A stationary exercise machine includes a system for electronically controlling a pedal resistance so as to simulate the riding of a road-going bicycle. The exercise machine includes a control system that monitors pedal velocity and that controls the resistive load generated by an electronically-controlled resistance mechanism. In one example, an electromagnetic device may vary a resistive load placed on a flywheel, which, in turn, varies the pedal resistance experienced by a user. When the user increases the pedal velocity, the resistance mechanism increases the resistive load. When the user decreases the pedal velocity, the resistance mechanism decreases the resistive load. In another example, the resistance mechanism varies the resistive load based on a gear selection by the user. The control system may also take into account other factors, such as the grade of the simulated ride, simulated wind resistance, or other frictional forces when calculating the resistive load.