Self-sensing active vibration damping is advantageous if sensors cannot be placed collocated to actuators or these sensors add too much weight or cost. When self-sensing, electrodynamic actuators are used, damping is directly added to the structure where they are attached without the need of electronic integrators or differentiators that could destabilize the system. Inertial actuators have also the advantage that they do not need to react relative to a fixed ground. In this paper self-sensing control with a shunted resistor, current feedback, induced voltage feedback with and without inductance compensation are investigated in simulations and experiments. Experiments with a lightweight, inertial actuator on a clamped plate show that vibration amplitude is decreased between 6dB and 13dB and control bandwidth is doubled when the appropriate control scheme is used.