This paper presents a methodology for the design of broadband electroacoustic resonators for low-frequency room equalization. An electroacoustic resonator denotes a loudspeaker used as a membrane resonator, the acoustic impedance of which can be modified through proportional feedback control, to match a target impedance. However, such impedance matching only occurs over a limited bandwidth around resonance, which can limit its use for the low-frequency equalization of rooms, requiring an effective control at least up to the Schroeder frequency. Previous experiments have shown that impedance matching can be achieved over a range of a few octaves using a simple proportional control law. But there is still a limit to the feedback gain, beyond which the feedback-controlled loudspeaker becomes non-dissipative. This paper evaluates the benefits of using PID control and phase compensation techniques to improve the overall performance of the electroacoustic resonator. More specifically, it is shown that some adverse effects due to high-order dynamics in the moving-coil transducer can be mitigated. The corresponding control settings are also identified with equivalent electroacoustic resonator parameters, allowing a straightforward design of the controller. Experimental results using PID control and phase compensation are finally compared in terms of sound absorption performances. As a conclusion the overall performances of electroacoustic resonators for damping the modal resonances inside a duct are presented, along with general discussions on practical implementation and the extension to actual room modes damping.