This paper deals with the resonance control of a test rig for vibrations in overhead transmission lines and corresponding nonlinear dampers (STOCKBRIDGE dampers). In the test rig, an electrodynamical shaker is used as an actuator and the input power is measured. Operating the rig requires the excitation of the mechanical system in resonance. A control law adjusting the frequency and amplitude of the excitation is developed. Sufficiently large vibrational amplitudes have to be realized with limited input power. Due to the large vibration amplitudes, the mechanical system may behave nonlinearly, complicating the appropriate control law. Nevertheless a resonance state of the nonlinear system usually features a minimal input power. This phenomenon is used to design a resonance control without detailed knowledge of the mechanical system.