A loop shaping perspective for tuning controllers with adaptive feedforward cancellation

This paper presents a loop-shaping perspective on the tuning of systems using adaptive feedforward cancellation (AFC). The AFC technique is very useful for reducing/eliminating errors in a controlled system at a selected set of harmonics. Such a technique has applicability for hard disk and optical disk track following, vibration rejection in spindle systems and helicopters, camshaft and piston machining, as well as in fast tool servos for diamond turning. This last application provides the motivation for the work described herein. The paper shows how an AFC loop with N resonators results in 2N parameters, a gain and phase advance parameter for each resonator, which must be adjusted to maximize closed-loop performance. This paper details a frequency shaping method of selecting the AFC phase advance parameters and resonator gains in multiple AFC resonator systems. We have applied these techniques to our prototype diamond turning machine with a fast tool servo for cutting ophthalmic lenses. Experimental results comparing the performance of this machine with and without AFC control are presented.