Control of an orbiting flexible square platform in the presence of solar radiation

A mathematical model for the solar radiation forces and moments acting on a square plate (platform) in orbit is obtained by considering the plate mode shapes as combinations of free-free beam shape functions. The moment expressions for a plate of arbitrary reflectivity coefficient are obtained as a function of the solar incidence angle. It is seen that only the first three flexible modes of the plate generate a first order net moment about the center of mass, and that the solar radiation pressure does not influence the flexible modes of the plate for small amplitude vibrations. The solar radiation disturbance model is then included in the dynamic model of a square plate nominally oriented along the local vertical and having the major surface of the plate normal to the orbital plane. The roll angle of the plate is seen to increase steadily due to the solar radiation pressure whereas the pitch and yaw motions oscillate with an amplitude of approximately 0.2° for a 100 m square thin aluminum plate in synchronous orbit. To control the shape and orientation of the plate two point actuators are assumed—one whose force axis is normal to the plane of the plate, the second with a force axis in the plane of the plate. The control law and the feedback gain values are obtained based on linear quadratic Gaussian methods. Transient responses and control requirements are simulated for local vertical and horizontal orientations.