Tuned vibration absorbers are effective devices for vibration control in the presence of tonal or broadband excitation. However, when the properties of the host structure or absorber change or, for tonal excitation, the excitation frequency varies they become detuned and their performance can degrade to an unacceptable level. It is therefore desirable, in any real application, that a TVA must be able to automatically adapt to variations in system operating parameters. In this paper an electromagnetic device with an adaptive electrical shunt impedance is described. The application focusses on tonal excitation. The shunt is implemented synthetically to allow the parameters and hence natural frequency of the TVA to be altered on demand. A proposed model-based feedforward controller updates the TVA parameters to ensure the natural frequency of the TVA tracks the excitation frequency. In the steady state the system therefore always operates with an antiresonance at the excitation frequency, maintaining optimal performance throughout a large range of excitation frequencies. Finally, additional adaptation is included to introduce robustness to model errors. Simulations and experimental results show that the adaptive controller demonstrates better performance than the equivalent non-adaptive system as well as an H-infinity optimally tuned system.