Spacecraft Control Systems: Hybrid Continuous/Impulsive Control

宇宙飞船有三种不同的运动形式。 它们在空间位置的演变是轨道动力学的课题。 它们相对于某些参照物（如地球）的定向演化由姿态动力学描述。 较大的航天器可能相当灵活，人们还关注其结构动力学，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运动，该反馈控制系统使用传感器来监测航天器运动，然后使用产生力和扭矩的适当致动器来校正误差。一个想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，一种可能的力致动器是一种推进器，它利用燃料的大量排出在航天器上产生反作用力。 这种方法的问题在于，它依赖于一种经常短缺的消耗品（燃料）。 一个创新的力的来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控制-其中一些是不可控制的。 这就意味着可以将连续作用的洛仑兹力与推进器的使用联合收割机结合起来。 推进器可以在短时间内使用;我们说它们是冲动的。 我们希望解决这个混合控制问题，其中一个要尽量减少使用连续和脉冲控制输入。 另一个航天器控制问题是磁姿态控制问题。 在这里，我们使用地球磁场作用于卫星上的载流线圈所产生的扭矩，以及成对推进器所产生的脉冲扭矩。太阳帆是一种有趣的航天器，它是一种大型薄膜结构，可以像镜子一样反射作用在其上的太阳辐射。由于来自太阳的光子的动量被改变，因此在帆上产生反作用力。 通过适当地操纵帆的取向，人们可以控制太阳辐射压力并使用它将太阳帆移动到期望的目的地。 一个有用的目的地是太阳和地球之间的一个点，太阳帆可以用来探测太阳风暴，并在风暴到达之前向地球发出警告。放置太阳帆的另一个有用的点是在一个“坐极”的位置，即帆不绕地球轨道运行，而是坐在北极上方，并随着地球绕太阳运行。 这样的轨道有助于加强加拿大在北极的主权。 为了使用这些特殊的轨道，人们需要制定实现它们的转向策略。 通常，人们希望在最短的时间内到达这些地方。 我们寻求开发适当的数字策略来解决这个问题。*

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.***********