NONLINEAR OBSERVER/CONTROLLER DESIGNS FOR SPACECRAFT ATTITUDE CONTROL SYSTEMS WITH UNCALIBRATED GYROS

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.