THE INFLUENCE ON STABILITY ROBUSTNESS OF COMPROMISING ON THE ZERO TRACKING ERROR REQUIREMENT IN REPETITIVE CONTROL

摘要

Repetitive control (RC) can be used to design active vibration isolation mounts that aim to cancel the influence of spacecraft vibrations on fine pointing equipment. It can cancel the influence of slight imbalance in momentum wheels, reaction wheels, and CMGs. Since RC aims for zero error, it requires reasonably accurate knowledge of the system dynamics all the way to Nyquist frequency. As a result special methods are needed to establish robustness to model error. A series of publications have demonstrated a method of averaging a cost function over models to increase the robustness. A previous paper improves on this by adjusting the learning rate as a function of frequency to further improve robustness, but there is still a hard limit on phase error. This paper considers yet one more approach, and all three can be used simultaneously. Here we compromise on the zero tracking error requirement for frequencies that require extra robustness. This allows one to extend this hard limit making a RC tolerate larger model errors. A quadratic cost is used that penalizes not just the rate of change of the input function, but also the size of the input function. We first establish how to do this for the sister field of iterative learning control, and then the frequency response characteristics are produced for design of repetitive control. The method can improve tracking error for a frequency interval above the frequency at which one would otherwise have to cut off the learning due to model error. Model uncertainty can be used directly in the design process to produce stable RC laws for any level of uncertainty. The design approach differs from typical earlier work that used a sharp frequency cutoff, and instead uses a minimal amount of attenuation needed to produce stability.