A multichannel amplitude and relative-phase controller for active sound quality control

Highlights

• A multichannel algorithm that deals with cross-channel interferences is proposed.

• Amplitude and relative-phase of complex sounds are independently controlled.

• Experiments in a small cavity verify attainment of burdensome control targets.

• Sound quality is independently enhanced for several listeners within an enclosure.

Abstract

The enhancement of the sound quality of periodic disturbances for a number of listeners within an enclosure often confronts difficulties given by cross-channel interferences, which arise from simultaneously profiling the primary sound at each error sensor. These interferences may deteriorate the original sound among each listener, which is an unacceptable result from the point of view of sound quality control. In this paper we provide experimental evidence on controlling both amplitude and relative-phase functions of stationary complex primary sounds for a number of listeners within a cavity, attaining amplifications of twice the original value, reductions on the order of 70 dB, and relative-phase shifts between $\pm \pi$ rad, still in a free-of-interference control scenario. To accomplish such burdensome control targets, we have designed a multichannel active sound profiling scheme that bases its operation on exchanging time-domain control signals among the control units during uptime. Provided the real parts of the eigenvalues of persistently excited control matrices are positive, the proposed multichannel array is able to counterbalance cross-channel interferences, while attaining demanding control targets. Moreover, regularization of unstable control matrices is not seen to prevent the proposed array to provide free-of-interference amplitude and relative-phase control, but the system performance is degraded, as a function of the amount of regularization needed. The assessment of Loudness and Roughness metrics on the controlled primary sound proves that the proposed distributed control scheme noticeably outperforms current techniques, since active amplitude- and/or relative-phase-based enhancement of the auditory qualities of a primary sound no longer implies in causing interferences among different positions. In this regard, experimental results also confirm the effectiveness of the proposed scheme on stably enhancing the sound qualities of periodic sounds for multiple listeners within a cavity.

Introduction

Based on the principle of linear superposition of acoustic signals, active noise control (ANC) has emerged as a promising technique for mitigating undesired sound fields some decades ago [1], [2]. Some engineering applications, such as automotive cavity interior, take advantage of such techniques to enhance [3], instead of merely reduce, the sound field caused as a by-product of machines and systems, by means of balancing the amplitudes [4], [5], [3], [6], [7], or shifting the relative phases [7], towards desired sound quality (SQ) targets [8], [9]. The principle of linear superposition still holds for the so-called active sound profiling [4] and active sound quality control (ASQC) techniques [10], [11], [12], [5], [6], [7], which are variants of the ANC technique that feature a specialized algorithmic handling of the error signal. These are, for the time being, the only available tools for the control designer to actively enhance the auditory qualities of such sound fields.

Single-input, single-output (SISO) feedforward active sound profiling and ASQC techniques have been demonstrated to be effective in enhancing the auditory qualities of periodic noises at a single location within an enclosure [10], [5], [13], [3], [6], [7]. The implementation of multiple SISO algorithms, which is the utmost level of decentralization of a multiple-input, multiple-output (MIMO) array, would then be a suitable strategy for enhancing the sound quality of periodic noises for multiple listeners, once that individual cost functions associated with each error sensor are optimized, instead of a global one that is typically minimized by centralized MIMO arrays [14], [11]. Moreover, decentralized ANC arrays are also known to be computationally efficient with respect to its centralized counterpart, since the computation burden and wiring effort are noticeably lesser [15], [16]. However, as the control output of a SISO ASQC unit propagates within a closed domain, the primary sound that reaches other listeners might suffer from amplitude and/or relative-phase interferences, which is an unsought effect from the SQ point of view. The enhancement of the auditory qualities of a given primary sound for a listener should not imply in the degradation of its perception for other listeners at the same enclosure. This issue could still reach at a higher level when a number of SISO algorithms are implemented within the enclosure, since the control units may induce cross-channel interferences among each other, likely to the extent that instabilities could arise.

Specialized ANC literature offers two strategies for facing the interaction among decentralized multichannel feedforward control algorithms, namely:

• Optimization of the sensor/actuator positioning [15], [17], [18], [19], [20]: the position of the sensor/actuator pairs (SAP) is optimized based upon the dynamics of the system. However, some applications, such as automotive interior, would not allow the control designer to freely move the SAPs, or just the actuators, so this strategy might be no practicable at all.

• Constraints on the control output [15], [21], [22], [23], [24], [25]: from the point of view of array stabilization, inclusion of constraints on the control output is a computationally attractive means to loosen up the above mentioned SAP requirement. This strategy could also be implemented for minimizing cross-channel interferences, by imposing rather high control output restrictions. However, some control scenarios may require the control engineer to limit the control outputs to such an extent that no control at all is obtained.

It is the purpose of this paper to introduce a novel multichannel feedforward control scheme for profiling the amplitude and/or relative-phase functions of periodic disturbances, which accounts for cross-channel interferences due to acoustic coupling. Its operation relies on exchanging data among channels, in order to compensate for amplitude and/or relative-phase interferences the signals coming from other control units may cause in the primary sound. While compensation for interferences takes place at each error sensor location, the control units profile either the amplitude or the relative-phase function, or a combination of both, so as to realize the targeted control aims at a number of locations within a cavity. The control performance is not degraded by the implementation of control output constraints, as long as the real parts of the eigenvalues of the estimated control matrix times the actual control matrix at the kth frequency are positive. When such a condition is met [15], the proposed multichannel control scheme is able to accomplish the maximum theoretical amplification and reduction amplitude bounds, as well as relative-phase shifts between $-\pi$ rad and π rad, in a free-of-interference fashion.

Experiments conducted on a 1:3-scaled, vehicle mock-up, where amplitude and relative-phase control on a complex sound composed by four harmonics is requested at three out of four positions, while keeping the sound at the remaining channel free of interferences, provide evidence on the effectiveness of the proposed multichannel scheme. Further SQ assessment based on Loudness and Roughness eventually suggests that the proposed algorithm should be the definite choice to implement independent-zone, active sound quality control, as the control scheme allows the stable realization of sound quality targets for multiple listeners, avoiding interferences among channels.

This paper is sectioned as follows: section two introduces the new decentralized control scheme, which is derived by following time- and frequency-domain adaptive rules, the latter being able to enhance complex, i.e. multi-harmonic sounds, by means of controlling both amplitude and relative-phase parameters. In section three, the link between active sound profiling tasks and sound quality control is discussed by associating two of the most relevant SQ metrics to the amplitude and relative-phase of low-frequency complex sounds, namely Loudness and auditory Roughness. Section four shows experimental evidence together with description of the followed methodology, as well as a discussion of observations. Section five ends this document with concluding remarks.

Mathematical notation: Bold entities denote either vectors or matrices, as defined in corresponding paragraphs. Systems are denoted by using z-transform, whereas signals are denoted by using discrete-time indices, e.g. n, or l. For the sake of understandability, current time for an adaptive system is denoted by using subscripts, e.g. C_n(z), instead of using $C[n]$.