Vibration control for machining using H∞ techniques

A robust control design is developed to minimize a system´s response to unknown disturbances. The method consists of on-line identification of the system´s state space equations coupled with an H _∞-optimal controller design. The H_∞ controller is designed such that the maximum of the system´s closed-loop transfer function is less than γ, where γ is a positive design variable chosen as the upper bound on the H_∞ norm of the closed-loop system. This robust controller is used to eliminate vibrations in cutting operations of a boring bar with an active dynamic absorber, a boring bar is a metal cutting tool with a large overhang (length-to-diameter ratio). Due to this large overhang, a typical boring bar is characterized by a low dynamic stiffness and is therefore susceptible to excessive vibrations during the cutting process. These vibrations often lead to cutting instability, known as machine tool chatter. In this paper, the control of vibrations of a boring bar with an active dynamic absorber is studied. The robustness of the H_∞-optimal controller is demonstrated by varying the system´s dynamic characteristics (i.e, changing the length-to-diameter ratio of the boring bar) without adjusting the calculated control parameters. The results obtained for the H_∞ case are compared to similar results for linear quadratic regulator control design