This paper describes the coupling of an oscillating U-shaped water tank, also called a U-tank, with a pitching floating Wave Energy Converter (WEC) to expand the response bandwidth. The performance of these energy converters strongly depends on their frequency response, and their resonance period is generally fixed once the geometric and inertial parameters of the system have been defined. The integration and appropriate control of dynamic inertial systems based on water ballast tanks enable slow tuning of the system's resonance with the incoming wave, maximizing energy extraction. The dynamic coupling of the hull with the water tank is then analyzed, and a passive control system is developed that acts on the air contained in the reservoirs of the U-tank by partitioning the volume within. Air expansion is then controlled by discretely adjusting the available, properly partitioned volume allowing the variation of the frequency response of the sloshing water tank and device. The resolution of the dynamics involves linear models based on the Boundary-Element-Method as far as hull hydrodynamics are concerned; a solution of the Euler equation describes the oscillating tank. Finally, the expansion and compression of the air contained in the reservoirs of the U-tank are assumed to be governed by a generic polytropic transformation law, and such a condition is linearized around the operating condition. The ISWEC device is adopted as a case study, and its energy harvesting working principle is based on the gyroscope technology. The results aim to confirm the ability to perform slow tuning of the device frequency response via regulation of the air volume of the sloshing water tanks.