MIN-MAX MERGED WITH QUADRATIC COST FOR REPETITIVE CONTROL OF NON-MINIMUM PHASE SYSTEMS

Repetitive control (RC) aims to eliminate the effects of a periodic disturbance to a control system. Spacecraft application include active vibration isolation from slight imbalance in CMG's or reaction wheels. Non-minimum phase systems present a design challenge. Previous work addressed this challenge, by using a Min-Max cost function to force faster learning at DC and low frequencies. This addresses the primary difficulty, but it is very sensitive to the common model error at high frequencies. To obtain robustness to high frequency model error it is best to learn slowly, but Min-Max aims for roughly uniform learning rate at all frequencies. This paper addresses these new difficulties in two ways. A merged cost function is created that has the good low frequency performance of Min-Max and the robustness of quadratic cost design at high frequencies, and this can be solved using Quadratically Constrained Quadratic Program software. The alternative is to use Min-Max up to a frequency and apply a zero-phase cutoff filter above this frequency. These results make the Min-Max design practical, and allow one to design effective repetitive controllers for non-minimum phase systems.