The investigation of an active control system based on acoustic energy density has led to the analysis and development of an inexpensive three-axes energy density sensor. The energy density sensor comprises six electret microphones mounted on the surface of a 0.025-m (1 in.) radius sphere. The bias errors for the potential, kinetic, and total energy density as well as the magnitude of intensity of a spherical sensor are compared to a sensor comprising six microphones suspended in space. Analytical, computer-modeled, and experimental data are presented for both sensor configurations in the case of traveling and standing wave fields, for an arbitrary incidence angle. It is shown that the energy density measurement is the most nearly accurate measurement of the four for the conditions presented. Experimentally, it is found that the spherical energy density sensor is within +/- 1.75 dB compared to reference measurements in the 110-400 Hz frequency range in a reverberant enclosure. The diffraction effects from the hard sphere enable the sensor to be made more compact by a factor of 3 compared to the sensor with suspended microphones.

An active control system based on the acoustic energy density is investigated. The system is targeted for use in three-dimensional enclosures, such as aircraft cabins and rooms. The acoustic energy density control method senses both the potential and kinetic energy densities, while the most popular control systems of the past have relied on the potential energy density alone. Energy density fields are more uniform than squared pressure fields, and therefore, energy density measurements are less sensitive to sensor location. Experimental results are compared to computer-generated results for control systems based on energy density and squared pressure for a rectangular enclosure measuring 1.5 x 2.4 x 1.9 m. Broadband and narrowband frequency pressure fields in the room are controlled experimentally. Pressure-field and mode-amplitude data are presented for the narrowband experiments, while spectra and pressure-field data are presented for the broadband experiment. It is found that the energy density control system has superior performance to the squared pressure control system since the energy density measurement is more capable of observing the modes of a pressure field. Up to 14.4 and 3.8 dB of cancellation are achieved for the energy density control method for the narrowband and broadband experiments presented, respectively.

Attenuating the sound pressure at a microphone in an enclosure typically results in a relatively small region of control, often referred to as a zone of silence. In an effort to increase the region of control for practical applications, as many as 30–50 microphones have been used to achieve a broader region of control. An alternative control method for achieving global control of the field, based on sensing and minimizing the total energy density at discrete locations, has been developed. Previous work using this method in one-dimensional enclosures has indicated that significant improvement in overall attenuation is possible. This improvement can be attributed to the fact that sensing the energy density monitors all of the modes of the enclosure, and thereby avoids the spillover problem which often plagues control systems that minimize only pressure. The work reported here extends the energy density approach to three-dimensional, rectangular enclosures. Numerical results are presented to compare the global attenuation achieved by minimizing the energy density and acoustic pressure at single and multiple discrete locations. These results are also compared with the control that one would achieve by minimizing the total potential energy in the enclosure.

An active control system has been constructed based on the minimization of the energy density at discrete points within an enclosure. Though most control systems for use in enclosures are based on squared pressure as a cost function, a system based on energy density is more capable of sensing modes contributing to the acoustic field. The enclosure used is lightly damped and measures 1.5×2.4×1.9 m. A measurement system within the enclosure is capable of spatially sampling the pressure field and decomposing the field into complex modal amplitudes, which yield insight into the control phenomena. The control system can use squared pressure as well as energy density as a cost function for comparisons of the two methods. The squared pressure and energy density control are consistent with predictions of active control performance in the case of single-frequency multiple sensor/source configurations. Global control of up to 18 dB is achieved. Broadband control results using a single sensor and control source are also presented.

In recent years, an alternative sensing approach has been developed for active control, based on minimizing the acoustic energy density at the error sensor location(s). This new approach has been tested both numerically and experimentally, with the results indicating that one can often achieve improved global attenuation of the field by minimizing the acoustic energy density, rather than the sum of the squared pressures. Previous results from minimizing the energy density at the error sensors have concentrated on investigating the control that can be achieved by looking at the global energy in the field before and after control, and also by looking at the attenuation that can be achieved as a function of frequency. However, it has also been found that additional insight can be gained by examining the acoustic field in terms of the acoustic modes contributing to the acoustic field. This paper will present some of the modal decomposition results obtained for different active control approaches. These results provide insight into the control mechanisms and provide indications as to why one can often achieve improved global attenuation by minimizing the acoustic energy density rather than the squared pressure.