Placing the repetitive controller inside or outside the feedback loop: Simultaneously achieving the feedback and repetitive control objectives

Spacecraft often have internal moving parts such as control moment gyros or reaction wheels. Slight imbalance in such equipment sets up vibrations in the spacecraft that can compromise the performance of any fine pointing equipment on board. Repetitive control (RC) is a relatively new field that creates control systems that can be used on active isolation mounts with the aim of eliminating the influence of periodic disturbance sources. In certain applications, one wants not only to meet this objective, but also to perform some unrelated tracking maneuver. This paper is devoted to presenting methods of using RC to accomplish both objectives. It is shown that when the repetitive controller is used to adjust the command to a feedback control system, the feedback properties in response to commands of arbitrary frequency content are not normally preserved. They can be preserved if one uses the RC inside the feedback control loop, uses a small RC gain, and uses RC designed using frequency response based optimization methods. Also, with some modification of the structure one can accomplish the same objective outside the loop using the same RC algorithm. The approach is seen to decouple the design objectives, allowing one to design the feedback system for the tracking purpose without considering the periodic disturbances, and design the RC without concern for tracking.