Robust time-delayed H_∞ synthesis for active control of chatter in internal turning

This research is motivated by the problem of regenerative chatter vibration, which is an extremely harmful phenomenon in machining in general, and in internal turning in particular. In addition to limiting the production rate and accelerating the tool wear, regenerative chatter deteriorates the surface finish, which is especially undesired in the context of precision machining. This paper presents an active control design method for slender bars with delayed excitation which can be applied to the problem of active control of regenerative chatter in internal turning. The presented control method is based on the delay-dependent output feedback controller synthesis. The contribution of the presented design approach stems from incorporating into the design procedure the delayed dynamics of the regenerative chatter, the flexible bar model uncertainty, and the hardware limitations. Furthermore, the delay dynamics is taken explicitly in the synthesis of an H_∞ output feedback controller by linear matrix inequalities. The resulting controller is tested by simulations and experiments using a testbed imitating the dynamics of the internal turning process. The results demonstrate the effectiveness of the presented controller synthesis method in comparison to the commonly used approaches.