Finite-frequency H∞ control for active chatter suppression in turning

Regenerative chatter deteriorates machining precision and accelerates tool wear, thereby limiting productivity. This paper presents the design, analysis, and verification of a novel finite-frequency band (FFB) H∞ state feedback control strategy, which is dedicated to chatter control of turning processes. In comparison with the available entire-frequency domain (EFD) controllers, one uniqueness of the proposed controller is that it achieves the finite-frequency band optimal control of chatter, and the user can specify the frequency band for optimization according to actual requirements. Dynamics of regenerative delay, cutting model uncertainty, and actuator output constraint are incorporated into the controller design. Utilizing the Lyapunov–Krasovskii functional (LKF) method and the generalized Kalman-Yakubovich-Popov (GKYP) lemma, a set of linear matrix inequalities (LMI) are derived and adopted to synthesize the FFB H∞ controller. The superiority of the developed controller versus EFD controllers is verified by carrying out both simulation and experimental studies. Results demonstrate that the chatter-free region can be substantially enlarged with the proposed method.