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Active Structural Acoustic Control of an Active Casing Placed in a Corner

Active Structural Acoustic Control of an Active Casing Placed in a Corner applied sciences Article Active Structural Acoustic Control of an Active Casing Placed in a Corner Anna Chraponska * , Stanislaw Wrona * , Jaroslaw Rzepecki, Krzysztof Mazur and Marek Pawelczyk Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland; jaroslaw.rzepecki@polsl.pl (J.R.); krzysztof.jan.mazur@polsl.pl (K.M.); marek.pawelczyk@polsl.pl (M.P.) * Correspondence: anna.chraponska@polsl.pl (A.C.); stanislaw.wrona@polsl.pl (S.W.) Received: 25 January 2019; Accepted: 10 March 2019; Published: 13 March 2019 Abstract: Electric appliances used in workplaces and everyday life often generate a low-frequency noise, which affects human body systems. Passive methods employed to reduce noise are not effective at low frequencies. The classical approach to active noise control practically involves the generation of local zones of quiet, whereas at other areas the noise is reinforced. Moreover, it usually requires a large number of secondary sound sources. Hence, an active casing approach has been developed. The active casing panels’ vibrations are controlled to reduce the device noise emission. Efficiency of this method has been previously confirmed by the authors and the results have been reported in multiple journal publications. However, in the previous research experiments, the active casing was placed at a distance from the enclosure walls. In this research, the active casing is located in a corner and such placement is intentionally used to facilitate the active control system’s operation. The noise reduction performance is investigated at multiple configurations, including a range of distances from the corner and different error microphone arrangements. The analysis of both primary and secondary paths is given. Advantages and drawbacks of different active casing configurations are presented and discussed. Keywords: active noise control; active casing; device noise control; modelling; feed-forward; room acoustics; filtered-x least mean squares 1. Introduction Nowadays, due to technological progress, noise level enhancement has been observed. Machines and devices commonly used in industry and everyday life generate noise, which may cause health damage. Noise is also one of the factors influencing mental performance [1]. Therefore, high efforts are made to reduce the noise pollution in the human environment. In general, noise can be divided into high-, mid- and low-frequency noise. Low-frequency noise, considered in the frequency range up to approximately 500 Hz, is most difficult to limit due to passive barriers’ inefficiency at this frequency range (when the noise frequency decreases, the mass, dimensions and cost of passive elements generally increases in order to be effective [2]). As an alternative or complementing solution, active control methods can be employed [3–6]. They can be used, e.g., to reduce noise entering through open windows [7,8]. Active methods are especially efficient at the low-frequency range, where passive barriers are infeasible [9]. However, when classically employed, they practically result in generating local zones of quiet, whereas at other areas the noise is reinforced. This requires additional care if the users are moving or the noise is nonstationary. Additionally, the number of secondary sound sources needed to make the zones controlled is high, which increases the total cost and highly interferes with the environment, making the solution unacceptable for many applications. Appl. Sci. 2019, 9, 1059; doi:10.3390/app9061059 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 1059 2 of 17 In this research, an active noise-reducing casing is investigated. The active casing encloses a device that generates an excessive noise. The original device casing may be used if it is made of thin walls or the device can be surrounded by an additional casing satisfying such requirement. The control system of the casing operates according to the Active Structural Acoustic Control (ASAC) approach. This means that by actively controlling vibrations of the casing panels, the noise emission to the environment is reduced. The ASAC approach represents several advantages over a typical Active Noise Control (ANC), where loudspeakers are used as the secondary sources [10,11]. The most important feature is that the active casing provides a global noise reduction in a whole room (reduces the noise emission), instead of creating only local zones of quiet and enhancing the noise elsewhere. This is a very desirable property of any active noise-reducing system. Efficiency of this method was previously investigated by the authors and the results have been reported in multiple publications [12–14]. However, in the previous research, the active casing was placed distant from the walls of the room the casing was enclosed by. In this paper, the active casing is located in a corner and such placement is intentionally used to facilitate the active control system’s operation. Moreover, such placement of a device can be commonly encountered in real life. The presented research aims to evaluate the hypothesis that placing the active casing in a corner and appropriately rearranging the microphones can lead to both enhanced noise reduction levels and a wider frequency range of global noise reduction (in the entire room). A proper theoretical justification for such behavior is provided. The noise reduction performance is investigated and compared for multiple configurations, including a range of distances from the corner and different error microphone arrangement. The analysis of both primary and secondary paths is also given. Advantages and drawbacks of different active casing configurations are presented and discussed. The remainder of the paper is organized in five sections. Section 2 describes the laboratory setup, i.e., the light-weight active casing and utilized actuators and sensors. Section 3 describes research experiment assumptions. The placement of the active casing in the corner is described and error microphones arrangements are depicted. Section 4 provides analysis of primary and secondary paths in terms of the amplitude functions of their frequency response functions. Section 5 introduces briefly the active control algorithm. Section 6 is dedicated to active control performance. Experimental results are presented and discussed. Finally, the conclusions are drawn based on the results. 2. The Laboratory Setup The employed laboratory setup is presented in Figure 1. It consists of a light-weight active casing placed in the corner of a room and the appropriately arranged microphones: one reference microphone, five error microphones and four room (monitoring) microphones. The active casing is placed in the corner with its back and right panels. It is built of five steel plates (1 mm thick) bolted together, forming a cuboid of dimensions 630 mm  800 mm  500 mm. The active casing is placed on a sound-insulating basis. Inside the casing, a loudspeaker is placed and it is used for the generation of a primary noise. The loudspeaker as a noise source provides a more reproducible environment for control system evaluation as compared to a real device (which is also examined in other studies performed by the authors). The employed active casing itself is described in more detail in [12,14,15]. It is important to emphasise that such a construction of the casing is very challenging from the control point of view. The casing panels are connected to each other directly without using any rigid explicit frame, and such mounting of their edges leads to both vibrational and acoustical couplings between them. Near the loudspeaker inside the casing, a reference microphone is placed to obtain a reference signal. It can provide information about the primary noise. Five error microphones are placed around the active casing at specific positions, described in detail in Section 3. There are also four room microphones, which are used to evaluate the noise reduction performance (they are not used by the control system). The room microphones are placed in four arbitrarily selected irregular locations in the Appl. Sci. 2019, 9, 1059 3 of 17 enclosure, at greater distances from the casing. Each position corresponds to a possible location of a listener [16]. Figure 1. The laboratory setup. To control vibrations of the active casing, inertial mass actuators EX-1 are used. They are light-weight (115 g) actuators of small dimensions (diameter 70 mm), compared to the size of the casing. They are attached to the inner side of the casing panels. In total, 21 actuators are used (5 actuators are attached to the top panel, 4 actuators are used per each of the remaining panels). The number of actuators and their placement is a result of analysis and optimization process maximizing a measure of the controllability of the system [15]. 3. The Experiment Assumptions The previous research experiments were performed with the active casing placed distantly from the laboratory enclosure walls. In a recent report, [17], primary and secondary paths of a casing placed only at a single wall of the enclosure were preliminarily examined. In this paper, the active casing is placed in the corner and extensive active control experiments are carried out. Hence, this research, besides the primary and secondary paths analysis, also presents a thorough study on active control system performance under such conditions, which is the main contribution of this paper. 3.1. Reflectivity of a Wall Surface One of the assumptions for the experiment concerns corner walls surfaces, which are assumed to be reflective (like in most real enclosures and rooms, industrial or domestic). The corner walls are dense and smooth. Hence, the absorption coefficient is low, providing considerable sound reflection from the walls [18]. The sound reflection between the active casing and the corner is intentional in this research. The influence of sound reflection on active control performance is investigated. The distance between corner walls and active casing’s back and right panels is small enough to expect that strong resonances may be induced, significantly influencing the primary and secondary paths and finally the control. 3.2. Distance between the Casing and the Corner If a sound source, e.g., a loudspeaker, is placed in an enclosure, its position is important, because it influences the sound perceived by the recipients. As stated in [19], a corner is the most efficient location for a non-directional source. A low-frequency loudspeaker, i.e., a subwoofer, is most efficient Appl. Sci. 2019, 9, 1059 4 of 17 if placed on a solid floor adjacent to a wall or in a corner, and coupled to reflecting surfaces at most one-sixth of the sound wavelength away [19]. In other words: d  ; (1) ls 6 f where d is the distance between the loudspeaker and the reflecting surface, v is the speed of sound ls in the air, and f is the frequency of sound emitted by the loudspeaker. The active noise control methods are most efficient at low frequencies up to about 500 Hz, therefore this is the frequency range of interest in this research. This is in agreement with the content of dominating frequencies of most common industrial devices and domestic appliances. Hence, to investigate the aforementioned phenomenon, the examined distances between the active casing and the corner should be in the range from about 0.1 m to 1.0 m. However, the maximum distance chosen for the experiment was 0.8 m due to dimensions of the laboratory enclosure. Hence, eight distances d , i = 1, 2, ..., 8, between two active casing panels and the corner walls in the room are examined, where d = 0.1 m, d = 0.2 m, ..., d = 0.8 m. 1 2 8 3.3. Placement of Error Microphones The active casing is placed in the corner with its back and right panels. These casing panels are equally distant from both corresponding corner walls with distance d , as marked in the scheme presented in Figure 2. Error microphone locations corresponding to the left, top and front active casing panels are marked with symbols L, T and F, respectively. They are located at a distance equal to 0.5 m from the corresponding panels’ centers. Error microphones corresponding to back and right casing panels are placed in two different ways. In the first approach, referred to as Setup 1, error microphones corresponding to back and right active casing panels are placed between the casing and the corner. Back error microphone location is noted by symbol B and is half the distance between the back casing panel’s center and the corresponding corner wall (the distance is equal to d /2). Analogously, right error microphone location is noted by symbol R and is half the distance between the right casing panel’s center and the corresponding corner wall (the distance is also equal to d /2). In the second approach, referred to below as Setup 2, error microphones corresponding to back and right active casing panels are moved from the gap between the casing and the corner to arbitrarily selected locations among error microphones corresponding to front, left and top active casing panels, based on results of preliminary control experiments. The new back error microphone location is noted by symbol B and is placed at the same height as the top error microphone, above the active casing’s corner (see Figure 2b). The new right error microphone location is noted by symbol R and is placed at the same height as both left and front error microphones, and its distance from active casing’s edge is equal to 0.5 m. In such arrangement, distances between error microphones become smaller, which affects the performance of active control. Both setups are examined to compare their influence. It is noteworthy that when the distance d between the casing panels and corner walls changes, all of the error microphones have to be moved, following the casing position. On the other hand, room microphones are always at the same locations. 500 /2 left panel left panel Appl. Sci. 2019, 9, 1059 5 of 17 corner bolts light-weight error casing microphone (a) Microphones arrangement in Setup 1. B' R' (b) Microphones arrangement in Setup 2. Figure 2. The schematic representation of the laboratory setup (all dimensions are given in mm). 4. Primary and Secondary Paths Active control is employed to reduce noise in this research, hence knowledge of the dynamic properties of primary and secondary paths in the frequency range of interest for active control will facilitate the control system development and implementation [12]. Their analysis is provided in this section. Primary and secondary paths’ models in the form of Finite Impulse Response (FIR) filters of length N = 128 were obtained experimentally. During the real system identification experiment, each path was excited with a optimized multi-tonal signal of 4096 samples. The signal was reproduced and the response was recorded eight times for each path. Afterwards, the correlation method was used to estimate the average impulse response of the considered path. The identified models were used both in the control system, e.g., for the Filtered-x part of the FxLMS algorithm, and for the paths’ analysis presented in this section. The amplitude function of the identified impulse response estimate is referred to as amplitude response. top panel top panel d /2 front panel front panel 500 Appl. Sci. 2019, 9, 1059 6 of 17 4.1. Primary Paths Analysis The primary path is considered as a path between the input signal to the primary noise source, Appl. Sci. 2019, xx, 5 6 of 17 i.e., the loudspeaker inside the active casing, and the signal acquired by one of the error microphones. Appl. Sci. 2019, xx, 5 6 of 17 The amplitude functions of the frequency functions of the impulse response estimates for the primary paths for both setups are presented side by side. The paths are presented in frequency range up to paths for both setups are presented side by side. The paths are presented in frequency range up to paths for both setups are presented side by side. The paths are presented in frequency range up to 500 Hz, in which active noise control methods are effective. In each figure, primary path frequency 500 Hz, in which active noise control methods are effective. In each figure, primary path frequency 500 Hz, in which active noise control methods are effective. In each figure, primary path frequency response response functions functions for for all all distances distances(0.1–0.8 (0.1–0.8m) m)ar are e pr presented. esented. response functions for all distances (0.1–0.8 m) are presented. The loudspeaker used as a noise source starts to transmit sound for frequencies above 40 Hz, The loudspeaker used as a noise source starts to transmit sound for frequencies above 40 Hz, The loudspeaker used as a noise source starts to transmit sound for frequencies above 40 Hz, what can be observed in Figures 3–5. In Figure 3, the primary paths for the error microphone which can be observed in Figures 3–5. In Figure 3, the primary paths for the error microphone what can be observed in Figures 3–5. In Figure 3, the primary paths 0 for the error microphone corresponding to right casing panel are presented (locations R and R ). The amplitude responses corresponding to right casing panel are presented (locations R and R ). The amplitude responses in corresponding to right casing panel are presented (locations R and R ). The amplitude responses in Setup 1 (Figure 3a) are distinctly different comparing to the amplitude responses obtained for Setup 1 (Figure 3a) are distinctly different comparing to the amplitude responses obtained for Setup 2 in Setup 1 (Figure 3a) are distinctly different comparing to the amplitude responses obtained for Setup 2 (Figure 3b). Maximum magnitudes in Figure 3a are substantially greater than in Figure 3b. (Figure 3b). Maximum magnitudes in Figure 3a are substantially greater than in Figure 3b. A general Setup 2 (Figure 3b). Maximum magnitudes in Figure 3a are substantially greater than in Figure 3b. A general trend observed in Figure 3a is an increase of magnitude for decreasing distance between the trend observed in Figure 3a is an increase of magnitude for decreasing distance between the casing A general trend observed in Figure 3a is an increase of magnitude for decreasing distance between the casing and the corner. Such effect is not evident in Figure 3b. It means that when decreasing distance and the corner. Such effect is not evident in Figure 3b. This means that when decreasing distance casing and the corner. Such effect is not evident in Figure 3b. It means that when decreasing distance d , the primary noise starts to resonate in the gap between the casing and the wall. Hence, if an error d , the primary noise starts to resonate in the gap between the casing and the wall. Hence, if an error i d , the primary noise starts to resonate in the gap between the casing and the wall. Hence, if an error microphone is placed in such a gap, the signal it measures becomes less representative for the general microphone is placed in such a gap, the signal it measures becomes less representative of the general microphone is placed in such a gap, the signal it measures becomes less representative for the general noise emitted by the given casing panel and it more represents a specific resonant effect, what may be noise noise emitted emitted byby the the given given casing casing panel panel and andititmor mor eerr epr epresents esents a a specific specific r resonant esonantef ef fect, fect,what which may may be be misleading for the adaptation of the control algorithm. For the evaluated laboratory setup, this is the misleading misleading forfor the the adaptation adaptation of of the thecontr contr ol olalgorithm. algorithm. For Forthe theevaluated evaluated laboratory laboratory setup, setup, this this is the is the case for d ≤ 0.4 m. case for d ≤ 0.4 m. case for d  0.4 m. In Figure 4, the primary paths for the error microphone corresponding to back casing panel in In Figure 4, the primary paths for the err0 or microphone corresponding to back casing panel in In Figure 4, the primary paths for the error microphone corresponding to back casing panel in both setups are presented (locations B and B ). Analogous behavior can be observed as in primary both setups are presented (locations B and B ). Analogous behavior can be observed as in primary both setups are presented (locations B and B ). Analogous behavior can be observed as in primary paths presented for the right error microphone in Figure 3, hence, for the sake of brevity, it is no further paths presented for the right error microphone in Figure 3, hence, for the sake of brevity, it is no further paths presented for the right error microphone in Figure 3, hence, for the sake of brevity, it is no discussed. discussed. further discussed. 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m −10 −10 0.3 m 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m 0.6 m −20 −20 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m −40 0 100 200 300 400 500 −40 0 100 200 300 400 500 0 100 F200 requency (Hz) 300 400 500 0 100 F200 requency (Hz) 300 400 500 Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 3. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 3. The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the right casing panel. Figure 3. The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the right casing panel. primary paths with the error microphone adjacent to the right casing panel. 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m −10 −10 0.3 m 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m 0.6 m −20 −20 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m −40 0 100 200 300 400 500 −40 0 100 200 300 400 500 0 100 F200 requency (Hz) 300 400 500 0 100 F200 requency (Hz) 300 400 500 Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 4. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 4. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 4. The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the back casing panel. primary paths with the error microphone adjacent to the back casing panel. primary paths with the error microphone adjacent to the back casing panel. In Figure 5, the primary paths for the error microphone corresponding to top casing panel in both In Figure 5, the primary paths for the error microphone corresponding to top casing panel in both setups are presented (the location T). The top error microphone placement is the same for both setups, setups are presented (the location T). The top error microphone placement is the same for both setups, and hence, amplitude responses are very similar for them. It confirms consistency of obtained results. and hence, amplitude responses are very similar for them. It confirms consistency of obtained results. Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Appl. Sci. 2019, 9, 1059 7 of 17 In Figure 5, the primary paths for the error microphone corresponding to top casing panel in both setups are presented (the location T). The top error microphone placement is the same for both setups, Appl. Sci. 2019, xx, 5 7 of 17 Appl. Sci. 2019, xx, 5 7 of 17 and hence, amplitude responses are very similar for them. This confirms consistency of obtained results. On the other hand, when the distance d changes, the sound emission pattern in the room On the other hand, when the distance d changes, the sound emission pattern in the room also changes. On the other hand, when the distance d changes, the sound emission pattern in the room also changes. also changes. It is noteworthy that in the i frequency range up to about 125 Hz, an effect of magnitude It is noteworthy that in the frequency range up to about 125 Hz, an effect of magnitude increase for It is noteworthy that in the frequency range up to about 125 Hz, an effect of magnitude increase for increase for decreasing distance d is observed. Above 125 Hz, such effect is not clearly visible. The decreasing distance d is observed. Above 125 Hz, such effect is not clearly visible. The effect observed decreasing distance d is observed. Above 125 Hz, such effect is not clearly visible. The effect observed effect observed below 125 Hz indicates that moving the casing closer to the corner causes slightly below 125 Hz indicates that moving the casing closer to the corner causes slightly stronger emission of below 125 Hz indicates that moving the casing closer to the corner causes slightly stronger emission of stronger emission of low frequencies in the laboratory enclosure, as it could be expected, based on the low frequencies in the laboratory enclosure, as it could be expected, basing on the theory recalled in low frequencies in the laboratory enclosure, as it could be expected, basing on the theory recalled in theory recalled in Section 3.2. Subsection 3.2. Subsection 3.2. The paths between the primary noise source and one of the room microphones are given in The paths between the primary noise source and one of the room microphones are given in The paths between the primary noise source and one of the room microphones are given in Figure 6. The magnitudes are in general lower than the ones obtained for error microphones, as Figure 6. The magnitudes are in general lower than the ones obtained for error microphones, as Figure 6. The magnitudes are in general lower than the ones obtained for error microphones, as the distances from the noise source to the room microphones are larger. Similarly as for the top the distances from the noise source to the room microphones are larger. Similarly as for the top the distances from the noise source to the room microphones are larger. Similarly as for the top error errmicr or micr ophone, ophone, the the paths paths ar ar e econsistent consistent for for both both setups. setups. However However , ,itit isis noteworthy noteworthy that that in in thethe error microphone, the paths are consistent for both setups. However, it is noteworthy that in the frequency frequency range range up up toto about about 125 125 Hz, Hz,aaslight slightef effect fect of of magnitude magnitudeincr incr ease ease for for decr decr easing easing distance distance d is d is i i frequency range up to about 125 Hz, a slight effect of magnitude increase for decreasing distance d is observed again. It confirms that moving the casing closer to the corner causes stronger excitation of observed again. It confirms that moving the casing closer to the corner causes stronger excitation of observed again. It confirms that moving the casing closer to the corner causes stronger excitation of low frequencies in the whole laboratory enclosure, as used for the sound reproducing systems in audio low frequencies in the whole laboratory enclosure, as used for the sound reproducing systems in audio low frequencies in the whole laboratory enclosure, as used for the sound reproducing systems in audio engineering. engineering. engineering. 10 10 10 10 0.1 m 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m 0.3 m −10 −10 −10 −10 0.4 m 0.4 m 0.5 m 0.5 m −20 −20 −20 −20 0.6 m 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m 0.8 m −40 −40 −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 5. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 5. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 5. The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the top casing panel. primary paths with the error microphone adjacent to the top casing panel. primary paths with the error microphone adjacent to the top casing panel. 10 10 10 10 0.1 m 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m 0.3 m −10 −10 −10 −10 0.4 m 0.4 m 0.5 m 0.5 m −20 −20 −20 −20 0.6 m 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m 0.8 m −40 −40 −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 6. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 6. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 6. The amplitude functions of the frequency functions of the impulse response estimates for the paths between one of the room microphones and the primary source for the eight different distances paths between one of the room microphones and the primary source for the eight different distances paths between one of the room microphones and the primary source for the eight different distances between the active casing and the wall. between the active casing and the wall. between the active casing and the wall. 4.2. Secondary Paths Analysis 4.2. Secondary Paths Analysis 4.2. Secondary Paths Analysis The secondary path is a path between the input signal to one of the actuators (exciters) mounted The secondary path is a path between the input signal to one of the actuators (exciters) mounted on The thesecondary inner side of path the is active a path casing betw panels, een the and input the signal signalacquir to one ed ofby the one actuators of the err (exciters) or microphone mounted s. on the inner side of the active casing panels, and the signal acquired by one of the error microphones. Selected secondary paths amplitude responses are presented. on the inner side of the active casing panels, and the signal acquired by one of the error microphones. Selected secondary paths amplitude responses are presented. In Figure 7, secondary paths between selected five actuators (one per casing panel), and the error Selected secondary paths amplitude responses are presented. In Figure 7, secondary paths between selected five actuators (one per casing panel), and the error microphone corresponding to right casing panel are presented. The casing was placed at a distance micr In ophone Figure 7 corr , secondary espondingpaths to right between casing panel the selected are presented. five actuators The casing (one was per placed casing at apanel), distance and d = 0.1 m. It is the smallest considered distance of d , where there are significant differences in paths’ d1 = 0.1 m. It is the smallest considered distance of di , where there are significant differences in paths’ the error microphone corresponding to right casing panel are presented. The casing was placed at 1 i magnitudes, depending on chosen setup (right error microphone placed at location R or R0). In Setup magnitudes, depending on chosen setup (right error microphone placed at location R or R ). In Setup Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Appl. Sci. 2019, 9, 1059 8 of 17 Appl. Sci. 2019, xx, 5 8 of 17 a distance d = 0.1 m. It is the smallest considered distance of d , where there are significant differences Appl. Sci. 2019, xx, 5 8 of 17 1 i in paths’ magnitudes, depending on chosen setup (right error microphone placed at location R or 0 0 0 R ).1 In (location Setup R 1),(location magnitudes R), ar magnitudes e much greater are than much in gr Setup eater 2 (location than in Setup R ). As 2 it (location could be R expected, ). As it the could 1 (location R), magnitudes are much greater than in Setup 2 (location R ). As it could be expected, the actuator mounted to the right panel contributes the most to the signal obtained with the right error be expected, the actuator mounted to the right panel contributes the most to the signal obtained actuator mounted to the right panel contributes the most to the signal obtained with the right error microphone when placed at location R. However, other secondary paths are also stronger when the with the right error microphone when placed at location R. However, other secondary paths are also microphone when placed at location R. However, other secondary paths are also stronger when the error microphone is placed at location R (Setup 1) comparing to location R (Setup 2). It means that stronger when the error microphone is placed at location R (Setup 1) compar0 ed to location R (Setup 2). error microphone is placed at location R (Setup 1) comparing to location R (Setup 2). It means that the narrow gap between the casing panel and the corner wall causes a resonance, amplifying sound This means that the narrow gap between the casing panel and the corner wall causes a resonance, the narrow gap between the casing panel and the corner wall causes a resonance, amplifying sound generated by any actuator, mounted to any of the casing panels. amplifying sound generated by any actuator, mounted to any of the casing panels. generated by any actuator, mounted to any of the casing panels. 10 10 10 10 Front Front Right 0 0 Right 0 0 Back Back −10 −10 Left −10 −10 Left Top −20 −20 Top −20 −20 −30 −30 −30 −30 −40 −40 −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 7. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 7. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 7. The amplitude functions of the frequency functions of the impulse response estimates for the secondary paths between each casing panel’s selected actuator and the error microphone adjacent to secondary paths between each casing panel’s selected actuator and the error microphone adjacent to secondary paths between each casing panel’s selected actuator and the error microphone adjacent to the right casing panel, at a distance 0.1 m, in both setups. the the right right casing casing panel, panel, atat a distance a distance of 0.1 0.1 m, m, inin both both setups. setups. In Figure 8, secondary paths between the selected actuator mounted to the right panel and the In Figure 8, secondary paths between the selected actuator mounted to the right panel and the In Figure 8, secondary paths between the selected actuator mounted to the right panel and the right error microphone are presented for all distances d . Magnitudes are in general greater in Setup right error microphone are presented for all distances d . Magnitudes are in general greater in Setup right error microphone are presented for all distances d .i Magnitudes are in general greater in Setup 1 1 (Figure 8a), especially when d ≤ 0.4 m. In nearly whole considered frequency range magnitude 1 (Figure 8a), especially when d ≤ 0.4 m. In nearly whole considered frequency range magnitude (Figure 8a), especially when d  0.4 m. In nearly the whole considered frequency range, magnitude increases as the distance d decreases. In Setup 2 (Figure 8b) such effect is not visible. increases as the distance d decreases. In Setup 2 (Figure 8b) such effect is not visible. increases as the distance d decreases. In Setup 2 (Figure 8b) such effect is not visible. 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m 0.3 m −10 −10 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m −20 −20 0.6 m 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 8. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 8. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 8. The amplitude functions of the frequency functions of the impulse response estimates for the secondary paths between right casing panel’s selected actuator and the error microphone adjacent to secondary paths between right casing panel’s selected actuator and the error microphone adjacent to secondary the rightpaths casing between panel, atright all distances, casing panel’s in both selected setups. actuator and the error microphone adjacent to the right casing panel, at all distances, in both setups. the right casing panel, at all distances, in both setups. Similar observations can be drawn from Figure 9, which presents responses of secondary paths Similar observations can be drawn from Figure 9, which presents responses of secondary paths between back casing panel’s selected actuator and the back error microphone at all distances. In Setup Similar observations can be drawn from Figure 9, which presents responses of secondary paths between back casing panel’s selected actuator and the back error microphone at all distances. In Setup 1 magnitude increases as the distance d decreases. On the other hand, in Setup 2 such effect is also between back casing panel’s selected actuator and the back error microphone at all distances. In 1 magnitude increases as the distance d decreases. On the other hand, in Setup 2 such effect is also visible, but only in a frequency range up to about 200 Hz. It shows that the narrow gap amplifies most Setup 1 magnitude increases as the distance d decreases. On the other hand, in Setup 2 such effect visible, but only in a frequency range up to about 200 Hz. It shows that the narrow gap amplifies most of the considered frequencies if a microphone is placed in the gap (location B). However, the actual is also visible, but only in a frequency range up to about 200 Hz. This shows that the narrow gap of the considered frequencies if a microphone is placed in the gap (location B). However, the actual emission (sound field excitation in the laboratory enclosure) can be slightly enhanced, due to casing amplifies most of the considered frequencies if a microphone is placed in the gap (location B). However, emission (sound field excitation in the laboratory enclosure) can be slightly enhanced, due to casing placement in the corner, rather only in a limited range of low frequencies (as the measurement at theplacement actual emission in the (sound corner, rather field excitation only in a in limited the laboratory range of low enclosur frequencies e) can be (asslightly the measur enhanced, ement at due location B shows). to casing location placement B shows).in the corner, only in a limited range of low frequencies (as the measurement at location B shows). Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Appl. Sci. 2019, xx, 5 9 of 17 10 10 0.1 m 0.2 m 0 0 0.3 m −10 −10 0.4 m 0.5 m −20 −20 0.6 m Appl. Sci. 2019, xx, 5 9 of 17 −30 −30 Appl. Sci. 2019, 9, 1059 0.7 m9 of 17 0.8 m −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 10 10 Frequency (Hz) Frequency (Hz) 0.1 m (a) Setup 1. (b) Setup 2. 0.2 m 0 0 Figure 9. The amplitude functions of the frequency functions of the impulse response estimates for the 0.3 m −10 −10 secondary paths between back casing panel’s selected actuator and the error microphone adjacent0.4 to m the back casing panel, at all distances, in both setups. 0.5 m −20 −20 0.6 m −30 In Figure 10, secondary paths between top−30 casing panel’s selected actuator and the top error 0.7 m microphone are presented at all distances. Amplitude responses for both setups (Figure 10a, Figur 0.8 e m 10b) −40 −40 are similar, confirming the consistency of obtained results. Similarly as for the back microphone placed 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) at location B , slight enhancement of magnitude for low frequency range up to approximately 180 Hz (a) Setup 1. (b) Setup 2. can be observed when the distance d decreases. Figure 9. The amplitude functions of the frequency functions of the impulse response estimates for the In Figures 11 and 12, the paths between selected actuators and one of the room microphones are Figure 9. The amplitude functions of the frequency functions of the impulse response estimates for the secondary paths between back casing panel’s selected actuator and the error microphone adjacent to presented. The room microphones are in constant locations during all experiments. The paths are secondary paths between back casing panel’s selected actuator and the error microphone adjacent to the back casing panel, at all distances, in both setups. compared in the same manner as before. In Figures 11 and 12, the selected actuators are mounted to the back casing panel, at all distances, in both setups. back and right casing panel, respectively. Once again, the magnitude increases for decreasing distance In Figure 10, secondary paths between top casing panel’s selected actuator and the top error d in a frequency range up to approximately 200 Hz. These paths also confirm, that placing the casing In Figure 10, secondary paths between top casing panel’s selected actuator and the top error microphone are presented at all distances. Amplitude responses for both setups (Figure 10a, Figure 10b) in a corner increases the magnitude of paths in the low frequency range (these frequencies are better microphone are presented at all distances. Amplitude responses for both setups (Figure 10a,b) are are similar, confirming the consistency of obtained results. Similarly as for the back microphone placed excited in the enclosure). However, it is also noteworthy that both primary and secondary paths’ similar, confirming 0 the consistency of obtained results. Similarly as for the back microphone placed at at location B , slight enhancement of magnitude for low frequency range up to approximately 180 Hz magnitudes 0 increase in similar manner, hence the balance between them should be sustained and the location B , slight enhancement of magnitude for low frequency range up to approximately 180 Hz can can be observed when the distance d decreases. noise reduction capabilities should not be impeded. be observed when the distance d decreases. In Figures 11 and 12, the paths i between selected actuators and one of the room microphones are presented. The room microphones are in constant locations during all experiments. The paths are 10 10 compared in the same manner as before. In Figures 11 and 12, the selected actuators are mounted to 0.1 m back and right casing panel, respectively. Once again, the magnitude increases for decreasing distance 0.2 m 0 0 0.3 m d in a frequency range up to approximately 200 Hz. These paths also confirm, that placing the casing −10 −10 0.4 m in a corner increases the magnitude of paths in the low frequency range (these frequencies are better 0.5 m excited −20 in the enclosure). However, it is also noteworthy −20 that both primary and secondary paths’ 0.6 m magnitudes increase in similar manner, hence the balance between them should be sustained and the −30 −30 0.7 m noise reduction capabilities should not be impeded. 0.8 m −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 10 10 Frequency (Hz) Frequency (Hz) 0.1 m (a) Setup 1. (b) Setup 2. 0.2 m 0 0 Figure 10. The amplitude functions of the frequency functions of the impulse response estimates for 0.3 m Figure 10. The amplitude functions of the frequency functions of the impulse response estimates for −10 −10 the secondary paths between top casing panel’s selected actuator and the error microphone adjacent to 0.4 m the secondary paths between top casing panel’s selected actuator and the error microphone adjacent to the top casing panel, at all distances, in both setups. 0.5 m −20 −20 the top casing panel, at all distances, in both setups. 0.6 m −30 −30 0.7 m In Figures 11 and 12, the paths between selected actuators and one of the room microphones are 0.8 m −40 −40 presented. The room microphones are in constant locations during all experiments. The paths are 0 100 200 300 400 500 0 100 200 300 400 500 compared in the same manner as before. In Figures 11 and 12, the selected actuators are mounted Frequency (Hz) Frequency (Hz) to the back and right(a) casing Setup 1. panel, respectively. Once again, the magnitu (b) Setup d 2.e increases for decreasing distance Figure d in 10. a frThe equency amplitude range functions up to of appr theoximatel frequencyyfunctions 200 Hz.of These the impulse pathsralso esponse confirm, estimates that forplacing the secondary paths between top casing panel’s selected actuator and the error microphone adjacent to the casing in a corner increases the magnitude of paths in the low frequency range (these frequencies the top casing panel, at all distances, in both setups. are better excited in the enclosure). However, it is also noteworthy that both primary and secondary paths’ magnitudes increase in a similar manner, hence the balance between them should be sustained and the noise reduction capabilities should not be impeded. Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Appl. Sci. 2019, xx, 5 10 of 17 Appl. Sci. 2019, 9, 1059 10 of 17 Appl. Sci. 2019, xx, 5 10 of 17 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0.3 m 0 0 −10 −10 0.3 m 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m 0.6 m −20 −20 −30 −30 0.6 m 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m 0 100 200 300 400 500 0 100 200 300 400 500 −40 −40 Frequency (Hz) Frequency (Hz) 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 11. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 11. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 11. The amplitude functions of the frequency functions of the impulse response estimates for the paths between back casing panel’s selected actuator and one of the room microphones, at all distances, paths between back casing panel’s selected actuator and one of the room microphones, at all distances, paths between back casing panel’s selected actuator and one of the room microphones, at all distances, in both setups. in both setups. in both setups. 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m −10 −10 0.3 m 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m 0.6 m −20 −20 −30 −30 0.6 m 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m 0 100 200 300 400 500 0 100 200 300 400 500 −40 −40 Frequency (Hz) Frequency (Hz) 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 12. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 12. The amplitude functions of the frequency functions of the impulse response estimates for the paths between right casing panel’s selected actuator and one of the room microphones, at all distances, Figure 12. The amplitude functions of the frequency functions of the impulse response estimates for the paths between right casing panel’s selected actuator and one of the room microphones, at all distances, in both setups. paths between right casing panel’s selected actuator and one of the room microphones, at all distances, in both setups. in both setups. 5. Active control algorithm 5. Active control algorithm 5. Active In Control the activeAlgorithm control systems, the FxLMS algorithm is frequently implemented [20,25]. Its advantages In the active control systems, the FxLMS algorithm is frequently implemented [20,25]. Its advantages are, e.g., simplicity of implementation, robustness and low complexity of computations [21]. A scheme In the active control systems, the FxLMS algorithm is frequently implemented [20,21]. Its advantages are, e.g., simplicity of implementation, robustness and low complexity of computations [21]. A scheme of basic FxLMS algorithm is presented in Figure 13, where P(z) is the primary path, S(z) is the are, e.g., simplicity of implementation, robustness and low complexity of computations [22]. A scheme of basic FxLMS algorithm is presented in Figure 13, where P(z) is the primary ˆpath, S(z) is the secondary path, W(z) is a control filter adapted by the LMS algorithm, and S(z) is a model of of basic FxLMS algorithm is presented in Figure 13, where P(z) is the primary ˆ path, S(z) is the secondary path, W(z) is a control filter adapted by the LMS algorithm, and S(z) is a model of secondary path S(z). The algorithm name FxLMS (Filtered-x Least Mean Squares) follows from usage secondary path, W(z) is a control filter adapted by the LMS algorithm, and S(z) is a model of secondary secondary ˆ path S(z). The algorithm name FxLMS (Filtered-x Least Mean Squares) follows from usage of S(z) model — the reference signal usually noted as x(n) is passed through the secondary path path S(z). The algorithm name FxLMS (Filtered-x Least Mean Squares) follows from usage of S(z) of S(z) model ˆ — the reference signal usually noted as x(n) is passed through the secondary path estimate S(z) to obtain a filtered reference signal r(n) [2]. It is also passed through the primary path ˆ ˆ model—the estimate Sr( efer z) to ence obtain signal a filter usually ed refer noted ence as signal x(n)ris (npasse ) [2]. It d thr is also ough passed the secondary through the path primary estimate path S(z) P(z), which outputs signal d(n) — the primary disturbance. Adaptive filter output u(n) is passed P(z), which outputs signal d(n) — the primary disturbance. Adaptive filter output u(n) is passed to obtain a filtered reference signal r(n) [2]. It is also passed through the primary path P(z), which through secondary path S(z) to obtain a signal that is summed with the primary disturbance d(n). through secondary path S(z) to obtain a signal that is summed with the primary disturbance d(n). outputs The summation signal d(n) r—the esultsprimary in signaldisturbance. e(n), which isAdaptive a residualfilter error output signal.uThe (n) contr is passed ol system through attempts secondary to The summation results in signal e(n), which is a residual error signal. The control system attempts to path minimize S(z) to obtain the sum a of signal squar that es of isthe summed error signal with e the (n)primary over thedisturbanc length of filter e d(n W)( . z The ). summation results minimize the sum of squares of the error signal e(n) over the length of filter W(z). in signal e(n), which is a residual error signal. The control system attempts to minimize the sum of x(n) d(n) e(n) squares of the error signal e(n) over the length of filter W(z)+ . P(z) x(n) d(n) e(n) P(z) x(n) d(n) − e(n) u(n) P(z) W(z) S(z) u(n) W(z) S(z) u(n) r(n) W(z) S(z) S(z) LMS r(n) S(z) LMS Figure 13. The scheme of the FxLMS algorithm [2]. r(n) Figure 13. The scheme of the FxLMS algorithm [2]. S(z) LMS Figure 13. The scheme of the FxLMS algorithm [2]. Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Appl. Sci. 2019, 9, 1059 11 of 17 The scheme presented in Figure 13 depicts a single-channel control system, however, if the plant is controlled by multiple inputs and returns multiple outputs, the control system can be generalized to a Multiple-Input Multiple-Output (MIMO) FxLMS, as described in [23], and such is used for this research. However, this paper is focused more on the investigation of the control system performance for specific configurations, rather than on introducing the control algorithm itself. Hence, the reader is referred to previous publications, where a more detailed description of the control system with a switched-error modification employed for the active casing is given [12,24]. It is noteworthy that varying the selected control algorithm may impact active control performance, e.g., the convergence rate or the final noise reduction levels. However, the preliminary experiments have shown that such an impact is similar for all evaluated experimental setups (it is independent of the particular configuration). Hence, it has been assumed that by employing the unchanged control algorithm through the whole research, the drawn conclusions also remain valid for altered or different control algorithms. 6. Active Control System Performance In this section, experimental evaluation of the investigated active control system is presented. The loudspeaker placed inside the active casing generates a tonal primary noise of frequency incremented by 5 Hz in the range from 1 Hz to 350 Hz. The considered frequency range includes the low frequencies where the speaker starts to transmit sound. To achieve the goal of global noise reduction, instantaneous square values of error signals are minimized by feedforward adaptive control system (introduced in the previous Section), controlling together 21 inertial actuators. The error signals are obtained by the error microphones (their arrangement is discussed in Section 3.3). The control performance is evaluated as noise reduction levels observed by the room microphones. Performance of the control system is tested in multiple configurations, including a range of distances from the corner d and different error microphones’ arrangement (Setup 1 or Setup 2). For each frequency of the primary disturbance, a 60 s experiment was performed. In its initial 5 s, the active control was off, and variance of signals acquired by different sensors was estimated as the reference point. Then, the active control was turned on. When the adaptive control algorithm converged, the final 5 s of the experiment were used to estimate the variance of signals acquired by corresponding sensors. In Figures 14 and 15, frequency characteristics for the active control experiments are presented. Time plots of signals obtained by individual sensors are not shown in this paper, as such insight into the control system behavior has been previously presented, e.g., in [12]. In the previous experiments, the active casing was placed distant from the enclosure walls and several control approaches were examined and described, e.g., in [12,14]. In the previous research, the maximum global noise reduction evaluated by mean noise reduction measured at all room microphones exceeded 15 dB. In this research, even higher performance has been achieved and the maximum global noise reduction level often exceeded even 25 dB, although these results rely on the specific circumstances of the experimental settings, which evolved over time. Hence, such direct comparison of noise reduction levels obtained for different settings is unjustified. However, that is not the aim of this research. The purpose of this paper is to evaluate the overall control performance of the active casing placed in a corner. Hence, the main point of investigation is the mean global noise reduction affected solely by the distance d and the error microphone arrangement (Setup 1 or Setup 2). The other experimental settings remained unchanged. Appl. Sci. 2019, xx, 5 12 of 17 Appl. Sci. 2019, 9, 1059 12 of 17 Control off - mean values Control on - Setup 1 Control off - Setup 1 Control on - Setup 2 Control off - Setup 2 50 50 40 40 30 30 20 20 10 10 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (a) Distance d = 0.1 m. (e) Distance d = 0.5 m. 1 5 50 50 40 40 30 30 20 20 10 10 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (b) Distance d = 0.2 m. (f) Distance d = 0.6 m. 2 6 50 50 40 40 30 30 20 20 10 10 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (c) Distance d = 0.3 m. (g) Distance d = 0.7 m. 3 7 50 50 40 40 30 30 20 20 10 10 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (d) Distance d = 0.4 m. (h) Distance d = 0.8 m. 4 8 Figure 14. The average variance of the room microphone signals for each of the primary noise tones in the range 1 Hz to 350 Hz with a step of 5 Hz, with and without active control, for both Setup 1 and Figure 14. The average variance of the room microphone signals for each of the primary noise tones in Setup 2. the range 1 Hz to 350 Hz with a step of 5 Hz, with and without active control, for both Setup 1 and Setup 2. Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Appl. Sci. 2019, xx, 5 13 of 17 Appl. Sci. 2019, 9, 1059 13 of 17 Control on - Setup 1 Control on - Setup 2 40 40 30 30 20 20 10 10 0 0 −10 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (a) Distance d = 0.1 m. (e) Distance d = 0.5 m. 1 5 40 40 30 30 20 20 10 10 0 0 −10 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (b) Distance d = 0.2 m. (f) Distance d = 0.6 m. 2 6 40 40 30 30 20 20 10 10 0 0 −10 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (c) Distance d = 0.3 m. (g) Distance d = 0.7 m. 3 7 40 40 30 30 20 20 10 10 0 0 −10 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (d) Distance d = 0.4 m. (h) Distance d = 0.8 m. 4 8 Figure 15. The averaged noise reduction for the noise sensed by the room microphones for each of the primary noise tones in the range 1 Hz to 350 Hz with a step of 5 Hz, for both Setup 1 and Setup 2. Figure 15. The averaged noise reduction for the noise sensed by the room microphones for each of the In Figure 14, the mean variance estimated based on the room microphones measurements is given primary noise tones in the range 1 Hz to 350 Hz with a step of 5 Hz, for both Setup 1 and Setup 2. for different distances d , ranging from 0.1 m to 0.8 m. For each distance d a plot is given, where i i In Figure 14, the mean variance estimated based on the room microphones measurements is given for different distances d , ranging from 0.1 m to 0.8 m. For each distance d a plot is given, where i i black color represents primary noise without active control; red and blue colors represent residual Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Appl. Sci. 2019, 9, 1059 14 of 17 Appl. Sci. 2019, xx, 5 14 of 17 noise when active reduction is turned on with error microphones arranged in Setup 1 and Setup 2, respectively. To facilitate the comparison of control performance obtained for different configurations, black color represents primary noise without active control; red and blue colors represent residual in Figure 15 the noise reduction characteristics are also given, calculated as a difference between noise noise when active reduction is turned on with error microphones arranged in Setup 1 and Setup 2, level without and with control (reduction for Setup 1 and Setup 2 is marked with red or blue color, respectively. To facilitate the comparison of control performance obtained for different configurations, respectively). in Figure 15 the noise reduction characteristics are also given, calculated as a difference between noise It follows from the analysis of Figures 14 and 15 that the error microphone arrangement affects level without and with control (reduction for Setup 1 and Setup 2 is marked with red or blue color, strongly the overall performance of the control system. The major conclusion is that when the active respectively). casing is distant from the corner, the Setup 1 with error microphones surrounding the casing performs It follows from the analysis of Figures 14-15 that the error microphones arrangement affects better than the Setup 2, where error microphones are moved away from the corner. On the other strongly the overall performance of the control system. The major conclusion is that when the active hand, casing when is the distant active from casing the corner is placed , the Setup close1to with the err walls or micr in the ophones corner surr (dounding = 0.1 m), theitcasing is the performs other way better than the Setup 2, where error microphones are moved away from the corner. On the other around—Setup 2 provides substantially better results. This leads to a conclusion that when the casing hand, when the active casing is placed close to the walls in the corner (d = 0.1 m), it is the other approaches the corner, there is a threshold distance when it is beneficial to move 1 the error microphones way around — the Setup 2 provides substantially better results. It leads to a conclusion that when out from the gap between the casing and the corner, and place them on the other side of the casing, the casing approaches the corner, there is a threshold distance when it is beneficial to move the error complementing the error microphones there. For the studied setup the threshold distance seems to be microphones out from the gap between the casing and the corner, and place them on the other side of d = 0.4 m, although, the general conclusion is to expect such threshold value. the casing, complementing the error microphones there. For the studied setup the threshold distance Moreover, it is worth mentioning that when the active casing is placed close to the walls in the seems to be d = 0.4 m, although, the general conclusion is to expect such threshold value. corner (d = 0.1 m), the error microphones placed in the gap at locations R and B in Setup 1 actually Moreover, it is worth mentioning that when the active casing is placed close to the walls in the impede the correct adaptation of the control system. Even unplugging them, leaving only three corner (d = 0.1 m), the error microphones placed in the gap at locations R and B in Setup 1 actually error microphones operating, improves the control performance, as shown in Figure 16 (the specific impede the correct adaptation of the control system. Even unplugging them, leaving only three configuration with disabled R and B error microphones is marked with green color). It is important error microphones operating, improves the control performance, as shown in Figure 16 (the specific to keep this conclusion in mind, when an obstacle with reflecting surface is in the proximity of an configuration with disabled R and B error microphones is marked with green color). It is important to active casing, as such location between the casing and the obstacle may be disadvantageous for keep this conclusion in mind, when an obstacle with reflecting surface is in proximity of an active casing, error microphones. as such location between the casing and the obstacle may be disadvantageous for error microphones. Control off - mean values Control on - Setup 1 Control off - Setup 1 Control on - disabled R and B error mic. Control off - Setup 2 Control on - Setup 2 50 40 40 30 30 20 20 10 10 0 0 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (a) (b) Figure 16. (a) The average variance of the room microphone signals for each of the primary noise Figure 16. (a) The average variance of the room microphone signals for each of the primary noise tones with and without active control and (b) the averaged noise reduction for the noise sensed by the tones with and without active control and (b) the averaged noise reduction for the noise sensed by the room microphones for each of the primary noise tones. For Setup 1, Setup 2 and Setup 1 with the error room microphones for each of the primary noise tones. For Setup 1, Setup 2 and Setup 1 with the error microphones B and R disabled, d = 0.1 m. microphones B and R disabled, d = 0.1 m. Another conclusion follows from a comparison of control performance for the casing placed at Another conclusion follows from a comparison of control performance for the casing placed at the distance d = 0.1 m in Setup 2, and placed at the distance d = 0.8 m in Setup 1. Both of these two the distance d = 0.1 m in Setup 2, and placed at the distance d = 0.8 m in Setup 1. Both of these two 1 8 opposite scenarios provide very satisfying performance, reaching very high mean reduction levels. opposite scenarios provide very satisfying performance, reaching very high mean reduction levels. However, the reduction levels observed for the casing placed in the corner are higher and over a wider However, the reduction levels observed for the casing placed in the corner are higher and are over a frequency band. Although the difference is not high, it is clearly visible and leads to a conclusion that wider frequency band. Although the difference is not high, it is clearly visible and leads to a conclusion placing the active casing in a corner can be beneficial comparing to be placed at locations distant from that placing the active casing in a corner can be beneficial compared to being placed at locations distant enclosure walls. At least, such configuration, if technically feasible, should provide results of the same from quality enclosur . Mor eeover walls. , itAt follows least,frsuch om the configuration, research that such if technically configuration, feasible, which should for many provide applications resultsisof the same quality. Moreover, it follows from the research that such configuration, which for many Variance of microphone signals (dB) Noise reduction (dB) Appl. Sci. 2019, 9, 1059 15 of 17 Appl. Sci. 2019, xx, 5 15 of 17 applications is more realistic, is not less efficient. These conclusions are some of the major contributions of this paper, as such configuration of the active casing has not yet been evaluated. more realistic, is not less efficient. These conclusions are some of the major contributions of this paper, In addition, one more test has been done to check how much the actuators mounted to the casing as such configuration of the active casing has not yet been evaluated. panels facing the corner contribute to the overall noise reduction. Hence, in addition to secondary In addition, one more test has been done to check how much the actuators mounted to the casing paths panels investigation, facing theacorner control contribute experiment to the hasoverall been performed noise reduction. with speci Hence, fic actuators in addition disabled. to secondary Firstly, paths investigation, a control experiment has been performed with specific actuators disabled. Firstly, the actuators mounted to the left and front panels were disabled. Then, the actuators mounted to the the actuators mounted to the left and front panels were disabled. Then, the actuators mounted to right and back panels were disabled. Obtained results compared with results for all actuators operating the right and back panels were disabled. Obtained results compared with results for all actuators are shown in Figure 17. What is interesting is that no significant difference can be noticed between operating are shown in Figure 17. What is interesting, no significant difference can be noticed between disabling front and left panels, or back and right panels (the same number of actuators were operating). disabling front and left panels, or back and right panels (the same number of actuators were operating). This proves that the actuators actually excite the whole casing with such efficiency that even placing It proves that the actuators excite actually whole casing with such efficiency that even placing them at them at panels facing the corner is equally beneficial as placing them at panels facing the enclosure panels facing the corner is equally beneficial as placing them at panels facing the enclosure interior. interior. This can be explained by very strong coupling between casing panels, which was studied This can be explained by very strong coupling between casing panels, what was studied in details in detail in [12]. It is also noteworthy that disabling eight of 21 actuators did not affect heavily the in [11]. It is also noteworthy that disabling 8 of 21 actuators did not affect heavily the overall noise overall noise reduction by the active casing. In the lower frequency range, where the inertial actuators reduction by the active casing. In the lower frequency range, where the inertial actuators lack efficiency, lack efficiency, the superiority of using more actuators is visible (lesser number of actuators lacks the superiority of using more actuators is visible (lesser number of actuators lacks power to control the power to control the lowest frequencies). However, for frequencies above approximately 100 Hz, very lowest frequencies). However, for frequencies above approximately 100 Hz, very comparable results comparable results have been obtained for all evaluated configurations (with all actuators operating, have been obtained for all evaluated configurations (with all actuators operating, and some of them and some of them disabled). This shows a robustness of the proposed active noise reducing casing. disabled). It shows a robustness of the proposed active noise reducing casing. Control off - mean values Control on - Setup 2 Control off - Setup 1 Control on - Setup 2; dis. left and front panels Control off - Setup 2 Control on - Setup 2; dis. right and back panels 50 40 40 30 30 20 20 10 10 0 0 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (a) (b) Figure 17. (a) The average variance of the room microphone signals for each of the primary noise tones Figure 17. (a) The average variance of the room microphone signals for each of the primary noise tones with and without active control and (b) the averaged noise reduction for the noise sensed by the room with and without active control and (b) the averaged noise reduction for the noise sensed by the room microphones for each of the primary noise tones. Observe, only active control with Setup 2, Setup 2 microphones for each of the primary noise tones. Observe, only active control with Setup 2, Setup 2 with the actuators on the left and the front panel disabled and Setup 2 with the actuators on the right with the actuators on the left and the front panel disabled and Setup 2 with the actuators on the right and the back panel disable, d = 0.1 m. and the back panel disable, d = 0.1 m. 7. Conclusions 7. Conclusions The active casing approach has been proven in previous research of the authors to provide The active casing approach has been proven in previous research of the authors to provide significant global noise reduction. However, the active casing was placed distant from the enclosure significant global noise reduction. However, the active casing was placed at a distance from the walls. In this paper, the active casing was located in a corner and such placement is intentionally used enclosure walls. In this paper, the active casing was located in a corner and such placement is to facilitate the active control system operation. On the other hand, such arrangement is common for intentionally used to facilitate the active control system operation. On the other hand, such arrangement many applications. Extensive active control experiments were carried out and a thorough study on is common for many applications. Extensive active control experiments were carried out and control system performance was presented, what is the main contribution of this paper. In the opinion a thor of ough the authors, studyth on e pr contr esented ol system researchperformance confirms the hypothesis was presented, that placing which the isactive the main casing contribution in a corner and appropriately rearranging the microphones can lead to both enhanced noise reduction levels and of this paper. In the opinion of the authors, the presented research confirms the hypothesis that placing a wider frequency range of global noise reduction. The analysis of both primary and secondary paths the active casing in a corner and appropriately rearranging the microphones can lead to both enhanced was also given as an additional insight into the investigated plant. noise reduction levels and a wider frequency range of global noise reduction. The analysis of both primary and secondary paths was also given as an additional insight into the investigated plant. Variance of microphone signals (dB) Noise reduction (dB) Appl. Sci. 2019, 9, 1059 16 of 17 The following conclusions can be drawn from the presented results. When the active casing approaches the corner, there is a threshold distance when it is beneficial to move the error microphones out from the gap between the casing and the corner, and place them on the other side of the casing, supporting the error microphones there (change from the Setup 1 to Setup 2). Then, the distance between the error microphones becomes smaller and the frequency range, in which acoustic emission is properly observable, becomes greater [25]. This results in higher mean reduction levels and in a wider frequency band, where the global noise reduction is achieved. For better representation of this behavior, let us assume that the noise source is surrounded by a sphere, at which a limited number of error microphones are placed. The effectiveness of the global noise reduction is limited in the frequency range by the distance between the error microphones—it should be smaller than the wavelength of noise to avoid spatial aliasing and to provide a proper observability of the emitted noise. In the previous research, when the active casing was distant from the enclosure walls, the introduced sphere was actually limited to a hemisphere, as the casing was placed on the floor. However, when the active casing is placed in a corner, the hemisphere is further reduced to approximately one-eighth of the sphere. Therefore, the remaining spherical surface which has to be covered with error microphones is smaller, hence the same number of microphones can be more densely distributed. This leads to smaller distances between error microphones, facilitating the operation of the active control system. Besides this major conclusion, two more observations are worth emphasizing. Firstly, an error microphone placed in a narrow gap between the casing and a sound-reflecting obstacle may not only be useless, but it may even impede the adaptation of the control system. Secondly, if the cross couplings between casing panels are strong, placing the actuators at panels facing the corner walls is as beneficial as placing them at panels facing the interior of the enclosure. This may be important when actuators placement is decided, and the surface available for actuators can be limited due to the device occupying most of the space inside the casing. This research also shows that placing the casing at the corner does not limit the performance in terms of globally reducing noise generated by the enclosed source. The authors believe that the presented research provides more insight into the operations of the active casing and helps to extend the applicability of the proposed active casing approach, as an efficient way to reduce noise generated by devices. Author Contributions: Conceptualization, A.C., S.W. and M.P.; methodology, A.C. and S.W.; software, S.W. and K.M.; validation, A.C., S.W., J.R., K.M. and M.P.; formal analysis, A.C. and S.W.; investigation, A.C. and S.W.; resources, A.C., S.W., J.R., K.M. and M.P.; data curation, A.C. and S.W.; writing–original draft preparation, A.C.; writing–review and editing, A.C., S.W., J.R., K.M. and M.P.; visualization, A.C. and S.W.; supervision, M.P.; funding acquisition, M.P.; project administration, M.P. Funding: The research reported in this paper has been supported by the National Science Centre, Poland, decision no. DEC-2017/25/B/ST7/02236. Acknowledgments: The authors are indebted to two anonymous reviewers for their precious comments and suggestions, which helped improve the paper. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. References 1. Alimohammadi, I.; Ebrahimi, H. Comparison Between Effects of Low and High Frequency Noise on Mental Performance. Appl. Acoust. 2017, 126, 131–135. [CrossRef] 2. Kuo, S.M.; Morgan, D. Active Noise Control Systems: Algorithms and DSP Implementations; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 1996; pp. 1–3. 3. Elliott, S.J.; Cheer, J.; Bhan, L.; Shi, C.; Gan, W. A Wavenumber Approach to Analysing the Active Control of Plane Waves with Arrays of Secondary Sources. J. Sound Vib. 2018, 419, 405–419. [CrossRef] Appl. Sci. 2019, 9, 1059 17 of 17 4. Antoñanzas, C.; Ferrer, M.; de Diego, M.; Gonzalez, A. Blockwise Frequency Domain Active Noise Controller over Distributed Networks. Appl. Sci. 2016, 6, 124. [CrossRef] 5. Wrona, S.; Pawelczyk, M. Active Reduction of Device Narrowband Noise by Controlling Vibration of Its Casing Based on Structural Sensors. In Proceedings of the 22nd International Congress on Sound and Vibration, Florence, Italy, 12–16 July 2015; pp. 1–8. 6. Loiseau, P.; Chevrel, P.; Yagoubi, M.; Duffal, J. Robust Active Noise Control in a Car Cabin: Evaluation of Achievable Performances with a Feedback Control Scheme. Control Eng. Pract. 2018, 81, 172–182. [CrossRef] 7. Murao, T.; Shi, C.; Gan, W.; Nishimura, M. Mixed-Error Approach for Multi-Channel Active Noise Control of Open Windows. Appl. Acoust. 2017, 127, 305–315. [CrossRef] 8. Lam, B.; Shi, C.; Shi, D.; Gan, W. Active Control of Sound Through Full-Sized Open Windows. Build. Environ. 2018, 141, 16–27. [CrossRef] 9. Fahy, F.J.; Gardonio, P. Sound and Structural Vibration: Radiation, Transmission and Response; Academic Press: Cambridge, MA, USA, 2007; pp. 521–523. 10. Mao, Q.; Pietrzko, S. Control of Noise and Structural Vibration; Springer: London, UK, 2013; pp. 3–4. 11. Pietrzko, S. Contributions to Noise and Vibration Control Technology; AGH University of Science and Technology: Cracow, Poland, 2009. 12. Wrona, S.; Pawelczyk, M. Feedforward Control of a Light-Weight Device Casing for Active Noise Reduction. Arch. Acoust. 2016, 41, 499–505. [CrossRef] 13. Mazur, K.; Wrona, S.; Pawelczyk, M. Design and Implementation of Multichannel Global Active Structural Acoustic Control for a Device Casing. Mech. Syst. Signal Process. 2018, 98, 877–889. [CrossRef] 14. Mazur, K.; Pawelczyk, M. Internal Model Control for a Light-Weight Active Noise-Reducing Casing. Arch. Acoust. 2016, 41, 315–322. [CrossRef] 15. Wrona, S.; Pawelczyk, M. Optimal Placement of Actuators for Active Structural Acoustic Control of a Light-Weight Device Casing. In Proceedings of the 23rd International Congress on Sound and Vibration, Athens, Greece, 10–14 July 2016; pp. 1–8. 16. Wiora, J.; Wrona, S.; Pawelczyk, M. Evaluation of Measurement Value and Uncertainty of Sound Pressure Level Difference Obtained by Active Device Noise Reduction. Measurement 2017, 96, 67–75. [CrossRef] 17. Chraponska, A.; Wrona, S.; Rzepecki, J.; Mazur, K.; Pawelczyk, M. Secondary Paths Analysis of an Active Casing Placed at a Wall. In Proceedings of the 2018 Joint Conference-Acoustics, Ustka, Poland, 11–14 September 2018; pp. 48–52. 18. Kuttruff, H. Room Acoustics; Spon Press: New York, NY, USA, 2009; pp. 35–42. 19. Long, M. Architectural Acoustics; Elsevier Academic Press: New York, NY, USA, 2006; p. 615. 20. Bismor, D.; Czyz, K.; Ogonowski, Z. Review and Comparison of Variable Step-Size LMS Algorithms. Int. J. Acoust. Vib. 2016, 21, 24–39. [CrossRef] 21. Nelson, P.A.; Elliott, S.J. Active Control of Sound; Academic Press: Cambridge, MA, USA, 1992. 22. Barkefors, A.; Sternad, M.; Brännmark, L. Design and Analysis of Linear Quadratic Gaussian Feedforward Controllers for Active Noise Control. IEEE/ACM Trans. Audio Speech Lang. Process. 2014, 22, 1777–1791. [CrossRef] 23. Elliott, S.; Stothers, I.; Nelson, P. A Multiple Error LMS Algorithm and Its Application to the Active Control of Sound and Vibration. IEEE Trans. Acoust. Speech Signal Process. 1987, 35, 1423–1434. [CrossRef] 24. Wrona, S.; Mazur, K.; Pawelczyk, M. Internal Model Control of a Washing Machine Casing for Active Noise Reduction. In Proceedings of the 24th International Congress on Sound and Vibration, London, UK, 23–27 July 2017; pp. 1–8. 25. Mazur, K.; Wrona, S.; Pawelczyk, M. Placement of Microphones for an Active Noise-Reducing Casing. In Proceedings of the 25th International Congress on Sound and Vibration, Hiroshima, Japan, 8–12 July 2018; pp. 1–8. c 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Sciences Multidisciplinary Digital Publishing Institute

Active Structural Acoustic Control of an Active Casing Placed in a Corner

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applied sciences Article Active Structural Acoustic Control of an Active Casing Placed in a Corner Anna Chraponska * , Stanislaw Wrona * , Jaroslaw Rzepecki, Krzysztof Mazur and Marek Pawelczyk Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland; jaroslaw.rzepecki@polsl.pl (J.R.); krzysztof.jan.mazur@polsl.pl (K.M.); marek.pawelczyk@polsl.pl (M.P.) * Correspondence: anna.chraponska@polsl.pl (A.C.); stanislaw.wrona@polsl.pl (S.W.) Received: 25 January 2019; Accepted: 10 March 2019; Published: 13 March 2019 Abstract: Electric appliances used in workplaces and everyday life often generate a low-frequency noise, which affects human body systems. Passive methods employed to reduce noise are not effective at low frequencies. The classical approach to active noise control practically involves the generation of local zones of quiet, whereas at other areas the noise is reinforced. Moreover, it usually requires a large number of secondary sound sources. Hence, an active casing approach has been developed. The active casing panels’ vibrations are controlled to reduce the device noise emission. Efficiency of this method has been previously confirmed by the authors and the results have been reported in multiple journal publications. However, in the previous research experiments, the active casing was placed at a distance from the enclosure walls. In this research, the active casing is located in a corner and such placement is intentionally used to facilitate the active control system’s operation. The noise reduction performance is investigated at multiple configurations, including a range of distances from the corner and different error microphone arrangements. The analysis of both primary and secondary paths is given. Advantages and drawbacks of different active casing configurations are presented and discussed. Keywords: active noise control; active casing; device noise control; modelling; feed-forward; room acoustics; filtered-x least mean squares 1. Introduction Nowadays, due to technological progress, noise level enhancement has been observed. Machines and devices commonly used in industry and everyday life generate noise, which may cause health damage. Noise is also one of the factors influencing mental performance [1]. Therefore, high efforts are made to reduce the noise pollution in the human environment. In general, noise can be divided into high-, mid- and low-frequency noise. Low-frequency noise, considered in the frequency range up to approximately 500 Hz, is most difficult to limit due to passive barriers’ inefficiency at this frequency range (when the noise frequency decreases, the mass, dimensions and cost of passive elements generally increases in order to be effective [2]). As an alternative or complementing solution, active control methods can be employed [3–6]. They can be used, e.g., to reduce noise entering through open windows [7,8]. Active methods are especially efficient at the low-frequency range, where passive barriers are infeasible [9]. However, when classically employed, they practically result in generating local zones of quiet, whereas at other areas the noise is reinforced. This requires additional care if the users are moving or the noise is nonstationary. Additionally, the number of secondary sound sources needed to make the zones controlled is high, which increases the total cost and highly interferes with the environment, making the solution unacceptable for many applications. Appl. Sci. 2019, 9, 1059; doi:10.3390/app9061059 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 1059 2 of 17 In this research, an active noise-reducing casing is investigated. The active casing encloses a device that generates an excessive noise. The original device casing may be used if it is made of thin walls or the device can be surrounded by an additional casing satisfying such requirement. The control system of the casing operates according to the Active Structural Acoustic Control (ASAC) approach. This means that by actively controlling vibrations of the casing panels, the noise emission to the environment is reduced. The ASAC approach represents several advantages over a typical Active Noise Control (ANC), where loudspeakers are used as the secondary sources [10,11]. The most important feature is that the active casing provides a global noise reduction in a whole room (reduces the noise emission), instead of creating only local zones of quiet and enhancing the noise elsewhere. This is a very desirable property of any active noise-reducing system. Efficiency of this method was previously investigated by the authors and the results have been reported in multiple publications [12–14]. However, in the previous research, the active casing was placed distant from the walls of the room the casing was enclosed by. In this paper, the active casing is located in a corner and such placement is intentionally used to facilitate the active control system’s operation. Moreover, such placement of a device can be commonly encountered in real life. The presented research aims to evaluate the hypothesis that placing the active casing in a corner and appropriately rearranging the microphones can lead to both enhanced noise reduction levels and a wider frequency range of global noise reduction (in the entire room). A proper theoretical justification for such behavior is provided. The noise reduction performance is investigated and compared for multiple configurations, including a range of distances from the corner and different error microphone arrangement. The analysis of both primary and secondary paths is also given. Advantages and drawbacks of different active casing configurations are presented and discussed. The remainder of the paper is organized in five sections. Section 2 describes the laboratory setup, i.e., the light-weight active casing and utilized actuators and sensors. Section 3 describes research experiment assumptions. The placement of the active casing in the corner is described and error microphones arrangements are depicted. Section 4 provides analysis of primary and secondary paths in terms of the amplitude functions of their frequency response functions. Section 5 introduces briefly the active control algorithm. Section 6 is dedicated to active control performance. Experimental results are presented and discussed. Finally, the conclusions are drawn based on the results. 2. The Laboratory Setup The employed laboratory setup is presented in Figure 1. It consists of a light-weight active casing placed in the corner of a room and the appropriately arranged microphones: one reference microphone, five error microphones and four room (monitoring) microphones. The active casing is placed in the corner with its back and right panels. It is built of five steel plates (1 mm thick) bolted together, forming a cuboid of dimensions 630 mm  800 mm  500 mm. The active casing is placed on a sound-insulating basis. Inside the casing, a loudspeaker is placed and it is used for the generation of a primary noise. The loudspeaker as a noise source provides a more reproducible environment for control system evaluation as compared to a real device (which is also examined in other studies performed by the authors). The employed active casing itself is described in more detail in [12,14,15]. It is important to emphasise that such a construction of the casing is very challenging from the control point of view. The casing panels are connected to each other directly without using any rigid explicit frame, and such mounting of their edges leads to both vibrational and acoustical couplings between them. Near the loudspeaker inside the casing, a reference microphone is placed to obtain a reference signal. It can provide information about the primary noise. Five error microphones are placed around the active casing at specific positions, described in detail in Section 3. There are also four room microphones, which are used to evaluate the noise reduction performance (they are not used by the control system). The room microphones are placed in four arbitrarily selected irregular locations in the Appl. Sci. 2019, 9, 1059 3 of 17 enclosure, at greater distances from the casing. Each position corresponds to a possible location of a listener [16]. Figure 1. The laboratory setup. To control vibrations of the active casing, inertial mass actuators EX-1 are used. They are light-weight (115 g) actuators of small dimensions (diameter 70 mm), compared to the size of the casing. They are attached to the inner side of the casing panels. In total, 21 actuators are used (5 actuators are attached to the top panel, 4 actuators are used per each of the remaining panels). The number of actuators and their placement is a result of analysis and optimization process maximizing a measure of the controllability of the system [15]. 3. The Experiment Assumptions The previous research experiments were performed with the active casing placed distantly from the laboratory enclosure walls. In a recent report, [17], primary and secondary paths of a casing placed only at a single wall of the enclosure were preliminarily examined. In this paper, the active casing is placed in the corner and extensive active control experiments are carried out. Hence, this research, besides the primary and secondary paths analysis, also presents a thorough study on active control system performance under such conditions, which is the main contribution of this paper. 3.1. Reflectivity of a Wall Surface One of the assumptions for the experiment concerns corner walls surfaces, which are assumed to be reflective (like in most real enclosures and rooms, industrial or domestic). The corner walls are dense and smooth. Hence, the absorption coefficient is low, providing considerable sound reflection from the walls [18]. The sound reflection between the active casing and the corner is intentional in this research. The influence of sound reflection on active control performance is investigated. The distance between corner walls and active casing’s back and right panels is small enough to expect that strong resonances may be induced, significantly influencing the primary and secondary paths and finally the control. 3.2. Distance between the Casing and the Corner If a sound source, e.g., a loudspeaker, is placed in an enclosure, its position is important, because it influences the sound perceived by the recipients. As stated in [19], a corner is the most efficient location for a non-directional source. A low-frequency loudspeaker, i.e., a subwoofer, is most efficient Appl. Sci. 2019, 9, 1059 4 of 17 if placed on a solid floor adjacent to a wall or in a corner, and coupled to reflecting surfaces at most one-sixth of the sound wavelength away [19]. In other words: d  ; (1) ls 6 f where d is the distance between the loudspeaker and the reflecting surface, v is the speed of sound ls in the air, and f is the frequency of sound emitted by the loudspeaker. The active noise control methods are most efficient at low frequencies up to about 500 Hz, therefore this is the frequency range of interest in this research. This is in agreement with the content of dominating frequencies of most common industrial devices and domestic appliances. Hence, to investigate the aforementioned phenomenon, the examined distances between the active casing and the corner should be in the range from about 0.1 m to 1.0 m. However, the maximum distance chosen for the experiment was 0.8 m due to dimensions of the laboratory enclosure. Hence, eight distances d , i = 1, 2, ..., 8, between two active casing panels and the corner walls in the room are examined, where d = 0.1 m, d = 0.2 m, ..., d = 0.8 m. 1 2 8 3.3. Placement of Error Microphones The active casing is placed in the corner with its back and right panels. These casing panels are equally distant from both corresponding corner walls with distance d , as marked in the scheme presented in Figure 2. Error microphone locations corresponding to the left, top and front active casing panels are marked with symbols L, T and F, respectively. They are located at a distance equal to 0.5 m from the corresponding panels’ centers. Error microphones corresponding to back and right casing panels are placed in two different ways. In the first approach, referred to as Setup 1, error microphones corresponding to back and right active casing panels are placed between the casing and the corner. Back error microphone location is noted by symbol B and is half the distance between the back casing panel’s center and the corresponding corner wall (the distance is equal to d /2). Analogously, right error microphone location is noted by symbol R and is half the distance between the right casing panel’s center and the corresponding corner wall (the distance is also equal to d /2). In the second approach, referred to below as Setup 2, error microphones corresponding to back and right active casing panels are moved from the gap between the casing and the corner to arbitrarily selected locations among error microphones corresponding to front, left and top active casing panels, based on results of preliminary control experiments. The new back error microphone location is noted by symbol B and is placed at the same height as the top error microphone, above the active casing’s corner (see Figure 2b). The new right error microphone location is noted by symbol R and is placed at the same height as both left and front error microphones, and its distance from active casing’s edge is equal to 0.5 m. In such arrangement, distances between error microphones become smaller, which affects the performance of active control. Both setups are examined to compare their influence. It is noteworthy that when the distance d between the casing panels and corner walls changes, all of the error microphones have to be moved, following the casing position. On the other hand, room microphones are always at the same locations. 500 /2 left panel left panel Appl. Sci. 2019, 9, 1059 5 of 17 corner bolts light-weight error casing microphone (a) Microphones arrangement in Setup 1. B' R' (b) Microphones arrangement in Setup 2. Figure 2. The schematic representation of the laboratory setup (all dimensions are given in mm). 4. Primary and Secondary Paths Active control is employed to reduce noise in this research, hence knowledge of the dynamic properties of primary and secondary paths in the frequency range of interest for active control will facilitate the control system development and implementation [12]. Their analysis is provided in this section. Primary and secondary paths’ models in the form of Finite Impulse Response (FIR) filters of length N = 128 were obtained experimentally. During the real system identification experiment, each path was excited with a optimized multi-tonal signal of 4096 samples. The signal was reproduced and the response was recorded eight times for each path. Afterwards, the correlation method was used to estimate the average impulse response of the considered path. The identified models were used both in the control system, e.g., for the Filtered-x part of the FxLMS algorithm, and for the paths’ analysis presented in this section. The amplitude function of the identified impulse response estimate is referred to as amplitude response. top panel top panel d /2 front panel front panel 500 Appl. Sci. 2019, 9, 1059 6 of 17 4.1. Primary Paths Analysis The primary path is considered as a path between the input signal to the primary noise source, Appl. Sci. 2019, xx, 5 6 of 17 i.e., the loudspeaker inside the active casing, and the signal acquired by one of the error microphones. Appl. Sci. 2019, xx, 5 6 of 17 The amplitude functions of the frequency functions of the impulse response estimates for the primary paths for both setups are presented side by side. The paths are presented in frequency range up to paths for both setups are presented side by side. The paths are presented in frequency range up to paths for both setups are presented side by side. The paths are presented in frequency range up to 500 Hz, in which active noise control methods are effective. In each figure, primary path frequency 500 Hz, in which active noise control methods are effective. In each figure, primary path frequency 500 Hz, in which active noise control methods are effective. In each figure, primary path frequency response response functions functions for for all all distances distances(0.1–0.8 (0.1–0.8m) m)ar are e pr presented. esented. response functions for all distances (0.1–0.8 m) are presented. The loudspeaker used as a noise source starts to transmit sound for frequencies above 40 Hz, The loudspeaker used as a noise source starts to transmit sound for frequencies above 40 Hz, The loudspeaker used as a noise source starts to transmit sound for frequencies above 40 Hz, what can be observed in Figures 3–5. In Figure 3, the primary paths for the error microphone which can be observed in Figures 3–5. In Figure 3, the primary paths for the error microphone what can be observed in Figures 3–5. In Figure 3, the primary paths 0 for the error microphone corresponding to right casing panel are presented (locations R and R ). The amplitude responses corresponding to right casing panel are presented (locations R and R ). The amplitude responses in corresponding to right casing panel are presented (locations R and R ). The amplitude responses in Setup 1 (Figure 3a) are distinctly different comparing to the amplitude responses obtained for Setup 1 (Figure 3a) are distinctly different comparing to the amplitude responses obtained for Setup 2 in Setup 1 (Figure 3a) are distinctly different comparing to the amplitude responses obtained for Setup 2 (Figure 3b). Maximum magnitudes in Figure 3a are substantially greater than in Figure 3b. (Figure 3b). Maximum magnitudes in Figure 3a are substantially greater than in Figure 3b. A general Setup 2 (Figure 3b). Maximum magnitudes in Figure 3a are substantially greater than in Figure 3b. A general trend observed in Figure 3a is an increase of magnitude for decreasing distance between the trend observed in Figure 3a is an increase of magnitude for decreasing distance between the casing A general trend observed in Figure 3a is an increase of magnitude for decreasing distance between the casing and the corner. Such effect is not evident in Figure 3b. It means that when decreasing distance and the corner. Such effect is not evident in Figure 3b. This means that when decreasing distance casing and the corner. Such effect is not evident in Figure 3b. It means that when decreasing distance d , the primary noise starts to resonate in the gap between the casing and the wall. Hence, if an error d , the primary noise starts to resonate in the gap between the casing and the wall. Hence, if an error i d , the primary noise starts to resonate in the gap between the casing and the wall. Hence, if an error microphone is placed in such a gap, the signal it measures becomes less representative for the general microphone is placed in such a gap, the signal it measures becomes less representative of the general microphone is placed in such a gap, the signal it measures becomes less representative for the general noise emitted by the given casing panel and it more represents a specific resonant effect, what may be noise noise emitted emitted byby the the given given casing casing panel panel and andititmor mor eerr epr epresents esents a a specific specific r resonant esonantef ef fect, fect,what which may may be be misleading for the adaptation of the control algorithm. For the evaluated laboratory setup, this is the misleading misleading forfor the the adaptation adaptation of of the thecontr contr ol olalgorithm. algorithm. For Forthe theevaluated evaluated laboratory laboratory setup, setup, this this is the is the case for d ≤ 0.4 m. case for d ≤ 0.4 m. case for d  0.4 m. In Figure 4, the primary paths for the error microphone corresponding to back casing panel in In Figure 4, the primary paths for the err0 or microphone corresponding to back casing panel in In Figure 4, the primary paths for the error microphone corresponding to back casing panel in both setups are presented (locations B and B ). Analogous behavior can be observed as in primary both setups are presented (locations B and B ). Analogous behavior can be observed as in primary both setups are presented (locations B and B ). Analogous behavior can be observed as in primary paths presented for the right error microphone in Figure 3, hence, for the sake of brevity, it is no further paths presented for the right error microphone in Figure 3, hence, for the sake of brevity, it is no further paths presented for the right error microphone in Figure 3, hence, for the sake of brevity, it is no discussed. discussed. further discussed. 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m −10 −10 0.3 m 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m 0.6 m −20 −20 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m −40 0 100 200 300 400 500 −40 0 100 200 300 400 500 0 100 F200 requency (Hz) 300 400 500 0 100 F200 requency (Hz) 300 400 500 Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 3. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 3. The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the right casing panel. Figure 3. The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the right casing panel. primary paths with the error microphone adjacent to the right casing panel. 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m −10 −10 0.3 m 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m 0.6 m −20 −20 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m −40 0 100 200 300 400 500 −40 0 100 200 300 400 500 0 100 F200 requency (Hz) 300 400 500 0 100 F200 requency (Hz) 300 400 500 Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 4. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 4. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 4. The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the back casing panel. primary paths with the error microphone adjacent to the back casing panel. primary paths with the error microphone adjacent to the back casing panel. In Figure 5, the primary paths for the error microphone corresponding to top casing panel in both In Figure 5, the primary paths for the error microphone corresponding to top casing panel in both setups are presented (the location T). The top error microphone placement is the same for both setups, setups are presented (the location T). The top error microphone placement is the same for both setups, and hence, amplitude responses are very similar for them. It confirms consistency of obtained results. and hence, amplitude responses are very similar for them. It confirms consistency of obtained results. Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Appl. Sci. 2019, 9, 1059 7 of 17 In Figure 5, the primary paths for the error microphone corresponding to top casing panel in both setups are presented (the location T). The top error microphone placement is the same for both setups, Appl. Sci. 2019, xx, 5 7 of 17 Appl. Sci. 2019, xx, 5 7 of 17 and hence, amplitude responses are very similar for them. This confirms consistency of obtained results. On the other hand, when the distance d changes, the sound emission pattern in the room On the other hand, when the distance d changes, the sound emission pattern in the room also changes. On the other hand, when the distance d changes, the sound emission pattern in the room also changes. also changes. It is noteworthy that in the i frequency range up to about 125 Hz, an effect of magnitude It is noteworthy that in the frequency range up to about 125 Hz, an effect of magnitude increase for It is noteworthy that in the frequency range up to about 125 Hz, an effect of magnitude increase for increase for decreasing distance d is observed. Above 125 Hz, such effect is not clearly visible. The decreasing distance d is observed. Above 125 Hz, such effect is not clearly visible. The effect observed decreasing distance d is observed. Above 125 Hz, such effect is not clearly visible. The effect observed effect observed below 125 Hz indicates that moving the casing closer to the corner causes slightly below 125 Hz indicates that moving the casing closer to the corner causes slightly stronger emission of below 125 Hz indicates that moving the casing closer to the corner causes slightly stronger emission of stronger emission of low frequencies in the laboratory enclosure, as it could be expected, based on the low frequencies in the laboratory enclosure, as it could be expected, basing on the theory recalled in low frequencies in the laboratory enclosure, as it could be expected, basing on the theory recalled in theory recalled in Section 3.2. Subsection 3.2. Subsection 3.2. The paths between the primary noise source and one of the room microphones are given in The paths between the primary noise source and one of the room microphones are given in The paths between the primary noise source and one of the room microphones are given in Figure 6. The magnitudes are in general lower than the ones obtained for error microphones, as Figure 6. The magnitudes are in general lower than the ones obtained for error microphones, as Figure 6. The magnitudes are in general lower than the ones obtained for error microphones, as the distances from the noise source to the room microphones are larger. Similarly as for the top the distances from the noise source to the room microphones are larger. Similarly as for the top the distances from the noise source to the room microphones are larger. Similarly as for the top error errmicr or micr ophone, ophone, the the paths paths ar ar e econsistent consistent for for both both setups. setups. However However , ,itit isis noteworthy noteworthy that that in in thethe error microphone, the paths are consistent for both setups. However, it is noteworthy that in the frequency frequency range range up up toto about about 125 125 Hz, Hz,aaslight slightef effect fect of of magnitude magnitudeincr incr ease ease for for decr decr easing easing distance distance d is d is i i frequency range up to about 125 Hz, a slight effect of magnitude increase for decreasing distance d is observed again. It confirms that moving the casing closer to the corner causes stronger excitation of observed again. It confirms that moving the casing closer to the corner causes stronger excitation of observed again. It confirms that moving the casing closer to the corner causes stronger excitation of low frequencies in the whole laboratory enclosure, as used for the sound reproducing systems in audio low frequencies in the whole laboratory enclosure, as used for the sound reproducing systems in audio low frequencies in the whole laboratory enclosure, as used for the sound reproducing systems in audio engineering. engineering. engineering. 10 10 10 10 0.1 m 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m 0.3 m −10 −10 −10 −10 0.4 m 0.4 m 0.5 m 0.5 m −20 −20 −20 −20 0.6 m 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m 0.8 m −40 −40 −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 5. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 5. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 5. The amplitude functions of the frequency functions of the impulse response estimates for the primary paths with the error microphone adjacent to the top casing panel. primary paths with the error microphone adjacent to the top casing panel. primary paths with the error microphone adjacent to the top casing panel. 10 10 10 10 0.1 m 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m 0.3 m −10 −10 −10 −10 0.4 m 0.4 m 0.5 m 0.5 m −20 −20 −20 −20 0.6 m 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m 0.8 m −40 −40 −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 6. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 6. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 6. The amplitude functions of the frequency functions of the impulse response estimates for the paths between one of the room microphones and the primary source for the eight different distances paths between one of the room microphones and the primary source for the eight different distances paths between one of the room microphones and the primary source for the eight different distances between the active casing and the wall. between the active casing and the wall. between the active casing and the wall. 4.2. Secondary Paths Analysis 4.2. Secondary Paths Analysis 4.2. Secondary Paths Analysis The secondary path is a path between the input signal to one of the actuators (exciters) mounted The secondary path is a path between the input signal to one of the actuators (exciters) mounted on The thesecondary inner side of path the is active a path casing betw panels, een the and input the signal signalacquir to one ed ofby the one actuators of the err (exciters) or microphone mounted s. on the inner side of the active casing panels, and the signal acquired by one of the error microphones. Selected secondary paths amplitude responses are presented. on the inner side of the active casing panels, and the signal acquired by one of the error microphones. Selected secondary paths amplitude responses are presented. In Figure 7, secondary paths between selected five actuators (one per casing panel), and the error Selected secondary paths amplitude responses are presented. In Figure 7, secondary paths between selected five actuators (one per casing panel), and the error microphone corresponding to right casing panel are presented. The casing was placed at a distance micr In ophone Figure 7 corr , secondary espondingpaths to right between casing panel the selected are presented. five actuators The casing (one was per placed casing at apanel), distance and d = 0.1 m. It is the smallest considered distance of d , where there are significant differences in paths’ d1 = 0.1 m. It is the smallest considered distance of di , where there are significant differences in paths’ the error microphone corresponding to right casing panel are presented. The casing was placed at 1 i magnitudes, depending on chosen setup (right error microphone placed at location R or R0). In Setup magnitudes, depending on chosen setup (right error microphone placed at location R or R ). In Setup Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Appl. Sci. 2019, 9, 1059 8 of 17 Appl. Sci. 2019, xx, 5 8 of 17 a distance d = 0.1 m. It is the smallest considered distance of d , where there are significant differences Appl. Sci. 2019, xx, 5 8 of 17 1 i in paths’ magnitudes, depending on chosen setup (right error microphone placed at location R or 0 0 0 R ).1 In (location Setup R 1),(location magnitudes R), ar magnitudes e much greater are than much in gr Setup eater 2 (location than in Setup R ). As 2 it (location could be R expected, ). As it the could 1 (location R), magnitudes are much greater than in Setup 2 (location R ). As it could be expected, the actuator mounted to the right panel contributes the most to the signal obtained with the right error be expected, the actuator mounted to the right panel contributes the most to the signal obtained actuator mounted to the right panel contributes the most to the signal obtained with the right error microphone when placed at location R. However, other secondary paths are also stronger when the with the right error microphone when placed at location R. However, other secondary paths are also microphone when placed at location R. However, other secondary paths are also stronger when the error microphone is placed at location R (Setup 1) comparing to location R (Setup 2). It means that stronger when the error microphone is placed at location R (Setup 1) compar0 ed to location R (Setup 2). error microphone is placed at location R (Setup 1) comparing to location R (Setup 2). It means that the narrow gap between the casing panel and the corner wall causes a resonance, amplifying sound This means that the narrow gap between the casing panel and the corner wall causes a resonance, the narrow gap between the casing panel and the corner wall causes a resonance, amplifying sound generated by any actuator, mounted to any of the casing panels. amplifying sound generated by any actuator, mounted to any of the casing panels. generated by any actuator, mounted to any of the casing panels. 10 10 10 10 Front Front Right 0 0 Right 0 0 Back Back −10 −10 Left −10 −10 Left Top −20 −20 Top −20 −20 −30 −30 −30 −30 −40 −40 −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 7. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 7. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 7. The amplitude functions of the frequency functions of the impulse response estimates for the secondary paths between each casing panel’s selected actuator and the error microphone adjacent to secondary paths between each casing panel’s selected actuator and the error microphone adjacent to secondary paths between each casing panel’s selected actuator and the error microphone adjacent to the right casing panel, at a distance 0.1 m, in both setups. the the right right casing casing panel, panel, atat a distance a distance of 0.1 0.1 m, m, inin both both setups. setups. In Figure 8, secondary paths between the selected actuator mounted to the right panel and the In Figure 8, secondary paths between the selected actuator mounted to the right panel and the In Figure 8, secondary paths between the selected actuator mounted to the right panel and the right error microphone are presented for all distances d . Magnitudes are in general greater in Setup right error microphone are presented for all distances d . Magnitudes are in general greater in Setup right error microphone are presented for all distances d .i Magnitudes are in general greater in Setup 1 1 (Figure 8a), especially when d ≤ 0.4 m. In nearly whole considered frequency range magnitude 1 (Figure 8a), especially when d ≤ 0.4 m. In nearly whole considered frequency range magnitude (Figure 8a), especially when d  0.4 m. In nearly the whole considered frequency range, magnitude increases as the distance d decreases. In Setup 2 (Figure 8b) such effect is not visible. increases as the distance d decreases. In Setup 2 (Figure 8b) such effect is not visible. increases as the distance d decreases. In Setup 2 (Figure 8b) such effect is not visible. 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m 0.3 m −10 −10 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m −20 −20 0.6 m 0.6 m −30 −30 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 8. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 8. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 8. The amplitude functions of the frequency functions of the impulse response estimates for the secondary paths between right casing panel’s selected actuator and the error microphone adjacent to secondary paths between right casing panel’s selected actuator and the error microphone adjacent to secondary the rightpaths casing between panel, atright all distances, casing panel’s in both selected setups. actuator and the error microphone adjacent to the right casing panel, at all distances, in both setups. the right casing panel, at all distances, in both setups. Similar observations can be drawn from Figure 9, which presents responses of secondary paths Similar observations can be drawn from Figure 9, which presents responses of secondary paths between back casing panel’s selected actuator and the back error microphone at all distances. In Setup Similar observations can be drawn from Figure 9, which presents responses of secondary paths between back casing panel’s selected actuator and the back error microphone at all distances. In Setup 1 magnitude increases as the distance d decreases. On the other hand, in Setup 2 such effect is also between back casing panel’s selected actuator and the back error microphone at all distances. In 1 magnitude increases as the distance d decreases. On the other hand, in Setup 2 such effect is also visible, but only in a frequency range up to about 200 Hz. It shows that the narrow gap amplifies most Setup 1 magnitude increases as the distance d decreases. On the other hand, in Setup 2 such effect visible, but only in a frequency range up to about 200 Hz. It shows that the narrow gap amplifies most of the considered frequencies if a microphone is placed in the gap (location B). However, the actual is also visible, but only in a frequency range up to about 200 Hz. This shows that the narrow gap of the considered frequencies if a microphone is placed in the gap (location B). However, the actual emission (sound field excitation in the laboratory enclosure) can be slightly enhanced, due to casing amplifies most of the considered frequencies if a microphone is placed in the gap (location B). However, emission (sound field excitation in the laboratory enclosure) can be slightly enhanced, due to casing placement in the corner, rather only in a limited range of low frequencies (as the measurement at theplacement actual emission in the (sound corner, rather field excitation only in a in limited the laboratory range of low enclosur frequencies e) can be (asslightly the measur enhanced, ement at due location B shows). to casing location placement B shows).in the corner, only in a limited range of low frequencies (as the measurement at location B shows). Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Appl. Sci. 2019, xx, 5 9 of 17 10 10 0.1 m 0.2 m 0 0 0.3 m −10 −10 0.4 m 0.5 m −20 −20 0.6 m Appl. Sci. 2019, xx, 5 9 of 17 −30 −30 Appl. Sci. 2019, 9, 1059 0.7 m9 of 17 0.8 m −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 10 10 Frequency (Hz) Frequency (Hz) 0.1 m (a) Setup 1. (b) Setup 2. 0.2 m 0 0 Figure 9. The amplitude functions of the frequency functions of the impulse response estimates for the 0.3 m −10 −10 secondary paths between back casing panel’s selected actuator and the error microphone adjacent0.4 to m the back casing panel, at all distances, in both setups. 0.5 m −20 −20 0.6 m −30 In Figure 10, secondary paths between top−30 casing panel’s selected actuator and the top error 0.7 m microphone are presented at all distances. Amplitude responses for both setups (Figure 10a, Figur 0.8 e m 10b) −40 −40 are similar, confirming the consistency of obtained results. Similarly as for the back microphone placed 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) at location B , slight enhancement of magnitude for low frequency range up to approximately 180 Hz (a) Setup 1. (b) Setup 2. can be observed when the distance d decreases. Figure 9. The amplitude functions of the frequency functions of the impulse response estimates for the In Figures 11 and 12, the paths between selected actuators and one of the room microphones are Figure 9. The amplitude functions of the frequency functions of the impulse response estimates for the secondary paths between back casing panel’s selected actuator and the error microphone adjacent to presented. The room microphones are in constant locations during all experiments. The paths are secondary paths between back casing panel’s selected actuator and the error microphone adjacent to the back casing panel, at all distances, in both setups. compared in the same manner as before. In Figures 11 and 12, the selected actuators are mounted to the back casing panel, at all distances, in both setups. back and right casing panel, respectively. Once again, the magnitude increases for decreasing distance In Figure 10, secondary paths between top casing panel’s selected actuator and the top error d in a frequency range up to approximately 200 Hz. These paths also confirm, that placing the casing In Figure 10, secondary paths between top casing panel’s selected actuator and the top error microphone are presented at all distances. Amplitude responses for both setups (Figure 10a, Figure 10b) in a corner increases the magnitude of paths in the low frequency range (these frequencies are better microphone are presented at all distances. Amplitude responses for both setups (Figure 10a,b) are are similar, confirming the consistency of obtained results. Similarly as for the back microphone placed excited in the enclosure). However, it is also noteworthy that both primary and secondary paths’ similar, confirming 0 the consistency of obtained results. Similarly as for the back microphone placed at at location B , slight enhancement of magnitude for low frequency range up to approximately 180 Hz magnitudes 0 increase in similar manner, hence the balance between them should be sustained and the location B , slight enhancement of magnitude for low frequency range up to approximately 180 Hz can can be observed when the distance d decreases. noise reduction capabilities should not be impeded. be observed when the distance d decreases. In Figures 11 and 12, the paths i between selected actuators and one of the room microphones are presented. The room microphones are in constant locations during all experiments. The paths are 10 10 compared in the same manner as before. In Figures 11 and 12, the selected actuators are mounted to 0.1 m back and right casing panel, respectively. Once again, the magnitude increases for decreasing distance 0.2 m 0 0 0.3 m d in a frequency range up to approximately 200 Hz. These paths also confirm, that placing the casing −10 −10 0.4 m in a corner increases the magnitude of paths in the low frequency range (these frequencies are better 0.5 m excited −20 in the enclosure). However, it is also noteworthy −20 that both primary and secondary paths’ 0.6 m magnitudes increase in similar manner, hence the balance between them should be sustained and the −30 −30 0.7 m noise reduction capabilities should not be impeded. 0.8 m −40 −40 0 100 200 300 400 500 0 100 200 300 400 500 10 10 Frequency (Hz) Frequency (Hz) 0.1 m (a) Setup 1. (b) Setup 2. 0.2 m 0 0 Figure 10. The amplitude functions of the frequency functions of the impulse response estimates for 0.3 m Figure 10. The amplitude functions of the frequency functions of the impulse response estimates for −10 −10 the secondary paths between top casing panel’s selected actuator and the error microphone adjacent to 0.4 m the secondary paths between top casing panel’s selected actuator and the error microphone adjacent to the top casing panel, at all distances, in both setups. 0.5 m −20 −20 the top casing panel, at all distances, in both setups. 0.6 m −30 −30 0.7 m In Figures 11 and 12, the paths between selected actuators and one of the room microphones are 0.8 m −40 −40 presented. The room microphones are in constant locations during all experiments. The paths are 0 100 200 300 400 500 0 100 200 300 400 500 compared in the same manner as before. In Figures 11 and 12, the selected actuators are mounted Frequency (Hz) Frequency (Hz) to the back and right(a) casing Setup 1. panel, respectively. Once again, the magnitu (b) Setup d 2.e increases for decreasing distance Figure d in 10. a frThe equency amplitude range functions up to of appr theoximatel frequencyyfunctions 200 Hz.of These the impulse pathsralso esponse confirm, estimates that forplacing the secondary paths between top casing panel’s selected actuator and the error microphone adjacent to the casing in a corner increases the magnitude of paths in the low frequency range (these frequencies the top casing panel, at all distances, in both setups. are better excited in the enclosure). However, it is also noteworthy that both primary and secondary paths’ magnitudes increase in a similar manner, hence the balance between them should be sustained and the noise reduction capabilities should not be impeded. Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Appl. Sci. 2019, xx, 5 10 of 17 Appl. Sci. 2019, 9, 1059 10 of 17 Appl. Sci. 2019, xx, 5 10 of 17 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0.3 m 0 0 −10 −10 0.3 m 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m 0.6 m −20 −20 −30 −30 0.6 m 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m 0 100 200 300 400 500 0 100 200 300 400 500 −40 −40 Frequency (Hz) Frequency (Hz) 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 11. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 11. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 11. The amplitude functions of the frequency functions of the impulse response estimates for the paths between back casing panel’s selected actuator and one of the room microphones, at all distances, paths between back casing panel’s selected actuator and one of the room microphones, at all distances, paths between back casing panel’s selected actuator and one of the room microphones, at all distances, in both setups. in both setups. in both setups. 10 10 0.1 m 10 10 0.1 m 0.2 m 0 0 0.2 m 0 0 0.3 m −10 −10 0.3 m 0.4 m −10 −10 0.4 m 0.5 m −20 −20 0.5 m 0.6 m −20 −20 −30 −30 0.6 m 0.7 m −30 −30 0.7 m 0.8 m −40 −40 0.8 m 0 100 200 300 400 500 0 100 200 300 400 500 −40 −40 Frequency (Hz) Frequency (Hz) 0 100 200 300 400 500 0 100 200 300 400 500 Frequency (Hz) Frequency (Hz) (a) Setup 1. (b) Setup 2. (a) Setup 1. (b) Setup 2. Figure 12. The amplitude functions of the frequency functions of the impulse response estimates for the Figure 12. The amplitude functions of the frequency functions of the impulse response estimates for the paths between right casing panel’s selected actuator and one of the room microphones, at all distances, Figure 12. The amplitude functions of the frequency functions of the impulse response estimates for the paths between right casing panel’s selected actuator and one of the room microphones, at all distances, in both setups. paths between right casing panel’s selected actuator and one of the room microphones, at all distances, in both setups. in both setups. 5. Active control algorithm 5. Active control algorithm 5. Active In Control the activeAlgorithm control systems, the FxLMS algorithm is frequently implemented [20,25]. Its advantages In the active control systems, the FxLMS algorithm is frequently implemented [20,25]. Its advantages are, e.g., simplicity of implementation, robustness and low complexity of computations [21]. A scheme In the active control systems, the FxLMS algorithm is frequently implemented [20,21]. Its advantages are, e.g., simplicity of implementation, robustness and low complexity of computations [21]. A scheme of basic FxLMS algorithm is presented in Figure 13, where P(z) is the primary path, S(z) is the are, e.g., simplicity of implementation, robustness and low complexity of computations [22]. A scheme of basic FxLMS algorithm is presented in Figure 13, where P(z) is the primary ˆpath, S(z) is the secondary path, W(z) is a control filter adapted by the LMS algorithm, and S(z) is a model of of basic FxLMS algorithm is presented in Figure 13, where P(z) is the primary ˆ path, S(z) is the secondary path, W(z) is a control filter adapted by the LMS algorithm, and S(z) is a model of secondary path S(z). The algorithm name FxLMS (Filtered-x Least Mean Squares) follows from usage secondary path, W(z) is a control filter adapted by the LMS algorithm, and S(z) is a model of secondary secondary ˆ path S(z). The algorithm name FxLMS (Filtered-x Least Mean Squares) follows from usage of S(z) model — the reference signal usually noted as x(n) is passed through the secondary path path S(z). The algorithm name FxLMS (Filtered-x Least Mean Squares) follows from usage of S(z) of S(z) model ˆ — the reference signal usually noted as x(n) is passed through the secondary path estimate S(z) to obtain a filtered reference signal r(n) [2]. It is also passed through the primary path ˆ ˆ model—the estimate Sr( efer z) to ence obtain signal a filter usually ed refer noted ence as signal x(n)ris (npasse ) [2]. It d thr is also ough passed the secondary through the path primary estimate path S(z) P(z), which outputs signal d(n) — the primary disturbance. Adaptive filter output u(n) is passed P(z), which outputs signal d(n) — the primary disturbance. Adaptive filter output u(n) is passed to obtain a filtered reference signal r(n) [2]. It is also passed through the primary path P(z), which through secondary path S(z) to obtain a signal that is summed with the primary disturbance d(n). through secondary path S(z) to obtain a signal that is summed with the primary disturbance d(n). outputs The summation signal d(n) r—the esultsprimary in signaldisturbance. e(n), which isAdaptive a residualfilter error output signal.uThe (n) contr is passed ol system through attempts secondary to The summation results in signal e(n), which is a residual error signal. The control system attempts to path minimize S(z) to obtain the sum a of signal squar that es of isthe summed error signal with e the (n)primary over thedisturbanc length of filter e d(n W)( . z The ). summation results minimize the sum of squares of the error signal e(n) over the length of filter W(z). in signal e(n), which is a residual error signal. The control system attempts to minimize the sum of x(n) d(n) e(n) squares of the error signal e(n) over the length of filter W(z)+ . P(z) x(n) d(n) e(n) P(z) x(n) d(n) − e(n) u(n) P(z) W(z) S(z) u(n) W(z) S(z) u(n) r(n) W(z) S(z) S(z) LMS r(n) S(z) LMS Figure 13. The scheme of the FxLMS algorithm [2]. r(n) Figure 13. The scheme of the FxLMS algorithm [2]. S(z) LMS Figure 13. The scheme of the FxLMS algorithm [2]. Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude (dB) Magnitude Magnitude (dB) (dB) Magnitude Magnitude (dB) (dB) Appl. Sci. 2019, 9, 1059 11 of 17 The scheme presented in Figure 13 depicts a single-channel control system, however, if the plant is controlled by multiple inputs and returns multiple outputs, the control system can be generalized to a Multiple-Input Multiple-Output (MIMO) FxLMS, as described in [23], and such is used for this research. However, this paper is focused more on the investigation of the control system performance for specific configurations, rather than on introducing the control algorithm itself. Hence, the reader is referred to previous publications, where a more detailed description of the control system with a switched-error modification employed for the active casing is given [12,24]. It is noteworthy that varying the selected control algorithm may impact active control performance, e.g., the convergence rate or the final noise reduction levels. However, the preliminary experiments have shown that such an impact is similar for all evaluated experimental setups (it is independent of the particular configuration). Hence, it has been assumed that by employing the unchanged control algorithm through the whole research, the drawn conclusions also remain valid for altered or different control algorithms. 6. Active Control System Performance In this section, experimental evaluation of the investigated active control system is presented. The loudspeaker placed inside the active casing generates a tonal primary noise of frequency incremented by 5 Hz in the range from 1 Hz to 350 Hz. The considered frequency range includes the low frequencies where the speaker starts to transmit sound. To achieve the goal of global noise reduction, instantaneous square values of error signals are minimized by feedforward adaptive control system (introduced in the previous Section), controlling together 21 inertial actuators. The error signals are obtained by the error microphones (their arrangement is discussed in Section 3.3). The control performance is evaluated as noise reduction levels observed by the room microphones. Performance of the control system is tested in multiple configurations, including a range of distances from the corner d and different error microphones’ arrangement (Setup 1 or Setup 2). For each frequency of the primary disturbance, a 60 s experiment was performed. In its initial 5 s, the active control was off, and variance of signals acquired by different sensors was estimated as the reference point. Then, the active control was turned on. When the adaptive control algorithm converged, the final 5 s of the experiment were used to estimate the variance of signals acquired by corresponding sensors. In Figures 14 and 15, frequency characteristics for the active control experiments are presented. Time plots of signals obtained by individual sensors are not shown in this paper, as such insight into the control system behavior has been previously presented, e.g., in [12]. In the previous experiments, the active casing was placed distant from the enclosure walls and several control approaches were examined and described, e.g., in [12,14]. In the previous research, the maximum global noise reduction evaluated by mean noise reduction measured at all room microphones exceeded 15 dB. In this research, even higher performance has been achieved and the maximum global noise reduction level often exceeded even 25 dB, although these results rely on the specific circumstances of the experimental settings, which evolved over time. Hence, such direct comparison of noise reduction levels obtained for different settings is unjustified. However, that is not the aim of this research. The purpose of this paper is to evaluate the overall control performance of the active casing placed in a corner. Hence, the main point of investigation is the mean global noise reduction affected solely by the distance d and the error microphone arrangement (Setup 1 or Setup 2). The other experimental settings remained unchanged. Appl. Sci. 2019, xx, 5 12 of 17 Appl. Sci. 2019, 9, 1059 12 of 17 Control off - mean values Control on - Setup 1 Control off - Setup 1 Control on - Setup 2 Control off - Setup 2 50 50 40 40 30 30 20 20 10 10 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (a) Distance d = 0.1 m. (e) Distance d = 0.5 m. 1 5 50 50 40 40 30 30 20 20 10 10 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (b) Distance d = 0.2 m. (f) Distance d = 0.6 m. 2 6 50 50 40 40 30 30 20 20 10 10 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (c) Distance d = 0.3 m. (g) Distance d = 0.7 m. 3 7 50 50 40 40 30 30 20 20 10 10 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (d) Distance d = 0.4 m. (h) Distance d = 0.8 m. 4 8 Figure 14. The average variance of the room microphone signals for each of the primary noise tones in the range 1 Hz to 350 Hz with a step of 5 Hz, with and without active control, for both Setup 1 and Figure 14. The average variance of the room microphone signals for each of the primary noise tones in Setup 2. the range 1 Hz to 350 Hz with a step of 5 Hz, with and without active control, for both Setup 1 and Setup 2. Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Variance of microphone signals (dB) Appl. Sci. 2019, xx, 5 13 of 17 Appl. Sci. 2019, 9, 1059 13 of 17 Control on - Setup 1 Control on - Setup 2 40 40 30 30 20 20 10 10 0 0 −10 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (a) Distance d = 0.1 m. (e) Distance d = 0.5 m. 1 5 40 40 30 30 20 20 10 10 0 0 −10 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (b) Distance d = 0.2 m. (f) Distance d = 0.6 m. 2 6 40 40 30 30 20 20 10 10 0 0 −10 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (c) Distance d = 0.3 m. (g) Distance d = 0.7 m. 3 7 40 40 30 30 20 20 10 10 0 0 −10 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (d) Distance d = 0.4 m. (h) Distance d = 0.8 m. 4 8 Figure 15. The averaged noise reduction for the noise sensed by the room microphones for each of the primary noise tones in the range 1 Hz to 350 Hz with a step of 5 Hz, for both Setup 1 and Setup 2. Figure 15. The averaged noise reduction for the noise sensed by the room microphones for each of the In Figure 14, the mean variance estimated based on the room microphones measurements is given primary noise tones in the range 1 Hz to 350 Hz with a step of 5 Hz, for both Setup 1 and Setup 2. for different distances d , ranging from 0.1 m to 0.8 m. For each distance d a plot is given, where i i In Figure 14, the mean variance estimated based on the room microphones measurements is given for different distances d , ranging from 0.1 m to 0.8 m. For each distance d a plot is given, where i i black color represents primary noise without active control; red and blue colors represent residual Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Noise reduction (dB) Appl. Sci. 2019, 9, 1059 14 of 17 Appl. Sci. 2019, xx, 5 14 of 17 noise when active reduction is turned on with error microphones arranged in Setup 1 and Setup 2, respectively. To facilitate the comparison of control performance obtained for different configurations, black color represents primary noise without active control; red and blue colors represent residual in Figure 15 the noise reduction characteristics are also given, calculated as a difference between noise noise when active reduction is turned on with error microphones arranged in Setup 1 and Setup 2, level without and with control (reduction for Setup 1 and Setup 2 is marked with red or blue color, respectively. To facilitate the comparison of control performance obtained for different configurations, respectively). in Figure 15 the noise reduction characteristics are also given, calculated as a difference between noise It follows from the analysis of Figures 14 and 15 that the error microphone arrangement affects level without and with control (reduction for Setup 1 and Setup 2 is marked with red or blue color, strongly the overall performance of the control system. The major conclusion is that when the active respectively). casing is distant from the corner, the Setup 1 with error microphones surrounding the casing performs It follows from the analysis of Figures 14-15 that the error microphones arrangement affects better than the Setup 2, where error microphones are moved away from the corner. On the other strongly the overall performance of the control system. The major conclusion is that when the active hand, casing when is the distant active from casing the corner is placed , the Setup close1to with the err walls or micr in the ophones corner surr (dounding = 0.1 m), theitcasing is the performs other way better than the Setup 2, where error microphones are moved away from the corner. On the other around—Setup 2 provides substantially better results. This leads to a conclusion that when the casing hand, when the active casing is placed close to the walls in the corner (d = 0.1 m), it is the other approaches the corner, there is a threshold distance when it is beneficial to move 1 the error microphones way around — the Setup 2 provides substantially better results. It leads to a conclusion that when out from the gap between the casing and the corner, and place them on the other side of the casing, the casing approaches the corner, there is a threshold distance when it is beneficial to move the error complementing the error microphones there. For the studied setup the threshold distance seems to be microphones out from the gap between the casing and the corner, and place them on the other side of d = 0.4 m, although, the general conclusion is to expect such threshold value. the casing, complementing the error microphones there. For the studied setup the threshold distance Moreover, it is worth mentioning that when the active casing is placed close to the walls in the seems to be d = 0.4 m, although, the general conclusion is to expect such threshold value. corner (d = 0.1 m), the error microphones placed in the gap at locations R and B in Setup 1 actually Moreover, it is worth mentioning that when the active casing is placed close to the walls in the impede the correct adaptation of the control system. Even unplugging them, leaving only three corner (d = 0.1 m), the error microphones placed in the gap at locations R and B in Setup 1 actually error microphones operating, improves the control performance, as shown in Figure 16 (the specific impede the correct adaptation of the control system. Even unplugging them, leaving only three configuration with disabled R and B error microphones is marked with green color). It is important error microphones operating, improves the control performance, as shown in Figure 16 (the specific to keep this conclusion in mind, when an obstacle with reflecting surface is in the proximity of an configuration with disabled R and B error microphones is marked with green color). It is important to active casing, as such location between the casing and the obstacle may be disadvantageous for keep this conclusion in mind, when an obstacle with reflecting surface is in proximity of an active casing, error microphones. as such location between the casing and the obstacle may be disadvantageous for error microphones. Control off - mean values Control on - Setup 1 Control off - Setup 1 Control on - disabled R and B error mic. Control off - Setup 2 Control on - Setup 2 50 40 40 30 30 20 20 10 10 0 0 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (a) (b) Figure 16. (a) The average variance of the room microphone signals for each of the primary noise Figure 16. (a) The average variance of the room microphone signals for each of the primary noise tones with and without active control and (b) the averaged noise reduction for the noise sensed by the tones with and without active control and (b) the averaged noise reduction for the noise sensed by the room microphones for each of the primary noise tones. For Setup 1, Setup 2 and Setup 1 with the error room microphones for each of the primary noise tones. For Setup 1, Setup 2 and Setup 1 with the error microphones B and R disabled, d = 0.1 m. microphones B and R disabled, d = 0.1 m. Another conclusion follows from a comparison of control performance for the casing placed at Another conclusion follows from a comparison of control performance for the casing placed at the distance d = 0.1 m in Setup 2, and placed at the distance d = 0.8 m in Setup 1. Both of these two the distance d = 0.1 m in Setup 2, and placed at the distance d = 0.8 m in Setup 1. Both of these two 1 8 opposite scenarios provide very satisfying performance, reaching very high mean reduction levels. opposite scenarios provide very satisfying performance, reaching very high mean reduction levels. However, the reduction levels observed for the casing placed in the corner are higher and over a wider However, the reduction levels observed for the casing placed in the corner are higher and are over a frequency band. Although the difference is not high, it is clearly visible and leads to a conclusion that wider frequency band. Although the difference is not high, it is clearly visible and leads to a conclusion placing the active casing in a corner can be beneficial comparing to be placed at locations distant from that placing the active casing in a corner can be beneficial compared to being placed at locations distant enclosure walls. At least, such configuration, if technically feasible, should provide results of the same from quality enclosur . Mor eeover walls. , itAt follows least,frsuch om the configuration, research that such if technically configuration, feasible, which should for many provide applications resultsisof the same quality. Moreover, it follows from the research that such configuration, which for many Variance of microphone signals (dB) Noise reduction (dB) Appl. Sci. 2019, 9, 1059 15 of 17 Appl. Sci. 2019, xx, 5 15 of 17 applications is more realistic, is not less efficient. These conclusions are some of the major contributions of this paper, as such configuration of the active casing has not yet been evaluated. more realistic, is not less efficient. These conclusions are some of the major contributions of this paper, In addition, one more test has been done to check how much the actuators mounted to the casing as such configuration of the active casing has not yet been evaluated. panels facing the corner contribute to the overall noise reduction. Hence, in addition to secondary In addition, one more test has been done to check how much the actuators mounted to the casing paths panels investigation, facing theacorner control contribute experiment to the hasoverall been performed noise reduction. with speci Hence, fic actuators in addition disabled. to secondary Firstly, paths investigation, a control experiment has been performed with specific actuators disabled. Firstly, the actuators mounted to the left and front panels were disabled. Then, the actuators mounted to the the actuators mounted to the left and front panels were disabled. Then, the actuators mounted to right and back panels were disabled. Obtained results compared with results for all actuators operating the right and back panels were disabled. Obtained results compared with results for all actuators are shown in Figure 17. What is interesting is that no significant difference can be noticed between operating are shown in Figure 17. What is interesting, no significant difference can be noticed between disabling front and left panels, or back and right panels (the same number of actuators were operating). disabling front and left panels, or back and right panels (the same number of actuators were operating). This proves that the actuators actually excite the whole casing with such efficiency that even placing It proves that the actuators excite actually whole casing with such efficiency that even placing them at them at panels facing the corner is equally beneficial as placing them at panels facing the enclosure panels facing the corner is equally beneficial as placing them at panels facing the enclosure interior. interior. This can be explained by very strong coupling between casing panels, which was studied This can be explained by very strong coupling between casing panels, what was studied in details in detail in [12]. It is also noteworthy that disabling eight of 21 actuators did not affect heavily the in [11]. It is also noteworthy that disabling 8 of 21 actuators did not affect heavily the overall noise overall noise reduction by the active casing. In the lower frequency range, where the inertial actuators reduction by the active casing. In the lower frequency range, where the inertial actuators lack efficiency, lack efficiency, the superiority of using more actuators is visible (lesser number of actuators lacks the superiority of using more actuators is visible (lesser number of actuators lacks power to control the power to control the lowest frequencies). However, for frequencies above approximately 100 Hz, very lowest frequencies). However, for frequencies above approximately 100 Hz, very comparable results comparable results have been obtained for all evaluated configurations (with all actuators operating, have been obtained for all evaluated configurations (with all actuators operating, and some of them and some of them disabled). This shows a robustness of the proposed active noise reducing casing. disabled). It shows a robustness of the proposed active noise reducing casing. Control off - mean values Control on - Setup 2 Control off - Setup 1 Control on - Setup 2; dis. left and front panels Control off - Setup 2 Control on - Setup 2; dis. right and back panels 50 40 40 30 30 20 20 10 10 0 0 −10 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Frequency (Hz) Frequency (Hz) (a) (b) Figure 17. (a) The average variance of the room microphone signals for each of the primary noise tones Figure 17. (a) The average variance of the room microphone signals for each of the primary noise tones with and without active control and (b) the averaged noise reduction for the noise sensed by the room with and without active control and (b) the averaged noise reduction for the noise sensed by the room microphones for each of the primary noise tones. Observe, only active control with Setup 2, Setup 2 microphones for each of the primary noise tones. Observe, only active control with Setup 2, Setup 2 with the actuators on the left and the front panel disabled and Setup 2 with the actuators on the right with the actuators on the left and the front panel disabled and Setup 2 with the actuators on the right and the back panel disable, d = 0.1 m. and the back panel disable, d = 0.1 m. 7. Conclusions 7. Conclusions The active casing approach has been proven in previous research of the authors to provide The active casing approach has been proven in previous research of the authors to provide significant global noise reduction. However, the active casing was placed distant from the enclosure significant global noise reduction. However, the active casing was placed at a distance from the walls. In this paper, the active casing was located in a corner and such placement is intentionally used enclosure walls. In this paper, the active casing was located in a corner and such placement is to facilitate the active control system operation. On the other hand, such arrangement is common for intentionally used to facilitate the active control system operation. On the other hand, such arrangement many applications. Extensive active control experiments were carried out and a thorough study on is common for many applications. Extensive active control experiments were carried out and control system performance was presented, what is the main contribution of this paper. In the opinion a thor of ough the authors, studyth on e pr contr esented ol system researchperformance confirms the hypothesis was presented, that placing which the isactive the main casing contribution in a corner and appropriately rearranging the microphones can lead to both enhanced noise reduction levels and of this paper. In the opinion of the authors, the presented research confirms the hypothesis that placing a wider frequency range of global noise reduction. The analysis of both primary and secondary paths the active casing in a corner and appropriately rearranging the microphones can lead to both enhanced was also given as an additional insight into the investigated plant. noise reduction levels and a wider frequency range of global noise reduction. The analysis of both primary and secondary paths was also given as an additional insight into the investigated plant. Variance of microphone signals (dB) Noise reduction (dB) Appl. Sci. 2019, 9, 1059 16 of 17 The following conclusions can be drawn from the presented results. When the active casing approaches the corner, there is a threshold distance when it is beneficial to move the error microphones out from the gap between the casing and the corner, and place them on the other side of the casing, supporting the error microphones there (change from the Setup 1 to Setup 2). Then, the distance between the error microphones becomes smaller and the frequency range, in which acoustic emission is properly observable, becomes greater [25]. This results in higher mean reduction levels and in a wider frequency band, where the global noise reduction is achieved. For better representation of this behavior, let us assume that the noise source is surrounded by a sphere, at which a limited number of error microphones are placed. The effectiveness of the global noise reduction is limited in the frequency range by the distance between the error microphones—it should be smaller than the wavelength of noise to avoid spatial aliasing and to provide a proper observability of the emitted noise. In the previous research, when the active casing was distant from the enclosure walls, the introduced sphere was actually limited to a hemisphere, as the casing was placed on the floor. However, when the active casing is placed in a corner, the hemisphere is further reduced to approximately one-eighth of the sphere. Therefore, the remaining spherical surface which has to be covered with error microphones is smaller, hence the same number of microphones can be more densely distributed. This leads to smaller distances between error microphones, facilitating the operation of the active control system. Besides this major conclusion, two more observations are worth emphasizing. Firstly, an error microphone placed in a narrow gap between the casing and a sound-reflecting obstacle may not only be useless, but it may even impede the adaptation of the control system. Secondly, if the cross couplings between casing panels are strong, placing the actuators at panels facing the corner walls is as beneficial as placing them at panels facing the interior of the enclosure. This may be important when actuators placement is decided, and the surface available for actuators can be limited due to the device occupying most of the space inside the casing. This research also shows that placing the casing at the corner does not limit the performance in terms of globally reducing noise generated by the enclosed source. The authors believe that the presented research provides more insight into the operations of the active casing and helps to extend the applicability of the proposed active casing approach, as an efficient way to reduce noise generated by devices. Author Contributions: Conceptualization, A.C., S.W. and M.P.; methodology, A.C. and S.W.; software, S.W. and K.M.; validation, A.C., S.W., J.R., K.M. and M.P.; formal analysis, A.C. and S.W.; investigation, A.C. and S.W.; resources, A.C., S.W., J.R., K.M. and M.P.; data curation, A.C. and S.W.; writing–original draft preparation, A.C.; writing–review and editing, A.C., S.W., J.R., K.M. and M.P.; visualization, A.C. and S.W.; supervision, M.P.; funding acquisition, M.P.; project administration, M.P. Funding: The research reported in this paper has been supported by the National Science Centre, Poland, decision no. DEC-2017/25/B/ST7/02236. Acknowledgments: The authors are indebted to two anonymous reviewers for their precious comments and suggestions, which helped improve the paper. Conflicts of Interest: The authors declare no conflict of interest. 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Published: Mar 13, 2019

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