Active Noise Control of a Forest Machine Cabin

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Institutionen för systemteknik

Department of Electrical Engineering

Examensarbete

Active Noise Control of a Forest Machine Cabin

Examensarbete utfört i Reglerteknik vid Tekniska högskolan i Linköping

av

Patrik Grylin Mårten Hedborg

LITH-ISY-EX--07/4014--SE

Linköping 2007

Department of Electrical Engineering Linköpings tekniska högskola

Linköpings universitet Linköpings universitet

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Active Noise Control of a Forest Machine Cabin

Examensarbete utfört i Automatic Control

vid Tekniska högskolan i Linköping

av

Patrik Grylin Mårten Hedborg

LITH-ISY-EX--07/4014--SE

Handledare: Johan Sjöberg

isy, Linköpings universitet

Kjell Rönnholm

Komatsu Forest AB

Examinator: Fredrik Gustafsson

isy, Linköpings universitet

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Avdelning, Institution

Division, Department

Division of Automatic Control Department of Electrical Engineering Linköpings universitet

SE-581 83 Linköping, Sweden

Datum Date 2007-03-22 Språk Language Svenska/Swedish Engelska/English Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport

URL för elektronisk version

http://www.control.isy.liu.se http://www.ep.liu.se/2007/4014 ISBN — ISRN LITH-ISY-EX--07/4014--SE

Serietitel och serienummer

Title of series, numbering

ISSN

—

Titel

Title

Aktiv Bullerdämpning av Förarhytt på Skogsmaskin Active Noise Control of a Forest Machine Cabin

Författare

Author

Patrik Grylin Mårten Hedborg

Sammanfattning

Abstract

Today, a high noise level is considered a problem in many working environments. The main reason is that it contributes to stress and fatigue. Traditional methods using passive noise control is only practicable for high frequencies. As a comple-ment to passive noise control, active noise control (ANC) can be used to reduce low frequency noise. The main idea of ANC is to use destructive interference of waves to cancel disturbing noises.

The purpose of this thesis is to design and implement an ANC system in the driver’s cabin of a Valmet 890 forest machine. The engine boom is one of the most disturbing noises and therefore the main subjective for the ANC system to suppress.

The ANC system is implemented on a Texas Instrument DSP development starter kit. Diﬀerent FxLMS algorithms are evaluated with feedback and feedfor-ward conﬁgurations.

The results indicate that an ANC system signiﬁcantly reduces the sound pressure level (SPL) in the cabin. Best performance of the evaluated systems is achieved for the feedforward FxLMS system. For a commonly used engine speed of 1500 rpm, the SPL is reduced with17 dB. The results show fast enough convergence and global suppression of low frequency noise.

Nyckelord

Keywords Active Noise Cancellation, Adaptive Filtering, Active Noise Control, Feedforward, Feedback, Active Noise Reduction

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Abstract

Today, a high noise level is considered a problem in many working environments. The main reason is that it contributes to stress and fatigue. Traditional methods using passive noise control is only practicable for high frequencies. As a comple-ment to passive noise control, active noise control (ANC) can be used to reduce low frequency noise. The main idea of ANC is to use destructive interference of waves to cancel disturbing noises.

The purpose of this thesis is to design and implement an ANC system in the driver’s cabin of a Valmet 890 forest machine. The engine boom is one of the most disturbing noises and therefore the main subjective for the ANC system to suppress.

The ANC system is implemented on a Texas Instrument DSP development starter kit. Diﬀerent FxLMS algorithms are evaluated with feedback and feedforward conﬁgurations.

The results indicate that an ANC system signiﬁcantly reduces the sound pressure level (SPL) in the cabin. Best performance of the evaluated systems is achieved for the feedforward FxLMS system. For a commonly used engine speed of 1500 rpm, the SPL is reduced with 17 dB. The results show fast enough convergence and global suppression of low frequency noise.

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Acknowledgments

First of all, we would like to express our gratitude to Fredrik Gustafsson and Jo-han Sjöberg at Linköping university. Of course, for their help during our master’s thesis but most of all for being excellent and inspiring teachers.

Kjell Rönnholm, Per Holmberg, Per Hedström and others - building the world’s best forest machines - for help and support during our time at Komatsu Forest. Mårten Nygren for kickstarting our project with valuable comments and sugges-tions.

Josse, grandpa Lasse, Fredrik & Co, Oscar G. & Kent P. at the division of Elec-tronic Systems, Y3c, Kuratorvägen and Uno-x in Bjurholm deserves to be men-tioned as well.

Patrik Grylin and Mårten Hedborg

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Introduction

1.1 Background

Today, a high noise level is considered a problem in many working environments. The main reason is that it contributes to stress and fatigue [3]. Traditional meth-ods using passive noise control are only practicable for high frequencies. The reason is that low frequency noise has long wavelengths compared to a typical acoustic absorber [4]. As a complement to passive noise control, active noise con-trol (ANC) can be used to reduce low frequency noise. The main idea of ANC is to use destructive interference of waves to cancel disturbing noises. The theory of ANC has been known for a long time but it is the development of fast digital signal processors (DSP:s) that have made practical applications feasible.

1.2 Purpose

The purpose of this thesis is to reduce the noise level in the driver’s cabin of a Valmet 890 forest machine, see Figure 1.1, by using an ANC system. One of the most disturbing noises is the engine boom which is the main noise to be suppressed by the ANC system.

1.3 Method

The project was divided into four main parts:

Literature studies: Old reports and articles concerning ANC were examined for

ideas and knowledge.

Design of a prototype: To be able to build a prototype, system hardware had

to be speciﬁed.

Implementation: ANC algorithms were implemented in a DSP. Evaluation: The algorithms were evaluated online in the cabin.

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2 Introduction

Figure 1.1. Valmet 890.

1.4 The concept of ANC

The concept of ANC is to cancel a disturbing primary noise by generating an anti noise of equal amplitude and opposite phase. The primary noise combined with the anti noise results in a cancellation of both noises. To generate the anti noise, two main configurations of ANC systems are often used, feedforward and feedback control, both using adaptive filters [4, 9]. For a feedforward ANC system two sensors are used. First a reference sensor is used to get a reference signal and second an error sensor is used to update the adaptive filter by measuring the residual of the anti noise and primary noise, see Figure 1.2. The feedback ANC system uses only one sensor, namely an error sensor. This sensor is used both to create the reference signal and to update the adaptive filter, see Figure 1.3. Both feedforward and feedback configurations will be evaluated in this thesis.

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1.5 Thesis outline 3

ANC Algorithm

Error Sensor Reference Sensor

Primary Noise Anti-Noise

Figure 1.2. An ANC feedforward system.

ANC Algorithm

Error Sensor Primary Noise Anti-Noise

Figure 1.3. An ANC feedback system.

1.5 Thesis outline

Chapter 1 An introduction to the thesis where the background and purpose are

presented.

Chapter 2 Fundamental principles for active noise control are introduced. Chapter 3 A presentation of ANC adaptive theory is given.

Chapter 4 The implementation of the system in a DSP is discussed. Chapter 5 The results of the work are given.

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4 Introduction

1.6 Nomenclature

1.6.1 Signals

x(n) Reference signal

d(n) Primary noise at the error sensor position

y(n) Adaptive ﬁlter output

y(n) Adaptive ﬁlter output after passing through a secondary path

e(n) Error signal

x(n) Reference signal after passing through a secondary path estimation

e0(n) Gaussian random noise

v(n) Generated Gaussian random noise

u(n) Low pass ﬁltered input for system identiﬁcation

y(n) u(n) after passing through a secondary path including unwanted noise X(z) Z -transform of reference signal

E(z) Z -transform of error signal

1.6.2 Transfer functions

P (z) Primary path

F (z) General ﬁlter

S(z) Secondary path

ˆ

S(z) Secondary path estimation ˆ

S(z|s) Secondary path estimation during its identiﬁcation

W (z|w) FIR ﬁlter

H(z) Transfer function representing unwanted noise, driven by Gaussian random noise

LP (z) Low-pass ﬁlter

1.6.3 Impulse responses, ﬁlter parameters

w, w(n) Filter parameters of W (z|w) s(n) Impulse response of S(z) p(n) Impulse response of P (z) ˆs(n) Impulse response of ˆS(z) ˆs Filter parameters of ˆS(z) s Filter parameters of ˆS(z|s)

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1.6 Nomenclature 5

1.6.4 Constants

µ Step size

α Very small number

γ Leaky constant

ν 1 − µγ

N Number of parameters in w(n)

J Number of reference sensors

M Number of error sensors

K Number of secondary sources

nτ Time delay of secondary path

Mτ Number of delays for calculating cross correlation

Nτ Number of samples when calculating cross correlation

1.6.5 Abbreviations

AD Analog Digital

ANC Active Noise Control

BIOS Basic Input Output System

CCStudio Code Composer Studio

CPU Central Processing Unit

DA Digital Analog

DRAM Dynamic Random Access Memory

DSK Development Starter Kit

DSP Digital Signal Processor

EDMA Enhanced Direct Memory Access

FIR Finite Impulse Response

FxLMS Filtered x Least Mean Square

LMS Least Mean Square

McBSP Multi Channel Buﬀered Serial Port

MC-FxLMS Multi Channel Filtered x Least Mean Square

MSE Mean Square Error

NLMS Normalized Least Mean Square

rpm Revolutions Per Minute

SPL Sound Pressure Level

TI Texas Instruments

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Chapter 2

ANC principles

In this chapter fundamental ANC principles and phenomenas are introduced.

2.1 Acoustics

2.1.1 Wave equation

A three dimensional harmonic wave can be expressed as

ψ(r, t) = Aek·r−ωt (2.1)

with angle velocity ω, time t, and

k· r = k_x_{x + k}_y_{y + k}_z_z (2.2)

where (kx, ky, kz) are the components of the propagation direction and (x, y, z) are the components of the point in space where the displacement ψ is evaluated. The diﬀerential wave equation satisﬁed by the harmonic wave (2.1) is given by

∇2_{ψ −} 1

c20

δ2ψ

δt2 = 0 (2.3)

where the Laplacian operator is deﬁned as

∇2_{= δ}2 δx2 + δ 2 δy2 + δ 2 δz2 (2.4)

and c0 is the propagation speed in air. More information about wave equations

can for example be found in [12].

2.1.2 Principle of superposition

The fundamental physical phenomena making an ANC system possible is the principle of superposition. The principle of superposition states that a linear

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8 ANC principles

combination of solutions is also a solution to the same linear system. To be more legible, if ψ1 and ψ2 are independent solutions of the wave equation (2.3), then the linear combination

ψ = aψ1+ bψ2 (2.5)

where a and b are constants, is also a solution [12].

Since the propagation of an acoustic wave is described fairly well by (2.3) also in practise, it is possible to use an anti noise of equal amplitude and opposite phase, see Figure 2.1.

Hence the objective for an ANC system is to measure the primary noise and generate the anti noise.

0 1 2 3 4 5 6 7 8 9 10 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 Primary noise Secondary noise

Primary noise + Secondary noise

Figure 2.1. Principle of superposition.

2.2 Feedforward system overview

In Figure 2.2, an overview of an ANC feedforward system is illustrated. The summation junction in the block diagram represents an acoustic superposition of sound waves.

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2.2 Feedforward system overview 9

P (z)

F (z)

S(z)

Σ − x(n) y(n) d(n) y(n) e(n)

Electrical domain Acoustical domain

Figure 2.2. Overview of an ANC feedforward system.

2.2.1 Primary path

The primary path P (z) is the acoustic transfer function from the reference sensor close to the noise source, to the error sensor at the point where the ANC system is operating. The primary noise being measured in an upstream position is referred to as x(n) and the primary noise at the error sensors is referred to as d(n).

2.2.2 Secondary path

The secondary path S(z) describes the transfer function from the ﬁlter output

y(n) to y(n), the acoustic point where the error sensor is placed. This transfer

function includes computer system delays, ampliﬁer and speaker dynamics and the acoustic path between speaker and error sensor. The speaker generating the anti noise is often referred to as the secondary source.

2.2.3 Digital ﬁlter

The noise x(n) is usually measured with a microphone and used by the digital ﬁlter

F (z) as a reference signal. As an output, the digital ﬁlter produces the signal y(n)

which is phase shifted and driven through the secondary source to become y(n) at the point where to cancel out d(n). The acoustic signal y(n) is often referred to as the anti noise or secondary noise. The error signal e(n) = d(n) − y(n) at this point is measured with a microphone and used by the digital ﬁlter to improve the estimation y(n).

In general, the digital filter F (z) contains an estimation W (z|w) of the trans-fer function P (z)S−1(z) and an adaptive algorithm which derives the estimated parameters w. The estimation W (z|w) is normally a finite impulse response (FIR) filter, that is a standard filter in acoustic path modeling [6], see Section 3.1.

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10 ANC principles

To improve F (z), other subsystems such as an estimation of S(z) are often in-cluded and some are described in Section 3.

A fundamental system limitation

For a feedforward system, the time delay of P (z) has to be longer then the time delay of F (z) and S(z). If this causality condition is met, the ANC system is capa-ble of cancelling random broad-band noise. Otherwise, only predictacapa-ble periodic noise can be cancelled out.

2.3 Feedback system overview

In Figure 2.3, an overview of an ANC feedback system is illustrated. The diﬀerence from a feedforward system is that no reference sensor is used and thus no primary path exists. Instead an internal synthesized reference signal is used to generate y(n), see Section 3.4.

F (z)

S(z)

Σ − d(n) y(n) y(n) e(n)

Electrical domain Acoustical domain

Figure 2.3. Overview of an ANC feedback system.

2.3.1 Secondary path

As for the feedforward system, a secondary path exists for the feedback system. For more information, see Section 2.2.2

2.3.2 Digital ﬁlter

The digital ﬁlter works the same way as in a feedforward system, see Section 2.2.3. The main diﬀerence is that the reference signal is synthesized instead of measured from a reference microphone.

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2.3 Feedback system overview 11

A fundamental system limitation

Since no reference signal from the primary noise exists in a feedback system, good performance is only achieved for periodic noise.

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Chapter 3

ANC adaptive ﬁlter theory

Here diﬀerent adaptive ﬁlter algorithms for ANC applications are presented.

3.1 Finite Impulse Response

The most commonly used filter for ANC applications is the FIR filter. The as-sumption of a FIR filter is that the output y(n) depends on a weighted combination of a finite number N of past input values x(n), expressed as

y(n) =

N i=0

wix(n − i) (3.1)

A FIR ﬁlter has a number of useful properties, e.g., all poles are at the origin which means that it is bounded input bounded output (BIBO) stable [5].

3.2 Least Mean Square

In this section the least mean square (LMS) algorithm for a system using a single reference input, a single error sensor and a single secondary source is derived. A FIR filter W (z|w) of order N and the signal definitions according to Figure 3.1 are used. Assume that the output of the filter is given as

y(n) = x(n)Tw(n) (3.2)

where

x(n) =_{x(n − 1), ..., x(n − N )}T (3.3) and

w(n) =_w₁(n), w₂(n), ..., wN(n)T_. (3.4) Using (3.3) and (3.4), an expression for the error signal can be found as

e(n) = d(n) − y(n) = d(n) − s(n) ∗ [x(n)Tw(n)] (3.5) 13

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14 ANC adaptive ﬁlter theory

P (z)

W (z|w)

LMS

S(z)

Σ − x(n) y(n) d(n) y(n) e(n)

Electrical domain Acoustic domain

Figure 3.1. Block diagram of a feedforward LMS system.

where s(n) is the impulse response of the transfer function S(z). The primary dis-turbance signal is given by d(n) = p(n) ∗ x(n), where p(n) is the impulse response of P (z), and the secondary noise is given by y(n) = s(n) ∗ y(n).

Assuming a mean square error (MSE) as a theoretical cost function

V (w) = E{e2(n)} (3.6)

the LMS-algorithm minimizes an estimation of (3.6), that is, ˆ

V (w) = e2(n). (3.7)

Using the steepest descent algorithm the LMS-algorithm is ﬁnally given by

w(n + 1) = w(n) −µ

2

d ˆV (w)

dw (3.8)

where µ is the step size, see Section 3.2.1. An example of the steepest descent algorithm is illustrated in Figure 3.2.

3.2.1 Normalized LMS

The step size, µ in (3.8), is a design parameter that aﬀects the convergence rate and the MSE. Large step sizes increase the convergence rate but will also result in an increased MSE, while small step sizes lead to small MSE but slow convergence rate. To decrease the inﬂuence of the amplitudes of x(n) and d(n), µ is normalized

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3.2 Least Mean Square 15 −50 0 50 −50 0 50 0 1000 2000 3000 4000 5000 w₁ w2 V(w)

Figure 3.2. Convergence of ˆV (w) towards the global optimum using LMS for a FIR

filter of order 2.

by the energy of x(n) i.e.

µ(n) = µ

α + xT(n)x(n) (3.9)

often referred to as normalized LMS (NLMS). To prevent singularities when

xT(n)x(n) is very small, a small number α is introduced.

3.2.2 Leaky LMS

ANC systems are often overloading their secondary sources, making the system nonlinear. Instead of introducing output power constraints, a modiﬁed cost func-tion

ˆ

Vl(w) = e2(n) + γwT(n)w(n) (3.10) including the weighted filter parameters can be used. This approach has several advantages. It has a stabilizing effect on the adaptive filter, and in finite-precision implementations it reduces numerical errors [9]. Using (3.8) and (3.10), the up-dating algorithm of the leaky LMS filter parameters become

w(n + 1) = νw(n) −µ

2d ˆV (w)_dw (3.11)

where

ν = 1 − γµ. (3.12)

A disadvantage with introducing the leaky parameter, ν, is that it adds a bias error to the residual.

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3.3 Feedforward ﬁltered-x LMS

To be able to use the LMS algorithm (3.8) in an ANC application the system has to compensate for the effect of the secondary path transfer function. Otherwise, when updating the filter parameters the error signal is not aligned in time with the reference signal and this will lead to instability [9]. An algorithm that com-pensates for this effect is derived below.

From (3.7) we obtain d ˆV (w) dw = de 2_(n) dw = 2[ de (n) dw ]e(n) (3.13)

and the diﬀerentiation of (3.5) yields

de(n)

dw = −s(n) ∗ x(n). (3.14)

Combining (3.8), (3.13) and (3.14) yields

w(n + 1) = w(n) −µ 2 d ˆV (w) dw = w(n) − µ 22 de (n) dw e(n) = w(n) + µ[s(n) ∗ x(n)]e(n). (3.15)

Here, the secondary path impulse response s(n) is not known and has to be esti-mated by ˆs(n).

By substituting s(n) with ˆs(n) and deﬁning

x(n) ˆs(n) ∗ x(n) =_x(n), ..., x(n − N + 1)T (3.16) the expression (3.15) can ﬁnally be written as

w(n + 1) = w(n) + µx(n)e(n) (3.17)

also known as the feedforward ﬁltered-x LMS (FxLMS) algorithm [11], illustrated in Figure 3.3. The z-transform of the error signal is

E(z) = [P (z) − S(z)W (z|w)]X(z) (3.18)

and to achieve a residual error equal to zero it is necessary that

W (z|w) = P (z)

S(z), (3.19)

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3.3 Feedforward ﬁltered-x LMS 17

P (z)

W (z|w)

LMS

ˆ

S(z)

Σ − x(n) y(n) d(n) y(n) x(n) e(n)

Figure 3.3. Block diagram of a feedforward FxLMS system.

3.3.1 Feedforward Multi Channel FxLMS

A commonly used notation for multi channel systems is J × M × K, meaning that J reference inputs, M error sensors and K secondary sources are used. In general, the theory for the single channel system can be applied on the multi dimensional case, but some functions have to be redeﬁned.

For a J × M × K system the FIR ﬁlter can be expressed as

yk(n) =

J j=1

xj(n)Tw(n)kj _{k = 1, 2, ..., K} (3.20)

and the cost function is approximated by ˆ V (w) = M m=1 e2_m(n). (3.21)

The parameters of the FIR ﬁlters will be updated according to

w_kj(n+1) = w_kj(n)+µ M m=1 x_jkm(n)e_m(n) k = 1, 2, ..., K; j = 1, 2, ..., J (3.22) where x_jkm(n) ˆs_mk(n) ∗ x_j(n) k = 1, 2, ..., K; m = 1, 2, ..., M. (3.23)

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The feedforward multi channel FxLMS (MC-FxLMS) system is illustrated in Fig-ure 3.4. The blockS represents M × K secondary path transfer functions Smk(z). The matrixP represents M × J primary path transfer functions Pmj(z) and the

K × J separate adaptive FIR ﬁlters are represented by W .

P

W

LMS

ˆS

S

Σ − x(n) J J y(n) K d(n) M y(n) M M x(n) J e(n)

Figure 3.4. Block diagram of a feedforward MC-FxLMS system.

3.4 Feedback FxLMS

A feedback FxLMS system is viewed as a feedforward FxLMS system that synte-sizes its own reference signal based on the adaptive ﬁlter output and error signal. The reference signal x(n) is synthesized as

x(n) = e(n) + ˆs(n) ∗ y(n) (3.24)

where ˆs(n) is the impulse response of ˆS(z), e(n) is the signal obtained from the

error sensor and y(n) is the secondary signal generated from the adaptive ﬁlter. In Figure 3.5, a feedback FxLMS system is illustrated.

If ˆS(z) = S(z) the z-transform of the error signal is

E(z) = [1 − S(z)W (z|w)]D(z) (3.25)

and the block diagram representing this equation is shown in Figure 3.6. In this way, the feedback problem has been transformed into a feedforward problem with

W (z|w) acting as a predictor for the primary noise d(n).

By viewing the feedback FxLMS system as in Figure 3.6 the importance of two statements made earlier is emphasized; the importance of a quality estimate of

S(z) and the need for d(n) to be predictable, see Section 3.3 and 2.3.2,

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3.4 Feedback FxLMS 19

W (z|w)

LMS

ˆ

S(z)

ˆ

S(z)

Σ − Σ d(n) y(n) y(n) x(n) x(n) _e(n)

Figure 3.5. Block diagram of a feedback FxLMS system.

S(z)

W (z)

LMS

Σ -d(n) e(n)

Figure 3.6. Equivalent block diagram to the system in Figure 3.5, under the assumption

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3.4.1 Feedback MC-FxLMS

Extending the earlier presented single channel FxLMS feedback methode to a mul-tiple channel feedback FxLMS system is fairly easy, see Figure (3.7).

A K × M feedback MC-FxLMS system consists of K × M secondary path trans-fer functions Smk(z) from the k:th secondary source to the m:th error sensor, estimated by the corresponding ﬁlter ˆSmk(z). To synthesize M reference signals

W

LMS

ˆS

S

ˆS

Σ − Σ d(n) M y(n) K y(n) M M x(n) x(n) M e(n)

Figure 3.7. Block diagram of a feedback MC-FxLMS system.

xm(n), M error signals em(n), M × K secondary path estimates ˆSmk(z) and K

secondary signals yk(n) are used according to

xm(n) = em(n) + K k=0 ˆsmk(n) ∗ yk(n) (3.26) where m = 1, 2, ..., M .

The coeﬃcients of the K × M adaptive ﬁlters Wkm(z) are updated by the MC-FxLMS algorithm similarly as in Section 3.3.1, for the special case J = M .

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3.5 Secondary path identiﬁcation 21

3.5 Secondary path identiﬁcation

Finding an estimate of the secondary path transfer function S(z) is done by system identification. As seen below, adaptive filtering is closely related to the wider subject of system identification.

LP (z)

White Noise Generator

H(z)

LMS

S(z)

ˆ

S(z|s)

Σ Σ − v(n) u(n) e0(n) y_(n) e(n)

Figure 3.8. Block diagram of a system estimating S(z) with ˆS(z|s).

There are several recursive identiﬁcation algorithms to choose between. A block diagram of a recursive LMS algorithm estimating S(z) with a FIR ﬁlter ˆS(z|s) is

shown in Figure 3.8.

3.5.1 Choosing an input signal u(n)

To identify the secondary path low-pass ﬁltered white noise is generated and driven through the secondary source. White noise is a random noise signal that has the same sound energy level at all frequencies, i.e., its spectrum can be written as

Φ(ω) = C, ∀ ω ∈ [0, ∞] (3.27)

where C is a constant. To assure that a proper model of the secondary path is derived for the lower frequencies, a low-pass ﬁlter is used to concentrate the energy to these frequencies [10]. The reason for this is explained below.

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trans-22 ANC adaptive ﬁlter theory form ˆ V (s) = e2(n) = _2π1 π −π Φe(ω)dω (3.28)

where Φ_e(ω) is the spectrum of the prediction errors {e(n)}. The system is given by

y(n) = S(z)u(n) + H(z)e0(n) (3.29)

where S(z) is the true system, u(n) are system inputs and unwanted noise is represented by H(z), a inversely stable monic1ﬁlter driven by white noise{e0(n)}.

Then, if u and e0 are independent, the following expressions are valid ˆs = arg min s ˆ V (θ) = arg min_s π −π

S(eiω_{) − ˆ}_S(eiω_|s)2_Q(ω)dω _(3.30)

Q(ω) = Φu(ω)

|H(eiω_)|2 (3.31)

where ˆs are the FIR ﬁlter parameters of ˆS(z) identiﬁed by the process.

For all frequencies, the diﬀerence between S(z) and ˆS(z) is weighted with Q(w)

which is dependent of the input energy for all frequencies. Hence the lower fre-quencies will be dominating in the minimization (3.30) when using a low-pass ﬁlter [10].

3.5.2 System latency

The secondary path S(z) has a latency that needs to be included in the estimation and it is measured in amount of samples nτ. Cross correlation is a method for estimating the similarity between signals, in this case u(n) and y(n). A high cross correlation value corresponds to high similarity between signals.

By calculating the cross correlation between u(n) and y(n + τ)

Ruy(τ) = lim Nτ→∞ 1 Nτ Nτ n=1 u(n)y(n + τ) (3.32)

for diﬀerent delays τ = 0, 1, 2...Mτ. The time delay, nτ, is chosen as the τ where

Ruy(τ) is signiﬁcantly greater than zero.

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Chapter 4

Implementation

In this chapter the implementation of the ANC system is presented.

4.1 DSP hardware and equipment

The computer platform for the ANC system is a Development Starter Kit TMS320C6713 DSP from Texas Instruments. Other equipments such as ampliﬁers, microphones and speakers are also used in diﬀerent setups. More information about the equip-ment can be found in Appendix A.

Figure 4.1. TMS320C6713 DSP DSK.

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24 Implementation

4.1.1 Development Starter Kit

The Development Starter Kit (DSK) is a card built to test and evaluate the TMS320C6713 DSP, see Figure 4.1. Some key features of the DSK include:

• A Texas Instrument ﬂoating point digital signal processor TMS320C6713

operating at 225MHz.

• An AIC23 audio codec (AD/DA converter) with stereo input and output. • 16 Mbytes of synchronous DRAM.

• 512 Kbytes of non-volatile Flash memory.

• USB communication with a host computer used for software development.

4.1.2 DSP

In Figure 4.2, a block diagram of the TMS320C6713 DSP is shown. The processor has many features, two of importance for the implementation of the ANC system are described below.

EMIF McBSPs Timers HPI Interrupt Selector Power Down Logic Boot Configuration Enhanced DMA Controller PLL L2 Memory L1P Cache C6000 DSP Core A Reg. File Data Path A L1 S1 M1 D1 B Reg. File Data Path B D2 M2 S2 L2 L1D Cache Instruction Fetch Instruction Dispatch Instruction Decode Interrupt Control In-Circuit Emulation Test Control Logic Control Registers

Figure 4.2. A block diagram of a TMS320C6713 DSP.

Multichannel Buﬀered Serial Port

The Multichannel Buﬀered Serial Port (McBSP) is a serial port that buﬀer samples automatically with the aid of the EDMA controller, described below. It consists of a data path and a control path, which connect to external devices, and four

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4.2 DSP software concepts and techniques 25

other pins that control clocking and frame synchronization. The DSP consists of two McBSPs that are used in the ANC system to communicate with the AD/DA converter. The ﬁrst one, McBSP0, is used for control and conﬁguration and the second one, McBSP1, is used to transfer data between the AD/DA converter and the CPU. [16]

Enhanced Direct Memory Access

Enhanced Direct Memory Access (EDMA) allows devices to transfer data inde-pendently of the CPU. Typically, block data transfers and transfer requests from peripherals, such as the AIC23 audio codec, are performed by the EDMA thus relieving the CPU to do performance-intensive operations. In this system, the EDMA controller is conﬁgured to take every 16-bit audio sample arriving on the McBSP1 and store it in a buﬀer in the memory until it can be processed. Once the data have been processed, the EDMA controller sends it back to the McBSP1. [15]

4.2 DSP software concepts and techniques

4.2.1 Code composer studio

Code composer studio (CCStudio) is a development tool used for programming the TMS320C6713 DSP. It is part of Texas Instrument’s real-time eXpressDSPTM software and development tool strategy. The program is run on a host PC and communicates with the target DSP through a USB interface.

4.2.2 DSP/BIOS

DSP/BIOS is a real-time kernel that is used on the TMS320C6713 [17]. It is designed for time applications and supports scheduling, synchronization, real-time instrumentation and host-to-target communication. It is designed to min-imize memory and CPU requirements on the DSP. There are many DSP/BIOS options for program development and some are listed below:

• Several thread types are supported such as hardware interrupts, software

interrupts, tasks, periodic tasks and idle functions.

• Semaphores, mailboxes and resource locks are provided to support

commu-nication and synchronization between threads.

• It is possible to use both dynamically and statically created objects.

Writing programs using the DSP/BIOS kernel is done by using CCStudio.

4.2.3 PING-PONG buﬀering

PING-PONG buffering is a technique where two buffers (referred to as the PING buffer and the PONG buffer) are used for a data transfer instead of only one. If only a single buffer is used, problems with new data overwriting the data being

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transmitted will occur. Using the PING-PONG technique, data in PING buffer is being processed while the next set of data is read into the PONG buffer, and vice versa. This ANC system is using PING-PONG buffers both when transmitting and receiving, for a total of four buffers.

4.3 DSP program design

The ANC program is implemented using the language C and an overview of the design solution is given in this section. In Figure 4.3 the design solution is illus-trated. ANC-off STATES ANC-on Identification Main function DSP/BIOS Idle-loop edmaHwi processBufferSwi THREADS return B u ff e ring c o m p le te d EDMA Interrupt

Buﬀering not completed

re turn DSP/BIOS

Kernel

Figure 4.3. An overview of the ANC program design solution.

4.3.1 Main function

When ﬁrst starting the program the main function is run. This is done only once and outside the DSP/BIOS real-time kernel. It initiates all functions, hardware setups and libraries the ANC program needs when entering the DSP/BIOS kernel. Important properties of the main function include:

• Initializing of the audio AIC23 codec on the DSK. The codec sample

fre-quency is set to 8000 Hz and returns an integer of 16 bits.

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4.4 Summary and conclusion 27 • The EDMA controller is set to transfer samples from the McBSP to the CPU

core using PING-PONG buﬀering.

• Memory space used by arrays in the ANC algorithm is cleared.

After the program has returned from the main function it enters the DSP/BIOS kernel and the DSP/BIOS idle loop.

4.3.2 DSP/BIOS threads

Three threads are used

• The DSP/BIOS idle-loop is the thread with lowest priority. This thread is

used for communication between the target (DSP) and the host (PC running CCStudio).

• edmaHwi is a hardware interrupt and is the highest prioritized thread. It is

trigged when a complete DMA frame has been received by the EDMA. If both the receive and transmit transfers have been completed, the processBuﬀerSwi is trigged.

• processBuﬀerSwi is a software interrupt that is trigged by the edmaHwi.

This task executes the signal processing and identiﬁcation algorithms de-scribed in Chapter 3 depending on the present state of the the system.

4.3.3 ANC system states

The ANC system has three diﬀerent states, ANC-on, ANC-oﬀ and

identifica-tion implemented in the processBufferSwi task. Switching between the different

states is done by editing two variables using a feature in CCStudio called watch window.

• Variable ident_onoff is set to 1/0 for on/oﬀ. Initially 0. • Variable anc_onoff is set to 1/0 for on/oﬀ. Initially 0.

In identiﬁcation mode, the system identiﬁes the secondary path according to Sec-tion 3.5, when completed ident_onoff is automatically set to 0.

4.4 Summary and conclusion

Implementing the ANC system using the TMS320C6713 DSK has both advantages and disadvantages. It is fairly easy to use and there are lots of open code written already. On the other hand, without adding extra hardware the ANC system is limited to use only two microphones and two speakers. Adding hardware is costly and extra code has to be written.

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eﬃcient. As an example, the loop through a system including sound card, speaker, air, microphone and back again takes 80 ms on aMatlab/Simulink implementa-tion using Windows XP. The same loop with the laptop replaced by a DSP takes only 3.6 ms. Hence, there is a big diﬀerence and for real time implementation a DSP implementation is preferable.

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Chapter 5

Results

In this chapter, detailed results for the feedforward and feedback system are pre-sented in Section 5.1 and Section 5.2, respectively. Due to the way the ANC systems are implemented, the DSP is halted for an instant when turning on the systems. This is causing a noise impulse, visible in some time plots. To calculate the reduction of sound pressure level (SPL), following formula is being used

Lp= 20 log10p_poﬀ on

dB (5.1)

where Lp is the SPL reduction, poﬀ is the 8000 samples root mean square error

being measured when the ANC system is oﬀ and ponwhen the ANC system is on.

5.1 Feedforward FxLMS

An overview of a feedforward system was presented in Section 2.2 and theory is available in Section 3.3. During the evaluation of the feedforward system two microphones are used, the reference microphone is put close to the engine and the error microphone is put close to the ceiling of the cabin.

5.1.1 Primary path

To achieve a good result, a strong dependence between noise in the reference microphone and noise in the error microphone is necessary. The dependence is here illustrated by coherence estimate plots. Coherence is a function of frequency with values between 0 and 1 that indicate how well two signals corresponds to each other at each frequency. A value of 1 indicates a strong dependence. In Figure 5.1, Figure 5.2 and Figure 5.3, coherence estimate plots are used to illustrate the dependence between error and reference singal for the engine speeds of 840, 1500 and 2150 revolutions per minute (rpm).

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30 Results 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency (kHz) Magnitude (dB)

Coherence Estimate via Welch

Figure 5.1. Coherence estimate between reference michrophone and error microphone

at an engine speed of 840 rpm. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency (kHz) Magnitude (dB)

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5.1 Feedforward FxLMS 31 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency (kHz) Magnitude (dB)

at an engine speed of 2150 rpm.

5.1.2 Secondary path

In Section 3.5 the theory of secondary path identification was presented. Low-pass filtered Gaussian random noise is used to estimate the secondary path and by using cross correlation the system delay is estimated. In Figure 5.4 the cross correlation between the output noise and the measured noise is shown at different time delays. The result of the secondary path identification is presented in Figure 5.5 where the parameters of the FIR filter ˆS(z) are plotted. Since the delay of the system

was 57 samples during the identiﬁcation, the same amount of samples are set to zero in ˆs, see Figure 5.5.

5.1.3 Constant engine speeds

To get a feeling of how well the ANC system is working for diﬀerent engine speeds three cases are studied: idling engine speed, maximum engine speed and an engine speed of 1500 rpm. The engine speed 1500 rpm is a commonly used engine speed for maximum performance and economical driving and will in the rest of this report be referred to as working enginge speed.

Idling engine speed (840 rpm)

In Figure 5.6, a distinct diﬀerence is visible for the operating ANC system and the convergence of the system is seen during the time interval 2− 2.3 seconds.

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32 Results 0 100 200 300 400 500 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 Lag

Sample Cross Correlation

Sample Cross Correlation Function (XCF)

Figure 5.4. Cross correlation between time delays.

0 100 200 300 400 500 −5 −4 −3 −2 −1 0 1 2 3 4 5x 10 −3 i si

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5.1 Feedforward FxLMS 33

The SPL is reduced with 15.5 dB. A plot of the power spectral density for the ANC system off and on is shown in Figure 5.7. Significant differences are visible especially for the peaks at 45 Hz and 90 Hz, but other frequencies are suppressed as well, while a few are enhanced.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.01 −0.008 −0.006 −0.004 −0.002 0 0.002 0.004 0.006 0.008 0.01 Time (s)

Figure 5.6. Time plot of error signal. The feedforward ANC system is turned on at

time2 s. Engine speed 840 rpm.

Working engine speed (1500 rpm)

A signiﬁcant diﬀerence is visible for the operating ANC system, see Figure 5.8. Looking at the power spectral density plot, Figure 5.9, the peak of 84 Hz is sup-pressed well. The SPL is reduced with 17.5 dB.

Maximum engine speed (2150 rpm)

For an engine running full speed, the ANC system is not making that big diﬀerence as for the previous cases, see Figure 5.10. The low frequenices do not have as much energy as in the previous cases, but the peak of 55 Hz is suppressed well, see Figure 5.11. The SPL is reduced with 2.5 dB.

5.1.4 Robustness

Robustness is crucial for a usable system. To evaluate the robustness two simple tests are done: ANC turned on with open door and ANC running while closing the door.

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34 Results 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 −120 −110 −100 −90 −80 −70 −60 −50 −40 −30 Frequency (kHz)

Power/frequency (dB/Hz) (Rel. arbitrary reference)

Periodogram Power Spectral Density Estimate

ANC off ANC on

Figure 5.7. Power spectral density of error signal for the feedforward ANC system.

Engine speed 840 rpm. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.01 −0.008 −0.006 −0.004 −0.002 0 0.002 0.004 0.006 0.008 0.01 Time (s)

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5.1 Feedforward FxLMS 35 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 −120 −110 −100 −90 −80 −70 −60 −50 −40 −30 Frequency (kHz)

ANC off ANC on

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36 Results 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 −120 −110 −100 −90 −80 −70 −60 −50 −40 −30 Frequency (kHz)

ANC off ANC on

Engine speed 2150 rpm.

ANC turned on with open door

In the ﬁrst case the secondary path is changed since identiﬁcation of S(z) was done with closed door. When the ANC system is turned on it is easy to see how the system converges despite a model error in ˆS(z), see Figure 5.12.

ANC running while closing the door

In the second case the door is open and the ANC system is running with a model error in ˆS(z). By closing the door, S(z) is changed back to normal. In Figure 5.13

it is visible that despite the change of the secondary path and a violent noise from the closing of the door, the system is working ﬁne.

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5.1 Feedforward FxLMS 37 0 1 2 3 4 5 6 7 8 9 10 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 Time (s)

Figure 5.12. Time plot of error signal with open door. The feedforward ANC system

is turned on at time5.8 s. Engine speed 840 rpm.

0 1 2 3 4 5 6 7 8 9 10 −0.1 −0.05 0 0.05 0.1 0.15 Time (s)

Figure 5.13. Time plot of error signal. The feedforward ANC system is running and

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38 Results

5.2 Feedback FxLMS

An overview of a feedback system was presented in Section 2.3 and the theory is brieﬂy described in Section 3.4. During the evaluation of the feedback system only one error microphone is used and it is put close to the ceiling of the cabin.

5.2.1 Secondary path

The identiﬁcation of the secondary path for the feedback system is identical as for the feedforward system, see Section 5.1.2.

5.2.2 Constant engine speeds

As for the feedforward system, three diﬀerent engine speeds are studied for the feedback system: idling engine speed, maximum engine speed and working engine speed.

Idling engine speed (840 rpm)

In Figure 5.14, a distinct diﬀerence is visible for the operating ANC system and the convergence of the system is seen during the time interval 2− 2.3 seconds. The SPL is reduced with 10.7 dB. A plot of the power spectral density is shown in Figure 5.15. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.01 −0.008 −0.006 −0.004 −0.002 0 0.002 0.004 0.006 0.008 0.01 Time (s)

Figure 5.14. Time plot of error signal. The feedback ANC system is turned on at time

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5.2 Feedback FxLMS 39 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 −120 −110 −100 −90 −80 −70 −60 −50 −40 −30 Frequency (kHz)

ANC off ANC on

Figure 5.15. Power spectral density of error signal for the feedback ANC system.

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40 Results Working engine speed (1500 rpm)

The time plot for the operating ANC system is shown in Figure 5.16 and the power spectral density plot is presented in Figure 5.17. The SPL is reduced with 14.9 dB.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.01 −0.008 −0.006 −0.004 −0.002 0 0.002 0.004 0.006 0.008 0.01 Time (s)

2 s. Engine speed 1500 rpm.

Maximum engine speed (2150 rpm)

For an engine running full speed, the ANC system is not making a big diﬀerence, see Figure 5.18. The peak of 118 Hz is suppressed, see Figure 5.19, and the SPL is reduced with 4.8 dB.

5.2.3 Robustness

As for the feedforward system, two simple tests are done to evaluate the robustness for the feedback system: ANC turned on with open door and ANC running while closing the door.

ANC turned on with open door

The feedback system does not become unstable with a signiﬁcant model error in ˆ

S(z) caused by an open door, see Figure 5.20. ANC running while closing the door

An impulse provocation of the system, closing the door, does not make the system unstable, see Figure 5.21.

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5.2 Feedback FxLMS 41 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 −120 −110 −100 −90 −80 −70 −60 −50 −40 −30 Frequency (kHz)

ANC off ANC on

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42 Results 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 −110 −100 −90 −80 −70 −60 −50 −40 −30 Frequency (kHz)

ANC off ANC on

Engine speed 2150 rpm. 0 1 2 3 4 5 6 7 8 9 10 −0.025 −0.02 −0.015 −0.01 −0.005 0 0.005 0.01 0.015 0.02 0.025 Time (s)

Figure 5.20. Time plot of error signal with open door. Feedback ANC system turned

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5.3 Global noise reduction in the cabin 43 0 1 2 3 4 5 6 7 8 9 10 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 Time (s)

Figure 5.21. Time plot of error signal. The feedback ANC system is running and the

door is closed at time5 s. Engine speed 840 rpm.

5.3 Global noise reduction in the cabin

All results in this section are measured from the error microphone. But since the noise is minimized at this position, the noise level does not necessary have to be decreased elsewhere in the cabin. To visualize what the driver is hearing, a monitor microphone is put close to the ear of the driver. In Figure 5.22 and 5.23, the error microphone and monitor microphone are presented for an idling engine. In this case, the feedback ANC system is used but the results are similar to the feedforward ANC system. The plots show that suppression is achieved globally in the cabin and not just locally at the position of the error microphone.

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44 Results 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 Time (s)

2 s. Engine speed 840 rpm. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 Time (s)

Figure 5.23. Time plot of monitor signal. The feedback ANC system is turned on at

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5.4 Summary of results 45

5.4 Summary of results

A summary of the results is presented in Table 5.1. ∆ SPL

rpm Feedforward Feedback

840 15.5 dB 10.7 dB

1500 17.5 dB 14.9 dB

2150 2.5 dB 4.8 dB

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Chapter 6

Concluding Remarks

In this chapter conclusions and suggestions of future work are discussed.

6.1 Conclusions

In this thesis we have evaluated active noise control of a forest machine cabin. Two different sensor configurations have been studied, feedforward and feedback. The feedforward system uses a reference sensor to get a reference signal, while the feedback system generates its own reference signal from the error signal and the adaptive filter output. In both cases the adaptive filter is updated by the error sensor. Microphones are being used as sensors in the evaluated systems. The FxLMS algorithm is being used for both feedforward and feedback to compensate for different effects that comes up running the system in real time.

The results show that the systems works best for idling engine speed and for a normal working engine speed, mainly because of the low frequency noise generated at these engine speeds. Both the feedforward and the feedback system show fast enough convergence and global suppression of low frequency noise in the cabin.

6.2 Future work

As a result of the time limit of the project, improvements of the system are pos-sible and some suggestions of future work follows below.

• For a feedforward system other reference sensors than microphones, such as

an engine speed sensor, should be evaluated.

• Evaluation of reference sensors at other positions should be done to cancel

out other disturbing noises, e.g., one possible position is close to the hydraulic pump.

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48 Concluding Remarks • A combination of a feedforward ANC and a feedback ANC system, often

referred to as a hybrid ANC should be evaluated since good results have been achieved in other projects [14], [8].

• Place speakers and microphones at the driver’s seat, close to the ears, to

achieve better results at higher frequencies as a complement to the existing subwoofer.

• To increase system performance, other step size algorithms should be

eval-uated, e.g., diﬀerent variable step size algorithms have been shown to be eﬃcient [1], [7].

• Low pass ﬁlter reference microphone signals to get rid of unwanted noise. • To keep ˆS(z) updated continuously, evaluation of online secondary path

mod-eling should be done [19].

• Implement a music compensator to improve system performance while using

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Bibliography

[1] Akhtar M.T., Abe M., Kawamata M. (2004). Modiﬁed-ﬁltered-x LMS

algo-rithm based active noise control system with improved on line secondary-path modeling. Proceedings of the IEEE International Midwest Symposium on

Cir-cuits and Systems, 1:I-13–I-16.

[2] Akhtar M.T., Abe M., Kawamata M. (2005). A method for on line secondary

path modeling in active noise control systems. Proceedings of the IEEE

In-ternational Midwest Symposium on Circuits and Systems, 1:264–267. [3] Arbetsmiljöverket. (2005) Buller. Arbetsmiljöverkets författningssamling,

AFS 2005:16.

[4] Elliott S.J., Nelson P.A. (1993). Active Noise Control. IEEE Signal Processing Magazine, 10(4):12–35.

[5] Glad T., Ljung L. (2003). Reglerteori. Studentlitteratur.

[6] Gustafsson F. (2000). Adaptive Filtering and Change Detection. John Wiley & Sons, Ltd.

[7] Haweel T.I. (2004). A simple variable step size LMS adaptive algorithm. In-ternational Journal on Circuit Theory and Applications, 32:523–536. [8] Kong X., Liu P., Kuo S.M. (1998). Multiple Channel Hybrid Active Noise

Con-trol Systems. IEEE Transactions on ConCon-trol Systems Technology, 6(6):719–

729.

[9] Kuo S.M., Morgan D.R. (1999). Active Noise Control: A Tutorial Review. Proceedings of the IEEE, 87(6):943–973.

[10] Ljung L. (1999). System Identiﬁcation, Theory for the User. 2nd edition Pren-tice Hall Information and System Sciences Series.

[11] Morgan D.R. (1980). An analysis of multiple correlation cancellation loops

with a ﬁlter in the auxiliary path. IEEE Transactions on Acoustics, Speech,

and Signal Processing, 5:454–467.

[12] Pedrotti F.L., Pedrotti L.S. (1993). Introduction to Optics, 2nd edition. Pren-tice Hall International Editions.

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50 Bibliography

[13] Sano H., Inoue T., Takahashi A., Terai K., Nakamura Y. (2001). Active

Control System for Low-Frequency Road Noise Combined With an Audio System. IEEE Transactions on Speech and Audio Processing, 9(7):755–763.

[14] Streeter A.D., Ray L.R., Collier R.D. (2004). Hybrid Feedforward-Feedback

Active Noise Control. Proceedings of the 2004 American Control Conference,

3:2876–2881.

[15] Texas Instruments. (2003).TMS320C6000 DSP Enhanced Direct Memory

Ac-cess (EDMA) Controller Reference. SPRU234.

[16] Texas Instruments. (2004).TMS320C6000 DSP Multichannel Buﬀered Serial

Port (McBSP) Reference Guide. SPRU580C.

[17] Texas Instruments. (2004). TMS320 DSP/BIOS User’s Guide. SPRU423D. [18] Texas Instruments. (2006).TMS320C67x DSP Library Programmer’s

Refer-ence Guide. SPRU657B.

[19] Zhang M., Lan H., Ser W. (2005). On comparison of online secondary path

modeling methods with auxiliary noise. IEEE Transactions on Speech and

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Appendix A

Equipment

Development card

One Texas instrument TMS320C6713 Development Starter Kit (DSK) is used as a signal processing hardware platform, see Figure 4.1. Key features of this card include:

• A Texas Instrument ﬂoating point digital signal processor TMS320C6713

operating at 225MHz.

• An AIC23 audio codec (AD/DA converter) with stereo input and output. • 16 Mbytes of synchronous DRAM.

• 512 Kbytes of non-volatile Flash memory.

• USB communication with a host computer used for software development. Ampliﬁer

One four-channel Reﬂexion X500:

• Max output power 4 x 225 W. • Signal to noise ratio >95 dB. • Frequency response 10 Hz - 45 kHz. Subwoofer

One 8 inch MDS subwoofer enclosure:

• Speaker with frequency response 24Hz - 3 kHz. • Built in ampliﬁer

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52 Equipment

Preampliﬁer

To power the microphones an Alto Mictube stereo preamplifier is used. This preamplifier is connected between microphones and the DSK and has specifica-tions:

• 48 V phantom power supply to power high quality condenser microphones. • Frequency response 20Hz - 22 kHz

Microphones

Two TW omni condenser lavaliere microphones are used.

• Frequency response 20Hz - 20 kHz.

• Omni directional, sensitive to sounds from all directionals.

One Superlux CM-H8K microphone for use in very high sound pressure environ-ments.

• Frequency response 40Hz - 20 kHz. • Sound pressure level 134 dB.

• Omni directional, sensitive to sounds in all directions. Mixer

One Helix board 12 FireWire mixer is used.

• 12-input small-format analog mixer with extremely low noise circuitry. • 96 kHz FireWire interface for streaming 10 independent channels of audio

to computer with near-zero latency.

• Four mono Mic/Line channels

• Two stereo channels, two stereo AUX returns, two AUX sends. • Inserts and phantom power on Mic channels.

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c

 Patrik Grylin

Active Noise Control of a Forest Machine Cabin

Institutionen för systemteknik

Department of Electrical Engineering

Examensarbete

Active Noise Control of a Forest Machine Cabin

Active Noise Control of a Forest Machine Cabin

Examensarbete utfört i Automatic Control

vid Tekniska högskolan i Linköping

av

Abstract

Acknowledgments

Contents

Chapter 1

Introduction

1.1

Background

1.2

Purpose

1.3

Method

1.4

The concept of ANC

1.5

Thesis outline

1.6

Nomenclature

1.6.1

Signals

1.6.2

Transfer functions

1.6.3

Impulse responses, ﬁlter parameters

1.6.4

Constants

1.6.5

Abbreviations

Chapter 2

ANC principles

2.1

Acoustics

2.1.1

Wave equation

2.1.2

Principle of superposition

2.2

Feedforward system overview

P (z)

F (z)

S(z)

2.2.1

Primary path

2.2.2

Secondary path

2.2.3

Digital ﬁlter

2.3

Feedback system overview

F (z)

S(z)

2.3.1

Secondary path

2.3.2

Digital ﬁlter

Chapter 3

ANC adaptive ﬁlter theory

3.1

Finite Impulse Response

3.2

Least Mean Square

P (z)

W (z|w)

LMS

S(z)

3.2.1

Normalized LMS

3.2.2

Leaky LMS

3.3

Feedforward ﬁltered-x LMS

P (z)