Investigation of the behaviour of a dynamically tuned gyroscope with a view of controller design
The strapdown dynamically tuned gyroscope (DTG) is a
candidate for use as the angular motion sensor in s'trapdown inertial
navigation systems and autopilots. However, the dynamic
performance of the strapdown DTG is one of the limiting factors
restricting usage of the instrument in these systems. This
research project considers control strategies to enhance the
strapdown DTG performance.
The DTG equations of motion are derived, with damping
terms, and angular speed components introduced about the spin
axis. The DTG equations of motion are solved numerically using a
4th order Runge-Kutta method, and taking advantage of rotating
reference frames to eliminate time varying elements in the system
matrix. This approach reduces the number of computations per
time step and improves numerical stability.
The tuning conditions for a multigimbal DTG are derived.
A modal analysis is carried out on the DTG system matrix for
different tuning conditions. This work provides the basis for the
reduction of the DTG equations of motion to a free rotor gyroscope
A parameter estimation procedure is designed which reflects
the sensitivity of the DTG dynamic characteristics to certain
parameters. A comprehensive experimental programme is carried
out to validate the DTG mathematical model and estimate the
numerical value of critical DTG parameters.
A control strategy which processes the torquer and
demodulator signals of the strapdown DTG is formulated. This
strategy, used on the strapdown DTG, improves the diagonal
dominance of the system transfer function matrix. Throughout the
bandwidth the amplitude of the nutation response is at least 20 dB
down on the amplitude of the precession response, compared with
only 6 dB down on an uncompensated strapdown DTG.
The compensator-strap down DTG system bandwidth is
extended, compared to the strapdown DTG. The increase in
bandwidth and improvement in system diagonal dominance depends
on the precise form of the compensator and the manner of
implementation; analogue, digital or hybrid.
The compensator is feed-forward and can therefore be
integrated into a system without altering the strapdown loops. The
flexibility of the strategy enables the system designer to balance
conflicting requirements of performance allied with minimal, cost,
hardware and processing increases.
An analogue and hybrid version of the compensator has
been added to a strapdown DTG with subsequent test results in
close agreement with theoretical studies. The control strategy has
potential applications wherever strapdown DTG's are used.