Nonlinear Multiple-Time-Scale Attitude Control of a Rigid Spacecraft with Uncertain Inertias
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© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. This paper develops a nonlinear multiple-time-scale attitude tracking controller for a generic rigid spacecraft with actuator dynamics and uncertainties in the inertias. The rotational dynamics of the spacecraft constitute a nonlinear, nonstandard system which evolves in multiple time-scales. Using insights from geometric singular perturbation theory, attitude tracking is classified as a slow state tracking problem in the context of nonstandard multiple-time-scale systems. A nonlinear slow state tracking controller is designed using the sequential approach for handling three time-scales: one time-scale each for the attitude parameters, angular velocities, and actuators. This controller uses the estimates of the constant but unknown parameters in the model. These parameters are functions of the inertias, and they are updated online by an estimator. The update laws are selected using composite Lyapunov analysis. This analysis proves the ultimate boundedness of the tracking errors, manifold errors and parameter estimation errors, and establishes lower and upper bounds of time-scale separation within which the ultimate boundedness of errors is guaranteed. Nonlinear simulation results in the paper demonstrate that the controller is adequate to accomplish attitude tracking. The errors and the control signals can be kept acceptably small by appropriate choices of gains.
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