Mathematical Modeling and Control of a Large Space Structure as Applied to a Shuttle-Antenna Configuration

摘要

The equations of motion of a flexible shuttle-beam-antenna system are developed and discretized using an assumed modes approximation. The system was modeled as a cantilever beam rigidly attached to the shuttle with the motion of the antenna accounted for as forces and moments on the beam's free end. The equations of motion for the system were formed from the linearized kinetic and potential energies using Lagrange's method. The equations were put into matrix form, and the matrices were diagonalized. Linear optimal regulator techniques were employed to control the system. Two proof-mass actuators were modeled at the 40- and 80-foot positions along the beam. The shuttle was assumed to be able to be torqued about it's axes, as was the antenna. Initial runs of the ACOSS computer program showed the system to be stable with unit weighting on the weighting matrix. The system was driven unstable by changing the weightings on the flexible modes. The suppression algorithm in the program re-stabilized the system, as expected.