Optimized Fractional-Order PID Control for Regenerative Vibration Mitigation in Flexible Cantilever Beam During Milling: A Genetic Algorithm Approach

Regenerative vibrations are a major hindrance to flexible cantilever structures during milling, resulting in a reduced tool life and diminished surface finish. In this research, two actively controlled methods are directly compared: a genetic algorithm (GA)-optimized classical proportional-integral-derivative (PID) controller and a GA-optimized fractional-order PID (FOPID) controller for a milling-dependent regenerative force on a flexible cantilever beam via numerical modeling, using piezoelectric actuator/sensor patches. The original aspect lies in synergistically combining fractional-order control with genetic algorithm-based optimization to actively reduce chatter and increase the machining stability of flexible milling systems. The simulation results from the GA-FOPID controller exhibited a reduction in vibration of approximately 92.70% compared with the open-loop system by reducing the RMS value from 1.5058 × 10−4 m to 1.0996 × 10−5 m. By reducing the vibration level and enlarging the predicted stable machining region, these improvements could potentially contribute to longer tool life, improved surface finish, and reduced post-processing requirements, although these technological benefits were not directly modeled in the present study. The main innovation of this work involves a unique combination of fractional-order control, PZT actuation, and genetic algorithm optimization in a regenerative milling delay architecture. To the best of the authors’ knowledge, based on the literature surveyed in this work, this combination of techniques has not previously been reported for active chatter suppression. The stability lobe diagram (SLD) analysis, conducted under the single-mode approximation that serves as the reference framework for the like-for-like comparison of the five investigated configurations, shows that the critical axial depth of cut at the representative spindle speed increases from ap,crit(1500) = 0.061 mm for the uncontrolled system to 0.52 mm under GA-FOPID control. This enlargement of the predicted stable machining region was further confirmed, at a comparable order of magnitude, when the structural model was extended to include the two next bending modes, indicating that the trend is not an artifact of the single-mode simplification. Therefore, although the results were obtained exclusively from numerical simulation and have not yet been experimentally validated, they support the use of optimization-based methods to implement FOPID strategies as a means to increase both reliability and performance of flexible milling configurations.