This paper is focussed on the extremum seeking online tuning of a shunted piezoelectric vibration absorber for the broadband control of the resonant response of a mechanical system subject to a stationary stochastic excitation. Two shunt circuits are considered, which are formed by a resistor and an inductor connected either in series or in parallel. The two components are tuned in such a way as to maximise the time-averaged electric power absorbed by the shunt, that is the timeaveraged electric power dissipated by the shunt resistor. The paper shows that the proposed tuning approach leads to the same optimal resistive-inductive components of the shunt that would minimise the time-averaged vibration response of the mechanical system. Also, it demonstrates that the electric power objective function is characterised by a bell-type non-convex surface with a single maximum. Furthermore, it shows that the cost function has two principal directions characterised by constant-resistance and constant-inductance respectively. Accordingly, a two paths tuning sequence is proposed, where the shunt inductance and resistance are tuned sequentially with an extremum seeking gradient search algorithm, which efficiently finds the optimal values by working along the two principal directions.
