Room Modal Equalisation with Electroacoustic Absorbers

PID-like active control strategy for electroacoustic resonators to design tunable single-degree-of-freedom sound absorbers

“…The main idea is to properly define the control law to enable the transfer from the sensed acoustic quantities to the output current which will be sent back to the ER. Such type of control on current is performed without the need to model the electrical part of the ER, thus it is more stable compared to other types of voltage-based control [11,16].…”

“…The concept of sound absorption by active electroacoustic means has been formally introduced by Olson and May [8], who applied a feedback control on an electrodynamic loudspeaker, based on the sensing of sound pressure in the vicinity of the loudspeaker, allowing modification of the acoustic impedance at its diaphragm. Thereafter, various control approaches have been developed on the ERs [9,10,11,12], such as shunting the electrical terminals of the loudspeaker with a matched electrical network [13,14,15,16], or feeding back a current/voltage prescribed from the measured acoustic pressure/velocity [9,17,13,18,14,15,19,16]. The latter control method through current/voltage assignment presents more advantages since its digital implementation offers more flexibility in control law definition and makes the reconfiguration of control much easier.…”

“…[16], the sensed sound pressure is converted into a current driving the ERs in real time, bypassing the electrical impedance, thus avoiding the inherent instabilities owing to the electrical inductance of the coil. The apparent acoustic impedance of the AER can be adjusted accordingly following the desired frequency dependence, leading to a family of designs of Single-Degree-Of-Freedom (SDOF) and Multiple-Degrees-Of-Freedom (MDOF) sound absorbers [13,20,21,16]. Such tunability is the key in many applications, such as room mode damping [22,16], wavefront shaping [23] or aircraft engine tonal noise reduction [24].…”

“…The apparent acoustic impedance of the AER can be adjusted accordingly following the desired frequency dependence, leading to a family of designs of Single-Degree-Of-Freedom (SDOF) and Multiple-Degrees-Of-Freedom (MDOF) sound absorbers [13,20,21,16]. Such tunability is the key in many applications, such as room mode damping [22,16], wavefront shaping [23] or aircraft engine tonal noise reduction [24]. Nevertheless, due to the unavoidable time delay in the control execution, as well as the inaccuracy in the parameter estimation required for control law definition, this type of feedforward-based control is always accompanied with a noticeable mismatch of the achieved acoustic impedance around the natural (passive) resonance of the ER, which could even make the controlled ER lost its passivity and produce instability.…”

“…Finally, the PID-like feedback control is further assessed in section 5.3 in terms of control accuracy, by comparing the acoustic performance of the achieved AER with the ones obtained with the feedforward control already developed in Ref. [16].…”