The invention relates to a device for controlling an auxiliary engine (8) comprising a gas generator and a free turbine suitable for being able to be connected mechanically to the rotor (12) of a helicopter in order to supply it with thrust power, characterised in that said control device comprises a proportional-integral controller (30) having a proportional gain (Kp) and an integral gain (Ki), which are dependent on the rotation speed of said gas generator, said controller (30) being configured to receive an error signal representing a speed error of said free turbine, and to generate a signal (Sc) for correcting the drive speed of said gas generator obtained by adding a signal proportional to said error signal in accordance with said proportional gain (Kp), and an integrated signal (Si) resulting from the addition of a signal proportional to said error signal in accordance with said integral gain (Ki) and a memory signal (Sm), supplied by a feedback loop (31) of said integrated signal (Si), said memory signal (Sm) being dependent on a measurement representing the rotation speed of said free turbine.

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