Spacecraft Control Systems: Hybrid Continuous/Impulsive Control

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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.