Control Activo Del Ruido Para Una Lavadora.pdf

Applied Acoustics 146 (2019) 89–95

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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust

Active noise control for a washing machine Krzysztof Mazur, Stanislaw Wrona ⇑, Marek Pawelczyk Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

a r t i c l e

i n f o

Article history: Received 5 July 2018 Received in revised form 20 September 2018 Accepted 6 November 2018

Keywords: Active noise control Adaptive control Active casing

a b s t r a c t An actively controlled thin barrier may provide better noise reduction results than common passive solutions. The performance of such active method has been confirmed by the authors using a dedicated noisecancelling laboratory casing. Now, such approach is developed and applied to a real device casing, what is a significant step toward commercialisation of the active casing method. An adaptive FXLMS algorithm with practical modifications is proposed for the active control of the casing to provide noise reduction. A feed-forward structure is used, with a reference microphone located inside the real device. Additionally, an Internal Model Control system with reference signal estimation is also implemented for a comparison. The performance of the resulting control systems is experimentally verified for a real washing machine (an off-the-shelf product), using a loudspeaker placed inside the washing machine to provide reproducible noise. Obtained results are reported and discussed. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction The use of active control for the whole device casing was initially proposed by Fuller et al. [1] and later significantly developed and implemented by the authors for a dedicated noise-cancelling rigid casing with steel frame [2], and for a light-weight casing [3,4]. When appropriately implemented, it results in a global noise reduction instead of only local zones of quiet at individual areas. There were, however, casings designed specifically for the active control purpose. In this paper, the proposed active casing method is developed and applied to an already existing real device casing, which was not designed for such purpose. According to the authors’ knowledge, it is a first successful realisation of an active control applied to a whole real device casing to reduce the device noise. It is a significant step toward commercialisation of the method. Many real devices use casings made of steel or aluminium, enabling the method to be applied. Vibroacoustic analysis of such structures is of scientific interest for many years, for instance power transformer casing [5]. The active control may be provided by loudspeakers located inside or outside the casing, or by mounting vibration actuators directly on the casing structure. In this paper, control by placing actuators on the casing is investigated, what is much more practical. This allows for control of walls considered as the primary sound transmission paths. The goal is to reduce noise generated ⇑ Corresponding author. E-mail addresses: [email protected] (K. Mazur), [email protected] (S. Wrona), [email protected] (M. Pawelczyk). https://doi.org/10.1016/j.apacoust.2018.11.010 0003-682X/Ó 2018 Elsevier Ltd. All rights reserved.

by the device globally in the room. Another possibility could be to use semi-active control of walls with shunt systems [6,7], what is out of the scope of this paper. The paper is organised as follows. Section 2 presents the adopted control algorithm with its practical modifications. A feed-forward structure is used, with a reference microphone located inside the real device. Additionally, an Internal Model Control system with reference signal estimation is also implemented for a comparison. In Section 3.1 the considered plant is described. The washing machine casing has different features, such as bending or embossing, not present in previously used dedicated noise-cancelling casings. It makes the task of actuators placement optimisation significantly more difficult. Device noise characteristics are also given. Then, Section 3.2 is devoted to the implemented control system, including hardware details. Afterwards, in Section 3.3 the obtained experimental results are presented and discussed. Finally, advantages and limits of the proposed approach are pointed out and conclusions for future research are drawn. 2. Control algorithm The goal of the control system is to globally reduce noise emitted by the device. Due to structure of the system, where the casing is between sound source and the observer, local noise reduction at error microphones actually provides global noise reduction, limiting the noise emission to the surrounding environment. The control is provided by actuators mounted on the casing. Fig. 1 shows a simplified block diagram of the ANC system. The primary disturbance dðiÞ propagates through primary paths P to

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Fig. 1. ANC system block diagram.

error microphones, which provides error signals eðiÞ. The control system contributes to errors using control signals uðiÞ through secondary paths S. A feed-forward structure is used. The control system obtains the reference signal xðiÞ, by acquiring the primary disturbance by the reference microphone with its electroacoustic path X. Control system outputs also propagate to the reference microphone by acoustic feedback paths F. Their influence is miti^ The reference siggated by acoustic feedback elimination paths F. 1

nal is later filtered by adaptive filters Wðz Þ. Each actuator is controlled using an adaptive linear finite impulse response filter: T

up;c ði þ 1Þ ¼ wp;c ðiÞ xu ðiÞ;

ð1Þ T

where wp;c ðiÞ ¼ ½wp;c;0 ðiÞ; wp;c;1 ðiÞ; . . . ; wp;c;NW 1 ðiÞ is a vector of parameters of the control filter for the c-th actuator on the p-th T

wall, xu ðiÞ ¼ ½xðiÞ; xði  1Þ; . . . ; xði  ðN W  1ÞÞ is a vector of regressors of the reference signal xðiÞ, and the N W is the number of parameters of each control filter. The reference signal xðiÞ is acquired by the reference microphone placed inside the casing, with acoustic feedback being eliminated:

xðiÞ ¼ xm ðiÞ 

p 1 P1 CX X

^f p;c ðiÞT up;c ðiÞ;

ð2Þ

p¼0 c¼0

T

up;c ðiÞ ¼ ½up;c ðiÞ; up;c ði  1Þ; . . . ; xp;c ði  ðNF  1ÞÞ is a vector of regressors of the c-th actuator of the p-th wall. NF is the number parameters of the acoustic feedback models. Due to high number of actuators and errors, the control filter coefficients are adapted using the Switched Error Leaky Filteredreference LMS algorithm with normalisation [8]:

wp;c ði þ 1Þ ¼ ð1  ln cÞwp;c ðiÞ  lp ðiÞrp;c;v ðiÞ ðiÞmðiÞev ðiÞ ðiÞ;

This algorithm significantly reduces the computational complexity compared to Multiple Error Filtered-reference LMS algorithm. In Eq. (3) ln is the normalised LMS step size, c is the leak factor, lp ðiÞ is the current LMS step size for the p-th wall, T

rp;c;v ðiÞ ðiÞ ¼ ½r p;c;v ðiÞ ðiÞ; r p;c;v ðiÞ ði  1Þ; . . . ; r p;c;v ðiÞ ði  ðN W  1ÞÞ is a vector of regressors of the filtered reference, mðiÞ is the mask signal equal to 0 or 1 used to disable adaptation when the rp;c;v ðiÞ vector is not fully filled yet after v ðiÞ change [8], v ðiÞ is the currently selected error signal, selected in a round-robin fashion [9]:

v ðiÞ ¼

  i modNE ; NI

ð4Þ

where N I is the period of error switching, and NE is the number of error signals. The filtered reference signals are obtained as:

rp;c;v ðiÞ ðiÞ ¼ ^sp;c;v ðiÞ ðiÞ xr ; T

where xm ðiÞ is the signal from the reference microphone, P is the number of controlled walls and C p is the number of actuators on the p-th wall, ^f p;c ðiÞ ¼ ½^f p;c;0 ðiÞ; ^f p;c;1 ðiÞ; . . . ; ^f p;c;N 1 ðiÞ is the model of F

acoustic feedback path from c-th actuator on p-th wall, and

ð3Þ

ð5Þ T

where xr ¼ ½xðiÞ; xði  1Þ; . . . ; xði  ðN S  1ÞÞ is a vector of regres^sp;c;v ðiÞ ðiÞ ¼ sors of the reference signal, ½^sp;c;v ðiÞ;0 ðiÞ; ^sp;c;v ðiÞ;1 ðiÞ; . . . ; ^sp;c;v ðiÞ;NS 1 ðiÞ is the model of the secondary

K. Mazur et al. / Applied Acoustics 146 (2019) 89–95

path from the c-th actuator on the p-th wall to the v ðiÞ-th error signal, and N S is the number of parameters of the model secondary path models. There are various variable-step LMS algorithms [10], which provide faster adaptation for different noise signals than the fixed-step size LMS algorithm. In this paper, the Normalised LMS-based approach is used. The current LMS step size is obtained as:

lp ðiÞ ¼

ln

Pp ðiÞ þ f

;

ð6Þ

where P p is an estimated filtered reference signals total power [8] and f is a small constant used to avoid division by zero if the estimated power is zero. 3. Experimental results 3.1. Plant For experimental verification, an off-the-shelf washing machine is used. The washing machine generates the loudest noise during spinning. In that phase a major part of the generated noise is a low frequency noise related to the drum rotations, up to 1200 rpm in used washing machine. Such low frequency noise caused by rotational parts is common in a number of industrial devices. Fig. 2a shows the washing machine used for experiments. The washing machine casing has different features, such as bending or embossing, not present in previously used dedicated noise-cancelling casings (see a schematic representation given in Fig. 2b). It makes the task of mathematical modelling of casing walls significantly more difficult. To handle it, a model based on the Mindlin plate theory is used, with its parameters identified (fitted) by a memetic algorithm. The model also includes the impact of inertial actuators’ masses used for active control. It is solved utilising the Rayleigh-Ritz assumed mode-shape method. Due to real (and hence imperfect) mountings of each of the casing walls, boundary conditions elastically restrained against both rotation and translation are employed. For a more detailed derivation of the model, the reader is referred to [11]. The model assumes that

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the walls are independent. Without that assumption the model is much more complex, even when a rigid frame is assumed [12]. The obtained model was employed for the process of optimisation of arrangement of actuators on the washing machine casing. The system is infinite dimensional and only approximate controllability can be obtained. The approximate controllability of such systems are extensively studied in [13–15]. In this paper the goal is to maximise the controllability of eigenmodes in the frequency range up to 300 Hz. Each wall is evaluated in this process separately, therefore it is performed in the similar manner as in [11], where the individual walls of the light-weight casing were considered. The optimisation itself is performed with a memetic algorithm. The optimisation variables are the coordinates of actuators on the plate surface. What complicates the process, is that the mathematical model is recalculated each time, when different arrangement of actuators is evaluated (as the actuators’ mass is taken into account in the plate model). The optimisation index J is a measure of controllability of the least controllable mode:

J ¼ minkc;i ; i

ð7Þ

where kc;i is the i-th diagonal element of the controllability Gramian matrix, corresponding to the i-th eigenmode [11]. Depending on the number of eigenmodes included in the given frequency range, different number of eigenmodes was considered for each wall of the casing. More detailed description of the optimisation process is given in [11]. Thirteen 5 Watt electrodynamic actuators were considered in total to be placed on the casing (four on top wall and three on each other controlled wall). The bottom and back walls are not actively controlled. The obtained arrangement of actuators is presented in Fig. 3. As the pair of walls is symmetrical (left and right), a symmetrical configuration is employed for the pair. Fig. 4 shows obtained amplitude response of secondary paths from actuators on the Front plate to the error microphone located in front of the Front plate. The operational frequency range of the actuators is limited by two factors. For low frequencies below approximately 50 Hz the employed inertial actuators are inefficient to properly excite the casing. On the other hand, the upper frequency limit above approximately 600 Hz is obtained due to

Fig. 2. A photograph and a schematic representation of the washing machine casing. All dimensions are given in [mm].

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Fig. 3. Arrangement of actuators on the washing machine casing walls. A pair of walls are symmetrical (left and right), hence only one of them is presented.

Fig. 4. Amplitude response of secondary paths from actuators on the Front plate to the error microphone located in front of the Front plate.

the utilised antialiasing filters (the adopted sampling frequency is equal to 2000 Hz and the filters have a wide transition band to limit the introduced phase delays). Inside the washing machine a reference microphone is placed. The washing machine is placed inside a laboratory room (Fig. 5). Four error microphones located in front of each wall are placed at the distance of 0.5 m. Additionally 5 monitoring microphones, M0– M4, are placed inside the room. The primary goal of the system is to reduce the noise generated by the washing machine during the spinning, the loudest stage of the washing cycle. The tested washing machine performs spinning nominally up to 1200 rpm. For the sake of the highest sound pressure level, 1200 rpm spinning speed is used. Fig. 6 shows the spec-

Fig. 5. The position of the washing machine and microphones in the laboratory room.

trogram of the whole 1200 rpm spinning cycle. The drum is spinning at different speeds in the whole cycle. For experiments, only the part, where the drum is spinning at full speed was used. It is the part where the highest sound pressure level was observed. To provide reproducible noise for comparing different algorithms and parameters a small loudspeaker was placed inside the

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is for the low frequencies, where the loudspeaker is unable to reproduce them. Correcting this would result in much lower obtainable sound pressure level, due to poor loudspeaker efficiency for the low frequencies. The spinning noise signal spectrum contains mostly harmonics of the spinning frequency of 19 Hz, slightly lower frequency than nominal 20 Hz for 1200 rpm. This makes a feedback approach as a possible alternative to feed-forward control. The proposed feedforward approach is, thus, compared to an IMC feedback system, with the same topology, and the only difference is the source of the reference signal: in the feed-forward approach the microphone placed in the washing machine is used, and in the IMC approach the reference signal is acquired from the Front error microphone. The spinning noise has also the 105–115 Hz band noise component. This corresponds to the frequency band, where the noise transmission of the casing without control is the highest.

3.2. Control system Fig. 6. Spectrogram for 1200 rpm spinning cycle.

Table 1 shows parameters of the control system. The number of parameters in the feedback model N F was selected based on impulse responses of the secondary paths for IMC. For feedforward approach the number of parameters could be 128 without noticeable difference in performance. The number of parameters in the secondary path models N S was selected based on impulse responses of the secondary paths, however, smaller number than N F have been selected, sufficient for stable operation. For comparison, an IMC system was also tested. The only difference in the control algorithm described in the Control algorithm section is the reference signal source, instead of reference microphone, the Front error microphone is used. Eq. 2 takes the form:

xðiÞ ¼ e0 ðiÞ 

p 1 P 1 CX X ^sp;c;0 ðiÞT up;c ðiÞ;

ð8Þ

p¼0 c¼0

Fig. 7. The washing machine spinning noise spectrum at 1200 rpm (nominally), recorded and reproduced.

washing machine drum. Firstly, the spinning noise with loaded machine was recorded and then for experiments it was reproduced by the loudspeaker. The loudspeaker transfer function is not corrected and the reproduced sound is different. Fig. 7 shows the recorded and reproduced spinning noise. The highest difference

The control algorithm was implemented using a system with four dSPACE DS1104 boards, one board per controlled wall. All ADCs and DACs were synchronised using an external trigger signal, generated by one board. All boards have been placed on a shared PCI (Pheripheral Component Interconnect) bus. All data between boards, including reference signal error signals and data needed for acoustic feedback elimination, was transmitted digitally through this bus. The sampling frequency of the control algorithm

Table 1 Parameters of the control system. NS 128

NW 128

NF 256

NI 256

NE 4

P 4

l

c

0.001

f

10

3

6

10

C 0 to C 2

C3

3

4

Table 2 The microphones signal levels for a different disturbances for different control strategies (F — Front, R — Right, L — Left, T — Top). F [dB]

R [dB]

L [dB]

Without control Feed-forward IMC

73.2 63.8 66.4

79.1 69.8 71.9

79.7 67.0 72.1

Without control Feed-forward IMC

78.0 55.7 53.9

84.9 63.2 62.5

85.0 55.4 55.0

T [dB]

M0 [dB]

M1 [dB]

M2 [dB]

M3 [dB]

M4 [dB]

69.9 59.5 62.9

62.8 57.4 60.1

67.0 58.3 60.1

64.0 57.6 61.2

65.4 60.8 62.6

113 Hz tonal disturbance 71.6 75.4 53.0 57.9 53.6 54.5

67.8 56.0 53.2

73.1 57.4 53.9

67.3 57.4 54.7

68.8 58.2 56.9

1200 rpm spinning 72.9 65.1 68.5

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Fig. 8. Power spectral densities of signals from microphones for reproduced spinning noise at 1200 rpm.

was 2 kHz. The control system is based on earlier implementation by the authors for the dedicated active noise-cancelling casing, details of the implementation of that system are available in [16]. 3.3. Results

Fig. 9. Power spectral densities of signals from Front microphone for 113 Hz tone.

Table 2 shows the SPL at all microphones for different control strategies and different disturbances. For the spinning noise the average sound pressure reduction at monitoring microphones is equal to 7.4 dB for the feed-forward system, and 4.7 dB for the IMC system. For tonal signals even higher global noise reduction levels are obtained. For instance, for 113 Hz (the 6-th, dominant, harmonics of the spinning noise) the control system is able to reduce noise by more than 13 dB on average. Fig. 8 shows the PSDs of signals from microphones for both proposed feed-forward approach and also IMC approach. The feed-

K. Mazur et al. / Applied Acoustics 146 (2019) 89–95

forward system performed much better than the IMC system. The noise turns out to be too difficult to predict for the IMC system. It has been found that the casing of the washing machine behaves nonlinearly, mostly due to nonlinear vibrations on panel edges. Such behaviour is slightly visible on spinning noise, but it can also be heard. This effect is clearly visible on simple tonal primary disturbance (Fig. 9). In such case the feed-forward system is unable to reduce noise generated by nonlinearities. The reference signal is obtained inside the casing, where harmonic frequencies are nearly not noticeable (the harmonic frequencies are not present in the reference signal). The IMC approach is more able to limit the generated harmonics, as they are present in the reference signal, which is estimated from a signal acquired outside the casing. Non-linear control filters that are linear with respect to parameters might be used to improve performance in that case. An alternative is to use fully non-linear control filters, such as neutral networks [17,18]. However in that case the adaptation, especially online adaptation, is much more difficult. The IMC system due to feedback actually performs better in that case, the average SPL on monitoring microphones in case of IMC system is equal to 16.4 dB, and the feed-forward system achieves 13.7 dB in that case. 4. Conclusions An adaptive active noise control system has been proposed for reduction of noise transmitted through a real device casing. Its operation has been experimentally verified on an unmodified (except for adding actuators) off-the-shelf washing machine. The feed-forward active control solution provides good global noise reduction of more than 7 dB on average at monitoring microphones located around the room, for the reproduced spinning noise. This noise reduction is about 3 dB higher than in case of feedback approach, mostly due to presence of non-tonal, hard to predict, components in the noise spectrum. On the other hand, for the 113 Hz tonal disturbance it is the opposite — the IMC approach performs better than the feed-forward control. Pure tonal or multi-tone disturbances can be easily predicted, hence the IMC provides better performance than for the spinning noise. Very high noise reduction levels can be obtained, reaching more than 10 dB globally in the entire room space. Also, the IMC approach is able to limit the generated harmonics, as they are present in the reference signal, which is estimated based on an error signal acquired outside the casing. For a feedforward control it is more difficult to reduce the harmonic frequencies, as the reference signal is obtained inside the casing, where the harmonics are nearly not noticeable (the harmonic frequencies are not present in the reference signal). It is worth mentioning that the noise reduction level may differ at different locations in the room. It is due to the fact that higher noise reduction levels are possible achieve at locations, where the primary noise is stronger without control. Moreover, it is worth emphasising that the noise is practically never enhanced. It means that the noise emission is reduced instead of creating only local zones of quiet. It is a great advantage comparing to a classical ANC with loudspeakers. Such results show that the active noise-cancelling casing approach can be successfully used not only on dedicated casings, but also on device’s casing. It is an important step toward successful commercial applications of the active casing method.

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Acknowledgements The authors are indebted to anonymous reviewers for their precious comments and suggestions, which helped improving the paper. The research reported in this paper has been supported by the National Science Centre, decision No. DEC-2017/25/B/ST7/02236, and by the Ministry of Higher Education and Science. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.apacoust.2018.11. 010. References [1] Fuller C, Mcloughlin M, Hildebrand S, Active acoustic transmission loss box, wO Patent App. PCT/US1992/008,401 (Apr. 28 1994). URL: http:// www.google.com/patents/WO1994009484A1?cl=en. [2] Mazur K, Pawelczyk M. Active control of noise emitted from a device casing. In: Proceedings of the 22nd International Congress of Sound and Vibration, Florence, Italy. [3] Mazur K, Pawelczyk M. Internal model control for a light-weight active noisereducing casing. Arch Acoust 2016;41(2):315–22. [4] Mazur K, Pawelczyk M. Virtual microphone control for a light-weight active noise-reducing casing. In: Proceedings of the 23nd International Congress of Sound and Vibration, Athens, Greece. [5] Rdzanek WP, Zawieska WM. Vibroacoustic analysis of a simply supported rectangular plate of a power transformer casing. Arch Acoust 2003;28 (2):117–25. [6] Pietrzko SJ. Contributions to noise and vibration control technology. Kraków: AGH—University of Science and Technology Press; 2009. [7] Mao Q, Pietrzko S. Control of noise and structural vibration. Springer; 2013. [8] Mazur K, Pawelczyk M. Virtual microphone control for an active noisecancelling casing. Solid State Phenomena 2016;248:57–66. [9] Michalczyk M, Wieczorek M. Parameterization of adaptive control algorithms for multi-channel active noise control system. 58th Open Seminar on Acoustics joint with 2nd Polish-German Structured Conference on Acoustics, Jurata, Poland, vol. 2. p. 73–8. [10] Bismor D, Czyz K, Ogonowski Z. Review and comparison of variable step-size LMS algorithms. Int J Acoust Vib 2016;21(1). [11] Wrona S, Pawelczyk M. Optimal placement of actuators for active structural acoustic control of a light-weight device casing. In: Proceedings of the 23nd International Congress of Sound and Vibration, Athens, Greece. [12] Wyrwal J, Zawiski R, Pawelczyk M, Klamka J. Modelling of coupled vibroacoustic interactions in an active casing for the purpose of control. Appl Math Model 2017;50:219–36. https://doi.org/10.1016/j.apm.2017.05.002. [13] Klamka J, Wyrwal J, Approximate controllability of stochastic nonlinear infinite dimensional systems. A short survey, in: 2016 21st International Conference on Methods and Models in Automation and Robotics (MMAR), 2016, pp. 505–510, 21st International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, POLAND, AUG 29-SEP 01; 2016. [14] Wyrwal J. Approximate controllability of infinite dimensional system with internal damping dependent on fractional powers of system operator. IET Control Theory Appl 2016;10(18):2370–7. https://doi.org/10.1049/ietcta.2016.0611. [15] Klamka J, Wyrwal J, Zawiski R. On controllability of second order dynamical systems – a survey. Bull Polish Acad Sci Tech Sci 2017;65(3):279–95. https:// doi.org/10.1515/bpasts-2017-0032. [16] 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;98:877–89. https://doi.org/10.1016/j.ymssp.2017.05.025. [17] Snyder SD, Tanaka N. Active control of vibration using a neural network. IEEE Trans Neural Netw 1995;6(4):819–28. [18] Cupial P, Lacny L. Neural network control design considerations for the active damping of a smart beam. J Theor Appl Mech 2015;53(4):767–74.