H-infinity controller design for chatter suppression in machining based on integrated cutting and flexible structure model

Abstract

This paper describes a feedback controller design for chatter suppression in machining based on combined flexible structure and cutting force models. To deal with time-delayed feedback effects from cutting forces, a linear time-delay control system is introduced that satisfies an H∞ norm-bound criterion. A corresponding set of linear matrix inequalities (LMIs) is derived from a delay-dependent Lyapunov–Krasovskii functional (LKF) and used to synthesize controllers that can achieve stable operation for specified material removal rates. Experiments on a hardware-in-the-loop flexible structure test-bed show that the LKF-LMI H∞ controller gives significant improvements in stability regions compared with robust (non-time-delay) controller designs, confirming the method’s potential for machining vibration control.