Spacecraft Control Systems: Hybrid Continuous/Impulsive 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。较大的航天器可以相当灵活，人们也关心它们的结构动力学，它描述了振动类型的行为。通常需要反馈控制系统来控制航天器的运动，它使用传感器来监测航天器的运动，然后使用适当的执行器来产生力和扭矩来纠正误差。一个需要控制航天器轨道的例子是编队飞行，其中需要控制多个卫星之间的相对运动。在这种情况下，一个可能的力致动器是一个推进器，它利用燃料的大量排出来对航天器产生反作用力。这种方法的问题在于它依赖于一种消耗品（燃料），而这种消耗品通常供不应求。一种创新的力源是由磁场对航天器携带的电荷产生的洛伦兹力。事实证明，并非航天器编队中所有的相对运动都可以用洛伦兹力来控制——有些是不可控的。这表明人们可以将连续作用的洛伦兹力与推进器的使用结合起来。推进器可以在短时间内使用；我们说他们行为冲动。我们希望解决这种混合控制问题，其中人们希望最小化连续和脉冲控制输入的使用。另一个航天器控制问题是磁姿态控制问题。在这里，我们利用地球磁场对卫星上载流线圈产生的转矩，以及一对推进器产生的脉冲转矩。

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 also concerned with their structural dynamics which describes vibrational type behaviour.    Usually, feedback control systems are required to control spacecraft motion which use sensors to monitor the spacecraft motion and then correct errors using appropriate actuators which produce forces and torques. An example where one wants to control the spacecraft orbit is formation flying where the relative motion between multiple satellites needs to be controlled. A possible force actuator in this case is a thruster which uses the mass expulsion of fuel to produce reaction forces on the spacecraft.  The problem with this approach is that it relies on an expendable (the fuel) which is often in short supply.  An innovative source of force is the Lorentz force produced by a magnetic field on the charge carried by a spacecraft.   It turns out that not all of the relative motion in a spacecraft formation can be controlled with the Lorentz force - some of it is uncontrollable.  This suggests that one might combine the Lorentz force, which acts continuously,  with the use of thrusters.  Thrusters can be used over short durations; we say that they act impulsively.  We wish to solve this hybrid control problem where one wants to minimize the use of both continuous and impulsive control inputs.  Another spacecraft control problem is the magnetic attitude control  problem.  Here one uses the torques  produced by the Earth's magnetic field acting on current-carrying loops of wire on-board the satellite in conjunction with  impulsive torques produced by pairs of thrusters. An interesting spacecraft is a solar sail, which is large filmy structure which acts as a mirror to reflect the solar radiation acting upon it.  This produces a reaction force on the sail since the momentum of the photons originating at the Sun is altered.  By appropriately steering the orientation of the sail, one can control the solar radiation pressure force and use it to move the solar sail to a desired destination.  One useful destination 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.  Such an orbit is useful for enforcing Canadian sovereignty in the Arctic.  To use these special orbits, one needs to develop steering strategies to achieve them.  Typically, one wants to reach these places in the shortest time possible.   We seek to develop appropriate numerical strategies for solving this problem.