A vibration control method for chatter mitigation in milling process based on sliding mode control and reinforcement learning

Chatter is a self-excited vibration phenomenon that limits the productivity, surface quality and tool life of milling operations. In this study, an active chatter mitigation strategy is proposed by integrating sliding mode control (SMC) with reinforcement learning (RL) and an active vibration damper (AVD). A two-degree-of-freedom milling model is first formulated to describe tool vibration in the feed and normal directions, including regenerative cutting-force effects, nonlinear force components and damper-friction dynamics. A continuous-time sliding mode controller is then developed to provide robust suppression of chatter under bounded nonlinearities and modelling uncertainties. To reduce the conservative switching action and improve adaptive compensation, an actor-critic reinforcement learning component is incorporated as a bounded auxiliary control signal. The RL agent uses vibration states, sliding variables and previous control information to learn compensation forces that reduce residual chatter while penalising excessive control effort and abrupt force variations. A Lyapunov-based boundedness theorem is established to show that the sliding surface, vibration error and closed-loop milling states remain uniformly ultimately bounded when the switching gain dominates the lumped uncertainty and bounded RL compensation. Numerical simulations are conducted using cutting and structural parameters extracted from established nonlinear milling chatter studies. The proposed SMC-RL controller is compared with an uncontrolled case and a conventional PID controller. The results show that the proposed method achieves faster vibration decay and lower residual chatter in both vibration directions. Based on the mean squared error indicator, the proposed controller achieves vibration attenuation of 86.27% in the x-direction and 87.09% in the y-direction, outperforming the PID benchmark. These findings demonstrate that combining SMC robustness with RL-based adaptive compensation provides a promising framework for active chatter suppression in high-productivity milling processes.