This paper proposes a Perturbation Observer-based Fractional-Order Proportional-Integral-Derivative (PoFoPID) control for a Permanent Magnetic Synchronous Generator (PMSG), through variable pitch control, to maintain captured power at its rated value when the wind speed is higher than the rated value. First, the system nonlinearities, parameter uncertainties, and unmodelled dynamics are aggregated into the new perturbation, which is estimated online by the perturbation observer. Then, the fractional-order proportional-integral-derivative control is employed to fully compensate the perturbation estimate, such that the dynamic performance can be significantly improved. Moreover, Grouped Beetle Antennae Search (GBAS) is applied to optimally tune the PoFoPID controller parameters. This avoids the defect of conventional PID control parameters which depend on manual tuning. Case studies, e.g., ramp wind, random wind, and parameter uncertainty, demonstrate that PoFoPID has stable effects of output power in comparison to that of vector control, perturbation observer based proportional-integral-derivative control, and feedback linearization control. The feasibility of implementation of the proposed method is verified by a hardware-in-loop test (HIL) based on dSpace.