Control and Stability of a Spinning Symmetric Satellite in an Elliptical Orbit.

摘要

This work is a continuation of work done by Shell in the stability evaluation of a scalar control applied to a time periodic system. The scalar controlled satellite is examined in a new controlled modal coordinate system. This coordinate system decouples the four modes of the linearized system with the controller. The stability of each mode can easily be evaluated in the uncoupled form. The stability of a spinning symmetric satellite in an elliptical orbit is analyzed using phase planes and surface of section techniques. The equations of motion for the satellite attitude are presented in a linearized and a non-linear form. Floquet Theory is applied to the development of a control system for two unstable modes of the satellite. A scalar control is applied using angle rates as feedback. The stability of the new controlled system is examined in controlled modal coordinates. Comparisons of the linear and non-linear system motions are made relative to changes in the control gains. Potential chaotic motion limits the controller gains of the non-linear system. Theses. (aw)