S.J. Elliott

Active noise control

Active noise control exploits the long wavelengths associated with low frequency sound. It works on the principle of destructive interference between the sound fields generated by the original primary sound source and that due to other secondary sources, acoustic outputs of which can be controlled. The acoustic objectives of different active noise control systems and the electrical control methodologies that are used to achieve these objectives are examined. The importance of having a clear understanding of the principles behind both the acoustics and the electrical control in order to appreciate the advantages and limitations of active noise control is emphasized. A brief discussion of the physical basis of active sound control that concentrates on three-dimensional sound fields is presented.<<ETX>>

Radiation modes and the active control of sound power

Two formulations for calculating the total acoustic power radiated by a structure are compared; in terms of the amplitudes of the structural modes and in terms of the velocities of an array of elemental radiators on the surface of the structure. In both cases, the sound radiation due to the vibration of one structural mode or element is dependent on the vibration of other structural modes or elements. Either of these formulations can be used to describe the sound power radiation in terms of a set of velocity distributions on the structure whose sound power radiation is independent of the amplitudes of the other velocity distributions. These velocity distributions are termed ‘‘radiation modes.’’ Examples of the shapes and radiation efficiencies of these radiation modes are discussed in the cases of a baffled beam and a baffled panel. The implications of this formulation for the active control of sound radiation from structures are discussed. In particular, the radiation mode formulation can be used to provide an estimate of the number of independent parameters of the structural response which need to be measured and controlled to give a required attenuation of the radiated sound power.

Active control of sound radiation using volume velocity cancellation

The active control of sound transmission through a panel has been formulated using a near‐field approach. The effects of minimizing the sound power radiated by the panel and of canceling the net volume velocity of the panel are compared not only in terms of the reduction in sound radiation but also in terms of the change in the space average mean‐squared velocity of the panel and the space average mean‐squared pressure at its surface. Simulations of a thin panel excited by an incident acoustic plane wave and a piezoelectric control actuator show that volume velocity cancellation gives similar reductions in the transmitted sound power to the minimization of sound power radiation up to frequencies at which the size of the plate is about half an acoustic wavelength. The acoustic radiation is analyzed in terms of the radiation modes of the panel which are also used to explain spillover effects. Spillover, which leads to increases in the mean‐squared velocity of the panel and to increases in near‐field pressur...

The active minimization of harmonic enclosed sound fields, part I: Theory

Abstract An analysis is presented of the effectiveness with which active methods can be used for producing global reductions in the amplitude of the pressure fluctuations in a harmonically excited enclosed sound field. The total time averaged acoustic potential energy is expressed as a quadratic function of the complex strengths of a number of secondary sources of sound introduced into the enclosure. For a given number and location of secondary sources, there is a unique set of source strengths which determines the minimum value of this function. The analysis is applied to the case of a lightly damped enclosure excited by a point primary source at a frequency above the Schroeder cut-off frequency. It is demonstrated that substantial reductions in the total time averaged acoustic potential energy are possible only if the secondary sources of sound are located at a distance from the primary source which is less than half a wavelength at the frequency of interest.

The behavior of a multiple channel active control system

The convergence behavior of an adaptive feedforward active control system is studied. This adjusts the outputs of a number of secondary sources to minimize a cost function comprising a combination of the sum of mean-square signals from a number of error sensors (the control error) and the sum of the mean-square signals fed to the secondary sources (the control effect). A steepest descent algorithm which performs this function is derived and analyzed. It is shown that some modes not only converge slowly but also require an excessive control effort for complete convergence. This ill-conditioned behavior can be controlled by the proper choice of the cost function minimized. Laboratory experiments using a 16-loudspeaker 32-microphone control system to control the harmonic sound in an enclosure are presented. The behavior of the practical system is accurately predicted from the theoretical analysis of the adaptive algorithm. The effect of errors in the assumed transfer matrix used by the steepest descent algorithm is briefly discussed. >

Active vibroacoustic control with multiple local feedback loops.

When multiple actuators and sensors are used to control the vibration of a panel, or its sound radiation, they are usually positioned so that they couple into specific modes and are all connected together with a centralized control system. This paper investigates the physical effects of having a regular array of actuator and sensor pairs that are connected only by local feedback loops. An array of 4×4 force actuators and velocity sensors is first simulated, for which such a decentralized controller can be shown to be unconditionally stable. Significant reductions in both the kinetic energy of the panel and in its radiated sound power can be obtained for an optimal value of feedback gain, although higher values of feedback gain can induce extra resonances in the system and degrade the performance. A more practical transducer pair, consisting of a piezoelectric actuator and velocity sensor, is also investigated and the simulations suggest that a decentralized controller with this arrangement is also stable over a wide range of feedback gains. The resulting reductions in kinetic energy and sound power are not as great as with the force actuators, due to the extra resonances being more prominent and at lower frequencies, but are still worthwhile. This suggests that an array of independent modular systems, each of which included an actuator, a sensor, and a local feedback control loop, could be a simple and robust method of controlling broadband sound transmission when integrated into a panel.

Adaptive inverse filters for stereophonic sound reproduction

A general theoretical basis for the design of adaptive digital filters used for the equalization of the response of multichannel sound reproduction systems is described. The approach is applied to the two-channel case and then extended to deal with arbitrary numbers of channels. The intention is to equalize not only the response of the loudspeakers and the listening room but also the crosstalk transmission from right loudspeaker to left ear and vice versa. The formulation is a generalization of the Atal-Schroeder crosstalk canceler. However, the use of a least-squares approach to the digital filter design and of appropriate modeling delays potentially allows the effective equalization of nonminimum phase components in the transmission path. A stochastic gradient algorithm which facilitates the adaptation of the digital filters to the optimal solution, thereby providing the possibility of designing the filters in situ, is presented. Some experimental results for the two-channel case are given. >

Performance of feedforward and feedback systems for active control

A consistent framework is presented for the calculation of the optimal performance of feedforward and feedback control systems in attenuating random disturbances. In both cases, the optimization problem is transformed into a quadratic form using an internal model of one part of the physical system under control. The resulting architecture for the feedback controller is known as internal model control (IMC) and is widely used in the H/sub /spl infin// control literature. With this controller architecture, the optimum performance of a multichannel feedback system can be readily calculated using the quadratic optimization techniques already developed in the sampled time domain for multichannel feedforward control. The robustness of the stability of such a feedback controller to changes in the plant response can be separately assessed using a generalization of the complementary sensitivity function, which has a particularly simple form when IMC is used. The stability robustness can be improved by incorporating various forms of effort weighting into the cost function being minimized, some of which are already used for adaptive feedforward controllers. By way of example, the performance is calculated of both feedforward and feedback controllers for the active attenuation of road noise in cars. The variation of performance with loop delay is calculated for both types of control, and it is found that in this example, the potential attenuation is greatest using feedback control but only if the loop delay is less than 1.5 ms.

The active minimization of harmonic enclosed sound fields, part II: A computer simulation

Abstract This paper is Part II in a series of three papers on the active minimization of harmonic enclosed sound fields. In Part I it was shown that in order to achieve appreciable reductions in the total time averaged acoustic potential energy, Ep, in an enclosed sound field of high modal density then the primary and secondary sources must be separated by less than one half wavelength, even when a relatively large number of secondary sources are used. In this report the same theoretical basis is used to investigate the application of active control to sound fields of low modal density. By the use of a computer model of a shallow rectangular enclosure it is demonstrated that whilst the reductions in Ep which can be achieved are still critically dependent on the source locations, the criteria governing the levels of reduction are somewhat different. In particular it is shown that for a lightly damped sound field of low modal density substantial reductions in Ep can be achieved by using a single secondary source placed greater than half a wavelength from the primary source, provided that the source is placed at a maximum of the primary sound field. The problems of applying this idealized form of active noise control are then discussed, and a more practical method is presented. This involves the sampling of the sound field at a number of discrete sensor locations, and then minimizing the sum of the squared pressures at these locations. Again by use of the computer model of a shallow rectangular enclosure, the effects of the number of sensors and of the locations of these sensors are investigated. It is demonstrated that when a single mode dominates the response near optimal reductions in Ep can be achieved by minimizing the pressure at a single sensor, provided the sensor is at a maximum of the primary sound field. When two or three modes dominate the response it is found that if only a limited number of sensors are available then minimizing the sum of the squared pressures in the corners of the enclosure gives the best reductions in Ep. The reasons for this behaviour are discussed.

The minimum power output of free field point sources and the active control of sound

Optimization techniques are used to enable an unambiguous quantification of the degree to which the sound power output of a distribution of point primary sources can be reduced by the addition of a number of point secondary sources. The near field technique developed by Levine is used to calculate the total power output from an arbitrary number of point primary and secondary sources. This power output is a quadratic function of the complex strengths of the secondary point sources. For a given arrangement of primary and secondary sources, this quadratic function has a unique minimum value associated with an optimal set of secondary source complex strengths. Results are presented for the minimum power radiated by the combination of a single point primary source and various arrangements and numbers of point secondary sources. In particular it is demonstrated that, for the number of secondary sources considered, substantial reductions in total power output can be achieved only if the secondary sources are separated from the primary source by a distance which is less than one half wavelength at the frequency of interest. It is possible, however, to produce net source distributions of unexpectedly low radiation efficiency with a relatively small number of secondary sources placed close to the primary source.