ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

Spacecraft use reaction wheels or control moment gyros as attitude control actuators. These wheels are nominally spinning to avoid nonlinear coulomb friction. Slight imbalance produces spacecraft vibrations making it important to isolate fine pointing equipment. Repetitive control is method that in theory can completely cancel periodic disturbances. Repetitive control systems usually look at errors one period back, in order to converge to zero error. An important difficulty is that repetitive control must be digital, so that one only has data from sample times, and there may be no error measurement one period back. One can solve this issue by introducing interpolation, but this can introduce substantial error at higher frequencies. An alternative approach is to project the data onto sinusoidal functions having the needed frequencies. Such functions allow one to interpolate without error. However, this process produces linear equations with time varying coefficients, making it harder to study repetitive control stability. A previous work showned that the equations projecting onto sinusoidal basis functions have an equivalent linear time invariant representation. It is the purpose of this paper to explore this time invariant equivalent and study the choices in how to implement the two versions of the repetitive control laws.