NONLINEAR OBSERVER/CONTROLLER DESIGNS FOR SPACECRAFT ATTITUDE CONTROL SYSTEMS WITH UNCALIBRATED GYROS
NONLINEAR OBSERVER/CONTROLLER DESIGNS FOR SPACECRAFT ATTITUDE CONTROL SYSTEMS WITH UNCALIBRATED GYROS
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Date
2004-04-27
Authors
Thienel, Julie K.
Advisor
Sanner, Robert M.
Citation
DRUM DOI
Abstract
Gyroscopes, or gyros, are vital sensors in
spacecraft onboard attitude control systems. Gyro measurements
are corrupted, though, due to errors in alignment and scale
factor, biases, and noise. This work proposes a class of adaptive
nonlinear observers for calibration of spacecraft gyros. Observers
for each of the calibration parameters are separately developed,
then combined. Lyapunov stability analysis is used to demonstrate
the stability and convergence properties of each design. First,
an observer to estimate gyro bias is developed, both with and
without added noise effects. The observer is shown to be
exponentially stable without any additional conditions. Next a
scale factor observer is developed, followed by an alignment
observer. The scale factor and alignment observers are both shown
to be Lyapunov stable. Additionally, if the angular velocity
meets a persistency of excitation (PE) condition, the scale factor
and alignment observers are exponentially stable. Finally, the
three observers are combined, and the combination is shown to be
stable, with exponential stability if the angular velocity is
persistently exciting. The specific PE condition for each
observer is given in detail.
Next, the adaptive observers are combined with a class of
nonlinear control algorithms designed to asymptotically track a
general time-varying reference attitude. This algorithm requires
feedback from rate sensors, such as gyros. The miscalibration
discussed above will seriously degrade the performance of these
controllers. While the adaptive observers can eliminate this
miscalibration, it is not immediately clear that the observers can
be safely combined with the controller in this case. There is, in
general, no "separation principle" for nonlinear systems, as there
is for linear systems. However, Lyapunov analysis of the coupled
controller-observer dynamics shows that the closed-loop system
will be stable for the class of observers proposed. With only
gyro bias miscalibration, the closed-loop system is in fact
asymptotically stable. For more general combinations of
miscalibration, closed-loop stability is ensured with modest
constraints on the observer/controller design parameters. These
constraints are identified in detail. It is also shown that the
constraints are not required if the angular velocity can be a
priori guaranteed to be persistently exciting.