Many devices have been proposed for generating electricity from the oscillatory motion of a floating body in waves which are generally irregular. This study undertakes numerical modelling and small-scale experimental testing of a power take-off system for a heaving float. A power take off system is employed to provide high speed rotational input to a standard induction generator. A numerical model of the coupled hydrodynamic and electrical system is described with particular focus on the effect of generator control strategy on the time-varying response and power output of the system. The numerical model with three empirical hydrodynamic coefficients is calibrated against experimental measurements in regular waves. The control method includes a static characteristic and a proportional integral (PI) controller to maximise average power output whilst reducing the peak rate of change of torque in the driveshaft compared to a system with no control applied. The control strategy is implemented within a model drive-train with a geometric scale of 1:67. Experimental tests are reported and model predictions of time-varying response have a form similar to the measured response. Average power output from irregular waves is predicted within 11% for frequencies less than 1.3 Hz (periods greater than 6.3 s full scale) and wave heights greater than 30 mm (2 m full scale).