The method of control according to the invention slaves a DC voltage generated by the alternator to a predetermined setpoint value by controlling an excitation current flowing in an excitation circuit comprising an excitation winding of a rotor of the alternator. The excitation current is controlled by means of a semiconductor switch, in turn controlled by a control signal having a predetermined period. The method comprises a detection of a failure of the excitation circuit. At least one short-circuit of the excitation winding is detected. According to another characteristic of the method, the control signal is generated on the basis of a combination of a setpoint signal formed by pulses of the predetermined period exhibiting a duty ratio representative of the setpoint value and of a detection signal indicative of the short-circuit.