Chatter is a self-excited and unstable vibration phenomenon during machining operations, which affects the workpiece surface quality and the production efficiency. Active chatter control has been intensively studied to mitigate chatter and expand the boundary of machining stability. This paper presents a discrete time-delay optimal control method for chatter suppression. A dynamical model incorporating the time-periodic and time-delayed characteristic of active chatter suppression during the milling process is first formulated. Next, the milling system is represented as a discrete linear time-invariant (LTI) system with state-space description through averaging and discretization. An optimal control strategy is then formulated to stabilize unstable cutting states, where the balanced realization method is applied to determine the weighting matrix without trial and error. Finally, a closed-loop stability lobe diagram (CLSLD) is proposed to evaluate the performance of the designed controller based on the proposed method. The CLSLD can provide the stability lobe diagram with control and evaluate the performance and robustness of the controller cross the tested spindle speeds. Through many numerical simulations and experimental studies, it demonstrates that the proposed control method can make the unstable cutting parameters stable with control on, reduce the control force to 21% of traditional weighting matrix selection method by trial and error in simulation, and reduce the amplitude of chatter frequency up to 78.6% in experiment. Hence, the designed controller reduces the performance requirements of actuators during active chatter suppression.

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