Fixed-structure robust controller design for chatter mitigation in high-speed milling

Chatter is an instability phenomenon in high-speed milling that limits machining productivity by the induction of tool vibrations, inferior machining accuracy, noise, and wear of machine components. In this paper, a fixed-structure active chatter control design methodology is proposed, which enables 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. Using this approach, fixed-structure dynamic (delayed) output feedback controllers can be synthesized. 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. All these benefits are important in milling practice. Representative examples illustrate the power of the proposed methodology in terms of increasing the chatter-free depth of cut, thereby enabling significant increases in machining productivity.