Hybrid PID-reinforcement learning control for active vibration suppression in milling processes

Abstract This study examines a PID baseline augmented by a bounded soft actor-critic (SAC) residual and a Lyapunov-inspired action filter for active vibration suppression in milling. A two-axis nonlinear regenerative model and equivalent active vibration damper define the simulation framework. The research question concerns the incremental value and actuation cost of residual learning relative to conventional feedback, rather than the novelty of combining PID and reinforcement learning. The retained numerical summaries report competitive nominal attenuation and lower aggregate vibration under parameter variation at greater RMS actuation effort. These summaries are considered descriptive reports of the integrated controller, not independently verified evidence that learning or filtering causes the reported differences. The theoretical analysis establishes conditional ultimate boundedness of a reduced PID error model under nominal Hurwitz stability and an independently justified additive-perturbation bound. It does not certify the complete regenerative-delay system, physical machine safety or SAC optimality. Model-parameter sensitivity is distinguished from generalization to unseen machining conditions, and mathematical boundedness is distinguished from chatter stability. Matched component ablations, traceable training and test records, and independent model validation remain necessary to substantiate the numerical claims and establish a manufacturing benefit. The contribution is therefore a constrained residual-control formulation and a qualified assessment of its reported vibration–actuation trade-off.