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.