Periodic sampling interval repetitive control and its application to variable spindle speed noncircular turning process

This paper addresses discrete-time, repetitive control for linear, periodic, time-varying systems. A periodic, repetitive control design method based on gain scheduling is proposed and the necessary and sufficient condition for closed-loop stability is presented. Utilizing the special structure of the repetitive controller, an efficient method for evaluating the closed-loop stability is developed. The algorithm is applied to the control of a piezoelectric fast-tool stage for variable spindle speed noncircular turning process. The tool performs dynamic variable depth of cut machining to generate noncircular workpiece profiles while the spindle carrying the workpiece rotates at a variable speed to inhibit machining instability (chatter). Experimental machining results are presented that demostrate the tracking performance of the period, time-varying controller design proposed, as well as the ability to increase machining stability using this approach.