Min-max merged with quadratic cost for repetitive control of minimum phase systems

Repetitive control (RC) is an effective method to eliminate the effects of a periodic disturbance to a feedback control system. Applications of RC include an active vibration isolation mount in spacecraft, servomechanisms, and robotic manipulators. Previous work develops a repetitive controller design for non-minimum phase systems using optimization in frequency domain. The objective of the design is to minimize the maximum error merged with quadratic cost, formulated as quadratically constrained linear programming. This work studies how to make use of the Min-Max merged with quadratic cost design for minimum phase systems. An understanding of how to make design choices for the interchange between Min-Max and quadratic cost for each frequency range is developed. The performance of the proposed design choice evaluated by using a simulation of a commercial robot link shows that the design can produce an effective compensator design for minimum phase systems.