developed. This model was used to explore the frequency response of the suspended mass, and its
relative output displacement to an input displacement, velocity or acceleration.
An extended control model for the application of force feedback was discussed. A number of
alternate displacement sensors, and their potential for use in force feedback accelerometer
systems, were investigated.
Each tine of the tuning fork was modelled as a separate vibrating cantilever. This mechanical
model was then combined with an electrical equivalent circuit model. The overall model was then
tested with actual data obtained from a 32.768 kHz piezoelectric tuning fork. The actual data
matched the theoretical response very closely, proving the accuracy of both the mechanical and
electrical model. From a simple noise analysis on the system the fundamental limits of the tuning
forks ability to measure displacement was obtained.
Operating the tuning fork as a displacement sensor required the measurement of its output
magnitude, and the phase measurement between the input and output sinusoidal waveforms.
Digital measurement systems were excluded as they required very high sampling rates to achieve
the required accuracy. Magnitude measurement was done using a simple filtered rectifier. The
importance of isolating the phase measurement from the magnitude measurement led to the
discussion of many different phase detectors. Logic gate phase detectors were, however, the only
simple phase detectors capable of measuring phase without letting changes in magnitude
influence the measurements.
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A shift in displacement was modelled as a change in the forces in the piezoelectric tuning
fork model. This change in force shifts the operating characteristics of the fork, which can then be
modelled as simply a change in operating frequency. For any shift of displacement, modelled as a
change in operating frequency, the output motion of the tuning fork can be divided into two
transient motions and one steady state motion. A new method had to be developed for the
combination of the transient and steady state responses into one total response. This total
response was then used to develop both the control models and the controllers for keeping the
tuning fork operating at a specific point in its resonant band. From the control models it was
found that it is advantageous to use phase rather than magnitude to control the crystal.
For the application of the force feedback response, electro-mechanical models of the
piezoelectric transducers were derived, and the sensitivity of the suspension system was obtained.
Numerous approach tests were also completed to find the most sensitive physical arrangement of
the tuning fork accelerometer. In the application of force feedback, two different control loops
were required. Using phase and resonant frequency as the control variables in these loops proved
to offer a better solution than using magnitude and phase.
A simple tuning fork accelerometer was designed and tested. It was compared to two
conventional devices to establish both the sensitivity and bandwidth. The object of the test was
not to be completely noise free, but rather to test the concept of the tuning fork accelerometer.
The tests gave a bandwidth of DC-25 Hz, with an estimated sensitivity of 13 g, which is close to
the theoretically calculated value. Noise signals produced in the operation and measurement
limited the sensitivity and bandwidth.
This thesis explored the previously unexamined option of using a piezoelectric tuning fork in
conjunction with a piezoelectric transducer to form a simple force balanced accelerometer. The
results obtained go some way in indicating the potential of using this system in future
accelerometer design.