Evaluation of low cost microphones for active noise control in duct

2.1. Feedforward control

In ventilation and exhaust systems a wide range of broadband noise is produced in their ducts. Such systems are evaluated by the construction of similar systems in laboratories compounds commonly by a noise source (noise generator), a reference sensor (microphone), an actuator (speaker), an error sensor (microphone) and an electronic of control. In Fig. 2 we define each component of an ANC system and acoustic systems involved.

Fig. 2Diagram of a feedforward controller broadband

Where $x\left(n\right)$ is the reference signal of the controller, $y\left(n\right)$ is the controller output signal, $e\left(n\right)$ the error signal, $P\left(z\right)$ the transfer function between the noise source and the microphone error (primary path), $S\left(z\right)$ is the transfer function between the actuator and the error microphone (secondary path) and $F\left(z\right)$ is the transfer function between the actuator and the reference microphone (feedback path).

As shown in this configuration, the reference microphone picks up unwanted signal at a later point the noise source, and generates $x\left(n\right)$, before this signal passes through the actuator. This signal $x\left(n\right)$ is processed by the ANC controller, which in turn generates a control signal $y\left(n\right)$ of equal amplitude and opposite phase of the incident signal, to the actuator. Where the signal $y\left(n\right)$, anti-noise, is used by the actuator to produce a canceling sound that attenuates the primary acoustic noise in the duct. The error microphone generates a signal $e\left(n\right)$ used to monitor controller performance.

The basic principle of feedforward control system is that the propagation delay of the sound wave between the reference microphone and speaker, offers sufficient time to calculate the control and activate the anti-noise, thus causing the cancellation. So that the distance between the reference microphone and canceling speaker satisfies the principle of causality.

The main goal of the feedforward controller is to anticipate the physical phenomenon in a predictive way through the information captured by the reference sensor, so that the noise was canceled when going through error sensor.

2.2. Algorithm of adaptive filtering

Sensors and actuators are administered through an electronic unit (controller) designed for cancellation of unwanted noise in the plant, which is based on the principle of wave superposition. It mostly consists of generating an anti-noise same amplitude and opposite phase to the unwanted noise in order to cause the cancellation of the noisy signal at a given point or region of interest [5, 6].

Although conceptually simple, there are several difficulties to be overcome when installing this type of controller. Significant variations in environmental conditions and non-linearity of the sensors and actuators can hamper and even compromise the controller’s efficiency because introduce unwanted disturbances in the system [7] and change the algorithms of the transfer functions.

In an attempt to counteract these disturbances and alterations, the researchers developed the automatically adaptive controllers. These are inserted in adaptive filters in digital signal processors (DSPs) that promote, through adjustment of its coefficients, the noise reduction system [8, 9]. For this procedure, the filter normally used is the type Finite Impulse Response (FIR) and the mechanism normally used in the setting of the filter coefficients are versions of variants LMS (Least Mean Square) classic. In this case was used the LMS algorithm along with FxLMS algorithm.

The active noise control reached a stage of development such that commercial systems are now available in major practical applications [10].

6.1. Experimental procedure I – characterization of the microphone in the frequency domain

Characterize the frequency response curve of the microphones allows us to know the frequency range that each microphone works with more efficiency. For this, a methodology aimed at identifying and comparing the values obtained in decibels for each predetermined frequency has been prepared. The proposal is to sweep the entire range of frequency of the microphones, with emphasis on frequencies up to 500 Hz.

Using a calculation program the value of the reference sound pressure, so that the microphone PCB having, is $P_0=$ 0.16896. This value is used to calculate the SPL ($L_p$) of the other pre-set frequencies for all microphones in Eq. (2):

After the treatment all signs acquired in the measurements was generated Fig. 4.

Note that, as mentioned earlier, that the microphone to the PCB SPL frequency of 1000 Hz is equal to 100 dB. This enables comparison of different types of microphones studied, as reference in all other values to a single value. With it, you can see the sensitivity of each microphone, identifying the most sensitive microphone is the microphone PCB and less sensitive microphone is the microphone Bruel & Kjaer.

Another feature that should be highlighted is the stabilization of values of the NSP for all microphones in the frequency range 150-500 Hz, with a variation of 2 dB for PCB and Samson microphones, but the microphones electret and Bruel & Kajaer undergo a somewhat greater variation being 3 dB and 4 dB, respectively.

The analysis of the data shown in Fig. 4 concludes that all microphones can be used in an active noise control system.

Fig. 4SPL to the microphones in a study using the reference sound pressure P0

6.2. Experimental procedure I – application of ANC

The evaluation of the microphones in the application of ANC aims to identify which of the microphones have better performance for this type of application.

The main parameter to be analyzed in this experiment was the attenuation obtained by applying the ANC. This was done using a sound pressure meter calibrated.

As the variable under consideration is the attenuation that the ANC causes and this calculation is performed by SPL difference before and after application of the ANC, was standardized as would be the measurements performed with the sound pressure meter. Set the position of this unit as the end of the duct, directing your microphone into the duct. Two measurements were made, prior to application of the ANC and the other measuring after application and the stabilization of the ANC. Each measurement time is 2 minutes and the results are presented in the discussion below.

The last point to be made is that the background noise in the room where was installed the product about 50 dB at the time of measurement.

The Table 2 below shows the overall SPL obtained at each measurement, making the difference between the values obtained before and after applying the ANC and with this result the column labeled attenuation.

Observing the results, we note that all the microphones were able to mitigate the noise generated significantly, reaching levels close or equal to the background noise. Through the comparisons made by graphic confirms the decline in the SPL in octave band whose center frequency is 250 Hz, regardless of microphone used. This directly influences the results presented in Table 2, because the value of the global SPL depends on the value of the SPL presented in each band.