This work first investigates the ability of a low order fluid-structure model to fit the vortex-induced vibrations (VIV) observed on a truncated hydrofoil in a hydrodynamic tunnel. A particular VIV area is scrutinized, for which a hydrodynamic excitation mechanism due to a Kármán-type vortex wake organization successively locks the first torsional and second bending mode of the cantilevered hydrofoil. Coupling two structure oscillators with a Van der Pol wake oscillator satisfactorily reproduces the amplitude response and the lock-in frequency. In order to build a low order model allowing to optimize control strategy, a fourth degree of freedom corresponding to the electric circuit of a resonant piezoelectric shunt has been added. Composed of an inductance and a resistance connected to a piezoelectric patch, the passive shunt was tuned to minimize the vibration amplitude in the frequency lock-in range. Model predictions are finally compared with experimental results.