带挠性梁的充液飞行器边界控制

考虑在惯性空间中全充液挠性飞行器的控制模型,轻挠性梁一端固于刚体,另一端自由。系统动力学方程由主刚体欧拉方程、液体的平均化Ｈｅｌｍｈｏｌｔｚ方程和梁的欧拉方程耦合而成。研究表明,借用适当的作用于梁自由端的边界控制,作用于主刚体的控制力矩及作用于液体“等效刚体”的阻尼力矩,能使整个系统稳定。

The boundary control of the liquid--filled spacecraft with a flexible beam

In this paper a flexible spacecraft filled with liquid in inertial space is considered a light flexible beam is clamped to the rigid body at one end and free at the other. The motion of the elastic members is described by a set of partial differential equations with appropriate boundary conditions ; the motion of the rigid parts is governed by a set of nonlinear ordinary differential equations; the motion of the ideal liquid is described by the averaged Helmholtz equations and the rigid members are coupled with elastic members and the liquid. It is shown that suitable boundary controls applied to the free end of the beam, a control torque applied to the rigid body and damping torque applied to "the equivalent rigid body" of the liquid stabilize the system. The proof is obtained by using the energy of the system as a Lyapunov functional.