Solar Sailing: Attitude, Orbit, and Shape Control

宇宙飞船表现出三种不同类型的运动。它们在空间中位置的演变是轨道动力学的主题。它们的方向相对于某些参照物（如地球）的演变是用姿态动力学来描述的。较大的航天器可以非常灵活，人们关注的是它们的结构动力学，它描述了振动和起皱类型的行为。控制这三种类型的运动通常需要反馈控制系统，该系统使用传感器来监测航天器的运动，然后使用产生力和扭矩的适当执行器来纠正错误。控制轨道需要力，而控制方向（也称为姿态）需要力矩。

Spacecraft exhibit three distinct types of motion. The evolution of their position in space is the subject of orbital dynamics. The evolution of their orientation with respect to some reference, such as the Earth, is described by attitude dynamics. Larger spacecraft can be quite flexible and one is concerned with their structural dynamics which describes vibrational and wrinkling types of behaviour. Controlling these three types of motion typically requires feedback control systems which use sensors to monitor the spacecraft motion and then correct errors using appropriate actuators which produce forces and torques. Forces are required to control orbits whereas torques are needed to control orientation (also called attitude). In some problems, the spacecraft's attitude can have a large effect on its orbit. An interesting example is a solar sail, which is a large, flimsy gossamer structure which acts a mirror to reflect the solar radiation acting upon it. This produces a reaction force on the sail. Controlling solar sails is a challenging application because the orbital dynamics, attitude dynamics, and structural dynamics are highly coupled. The orbital path and the orientation of the sail are coupled because the forces stemming from radiation pressure act in a direction that depends on the sail attitude. This is analogous to the motion of a sailboat moving on the surface of a lake in wind. A useful destination for a solar sail is a point between the Sun and the Earth where the solar sail can be used to detect solar storms and communicate a warning to the Earth before the storm arrives. Another useful point to place a solar sail is in a "pole-sitter" position whereby the sail does not orbit the Earth but rather sits above the North Pole and moves with the Earth as it moves around the Sun. In order to use these special orbits, one needs to develop steering strategies to achieve them. We would like to determine attitude motions to reach these places in the shortest time possible. Given the solution of the previous problem, we would like to determine control approaches to follow a prescribed attitude motion. Two actuation approaches will be studied: the use of tip vanes (little miniature solar sails gimballed to the corners of the main sail) and the use of balance masses. The key problem that needs to be solved initially is the determination of the actuator motion required to provide the control torques required by the control system. Having handled the coupled attitude-orbit control problem, the next problem in the hierarchy to be studied brings shape control into play. There are two subproblems to be considered: vibration suppression and wrinkle prevention. Both are complicated by the lack of distributed actuation and sensing and the fact that the actuation is physically noncollocated with the typical sensing which one assumes would include the attitude and angular rate information measured at the centre of the sail.