Nonlinear momentum transfer control of a Gyrostat with a discrete damper using neural networks

Abstract

This thesis is mainly concerned with the momentum transfer control of a spacecraft installed with a single momentum wheel and an energy dissipation device, namely, a sprin-mass-dashpot damper. First, the governing equations of motion are derived by using Newton-Euler approach, and they can be put into a general nonlinear state equation of the form consisting of a single rotor gyrostat representing the best estimates and modeling error terms including internal motion variables as uncertainties. Therefore, the feedback linearization technique is employed as a baseline controller design for a single rotor gyrostat without a discrete damper. The total spacecraft angular momentum component of the wheel spin axis selected as an output function for the feedback linearization. Thus, a desired output function is predefined for which the total angular momentum fo the spacecraft is absorbed into the wheel spin direction at the steady-state with a nutation angle converging to zero. The asymptotic stability of the linearized error dynamics is proved by choosing a proper feedback gains for Hurwitz. It is also proved that the internal dynamics is (Lyapunov) stable, since it is equvalent to the output function for the feedback linearization. Then, a neural network is augmented to the baseline control law to adaptively compensate for the model error uncertainties of internal damper dynamics. The stability analysis of the closed-loop system with the neural network is rather complicated and difficult to understand, and sometimes unnecessary assumptions are involved. As a new result, the unnecessary assumptions for stability analysis are avoided by using the neural network with input normalization technique. The ultimate boundedness of the tracking error is proved by the Lyapunov stability theory. The closed loop stability analysis guarantees the asymptotic stability, but there is no relationship between stability conditions and spacecraft dynamics. Therefore, the open loop stabi...