Robust Active Disturbance Rejection Fractional-Order Control for Regenerative Chatter Suppression in Milling

End milling productivity is reduced by regenerative chatter. In this paper, a hybrid Fractional-Order PID with Active Disturbance Rejection Control (ADRC-FOPID) is proposed to suppress chatter in half-immersion milling. A Timoshenko cantilever flexible workpiece is modeled together with a delay-dependent regenerative cutting-force model. The lumped disturbance is canceled on-line by an Extended State Observer, and the five FOPID gains are tuned off-line using Particle Swarm Optimization with a ±27 N actuator-saturation constraint. The RMS tip displacement is reduced by 68.5% by the ADRC-FOPID controller. Moreover, it increases the minimum and maximum stable depth of cut from 1.00 mm to 2.67 mm and from 23.17 mm to 37.67 mm, respectively. A robustness analysis over plant uncertainties and the operating window, with 38 points, results in a low mean RMS of 4.2 µm. Compared with classical controllers and robust controllers such as PID, LQR, H∞, and μ-synthesis, ADRC-FOPID achieves the highest critical limiting depth (7.58 mm) and peak stable depth (49.52 mm) on the same benchmark. Thus, the proposed strategy is an effective, robust candidate strategy for chatter suppression in milling.