Researchers have proposed hybrid systems to achieve high sound absorption over a wide frequency range. The passive component of the system is comprised of a layer of sound absorbing material positioned at a distance from a movable wall, leaving an air space. The wall is the active component and is used to increase the absorption of the system at frequencies where the passive system is not effective. The control input that drives the active wall is determined in order to achieve a desired boundary condition at the back of the absorbing layer. Both pressure-release (i.e., minimizing the pressure at the back surface of the layer) and impedance-matching (i.e., minimizing the reflected wave in the cavity) conditions have been proposed to increase the absorption of the system. The performance of the hybrid system for these two boundary conditions is compared for broadband disturbances over a frequency range of 0--1000 Hz. The passive system showed absorption coefficients greater than 0.7 only above 500 Hz. The impedance-matching condition yielded absorption coefficients of 0.8--1.0 over the 100- to 1000-Hz range, which was significantly better than the absorption achieved with the pressure-release condition. Sensitivities of these two control approaches to system parameters are also investigated.