Chatter is an instability phenomenon in high-speed milling that limits machining productivity by the induction of tool vibrations. In this paper, a design methodology for loworder Pyragas-type delayed feedback controllers is proposed. These controllers enable dedicated shaping of the chatter stability boundary such that working points of higher machining productivity become feasible while avoiding chatter. The control design problem is cast into a nonsmooth optimization problem, which is solved using bundle methods. Distinct benefits of this approach are the a priori fixing of the controller order, the limitation of the control action, and the fact that no finite-dimensional model approximations and online chatter estimation techniques are required. A representative example illustrates the merit of the proposed methodology in terms of increasing the chatter-free depth of cut, thereby enabling significant increases in the productivity of milling processes.
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