Experimental implementation of acoustic impedance control by a 2D network of distributed smart cells

Experimental implementation of acoustic

impedance control by 2D network of

distributed smart cells.

P. David, M. Collet, J.-M. Cote

dM

em

s2

01

0,

Be

san

çon

2dMems 2010, BesançonJuin 2010

Outline

1. Introduction

a. Structural Control : decentralized strategy

b. Structural Control : centralized strategy

c. A new approach

2. Integrated Distributed System :

a. Metacomposites and Métamaterial

b. Operators and Architecture

3. Implementation of acoustic impedance control by 2D network of

distributed smart cells

a. Impedance Operator

b. Strategy Discretization onto a set of active cells

c. Integrated active skin

d. Experimental Results

e. Comparison with classical strategies

4. Conclusions


Introduction

How can we optimize the vibroacoustical energy flux inside complex systems ?


Introduction

ActuatorsVibroAcoustical

SystemSensors

Intégration des Systèmes

Control

Algorithm

Multiphysics Modeling

Multidisciplinary competencies

Technologies developments

Acoustic, Mechanic, Electronic, Automatic, Mathematics…

Integrated Systems

Communication

Energy

Communication

Energy


Introduction

Structural Control : decentralized strategy

Collocated Active Control

(FEMTO-ST / PSA [Monnier 2001])

Results :

• Design Variables and Optimization tools

• Experimental characterization and prototypes

Decentralized

Control

Gi(jw)

Damping


Introduction

Structural Control : Centralized strategy

Centralized Control:

G(jωωωω,C,B)

Semi-distributed Active control

(FEMTO-ST / LCPC [Ratier 2000])

Shaker

Sign

al C

ondi

tion

er

SC

ADC

State estimators

G DAC Amplifier

Nœuds

Mode 4

Sensor 1

Sensor 2

Sensor 3

Sensor 4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−120

−100

−80

−60W−Norm : ome=0.1

No

rm in

dB

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−200

−150

−100


No

rm in

dB

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−200

−150

−100


No

rm in

dB

time in s

Results :

• Designs variables, modal filtering techniques

• Experimental characterization and validation


Introduction

A new approach…

Whatever be the wanted vibroacoustical properties (transparency, absorption, reflexion…) we propose a new

approach :

To directly optimize the structural constitutive relationships as Hybride composite structures (active/passive) by

using a distributed set of smart cells including transducers and control electronics…

Summary :

These systems have difficulties to find ‘industrial Applications’ :

� Numerical and technologicapl complexity

� Difficult to include into the design process

� Energy Cost

=> We can propose a new approch…

G

GG

G

GG

GGGG

GG

Z(iω)Z(iω)

Cell

Z(iω) Z(iω)

Z(iω)Z(iω) Z(iω) Z(iω)

Z(iω)Z(iω) Z( iω) Z(iω)

Z(iω)Z(iω)Z(iω)Z(iω)

Cell

Z(iω)Z(iω)

Cell

Z(iω)Z(iω)Z(iω) Z(iω)Z(iω)Z(iω)

Z(iω)Z(iω)Z(iω)Z(iω)Z(iω)Z(iω) Z(iω)Z(iω)Z(iω) Z(iω)Z(iω)Z(iω)

Z(iω)Z(iω)Z(iω)Z(iω)Z(iω)Z(iω) Z( iω)Z( iω)Z( iω) Z(iω)Z(iω)Z(iω)


Integrated Distributed System :

Metacomposites and Métamaterial

operator

« constitutive relationship »

Concept of «Adaptive Genreralized Impedance»

G : Spatio-temporal

Differential or Pseudo-Differencial Operator

Medium 2

Transducers

Hybrid Distributed Interface

Medium 1Incoming Flow

Reflected Flow

Transmitted Flow

Gi(ωωωω) Gi+2(ωωωω) Gi+3(ωωωω)Gi-1(ωωωω) Harvested Flow



Metacomposites and Métamaterial

Liu Z. et al. “Locally Resonant Sonic Materials” Science, Vol. 289, September 2000, pp. 1734-1736.

N. Fang et al., “Ultrasonic Metamaterials With Negative Modulus” Nature Materials, Vol. 5, June 2006, pp. 452-456



Operators and Architecture

Architectures for distributed smart cells and Control Operators

Order 1 centralized

control

Gi(jωωωω,jkx,jky)

Centralized Control:

G(jωωωω,jkx,jky)Decentralized

Control

Gi(jωωωω)


Implementation of acoustic impedance control by 2D network of


Impedance Operator

The Objectives: Theoretical Aspects

Input Energy Transmitted Energy

y

x0

=

Initial System

Active Skin

Active Skin

Transfer

0

y

x

Transmitted Energy ≈ 0

Controlled Equivalent Systems

or

Input Energy > Transmitted Energyy

0 x

What are these controlling PDEs?


We search :

So that : Kxr ≤ 0

u(x,t)=G(p(x,0,t))



Impedance Operator

x

y

Active Boundary0

Acoustic Domain

Input WavesFree Reflected Waves

ixk

iyk

rxk

ryk

Controlled Reflected Waves

),(),( 0 txwtxu &&ρρρρ−−−−====




Impedance Operator

One can prove that all interacting waves areSo as : kx< 0

EDP of the coupled system :

Control law (Advection):

EDP of the controlled system

Order 1 centralized

control

Gi(jωωωω,jkx,jky)

M Collet, P. David, M. BerthillierActive acoustical impedance using distributed elect rodynamical transducers, Journal of Acoustical Socie ty of America, 125(2), 882–894, 2009


Discret Control law :



Strategy Discretization onto a set of active cells

Controlling Loudspeaker Microphones

Gi(jω)Gi-1(jω) Gi+1(jω)vipk pk+1

Mono-modal modelling ofThe used LP :



distributed smart cells :

Integrated active skin

P. David, M. Collet, J. M. Cote,Experimental implementation of acoustic impedance c ontrol by 2D network of distributed smart cells, Sm art Materials and Structures, Accepter , 2009




Experimental Results

-30 dB max

Needed Power < 20 W

Contrôlé

Non Contrôlé


Energy comparison with X-Filtered LMS strategy :



Comparison with classical strategies




Comparison with classical strategies

0 200 400 600 800 1000 1200 1400 1600 1800 2000

10-6

10-5

10-4

input power

frequency (Hz)

acou

stic

inte

nsity

no contLMSDistr

Power Flow comparison :

ΓΓΓΓ

∂∂∂∂∂∂∂∂⋅⋅⋅⋅==== ∫∫∫∫ΓΓΓΓ d

iRe

2

1*

n

ppI r

ρωρωρωρω

0 200 400 600 800 1000 1200 1400 1600 1800 200010

-18

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

output power

frequency (Hz)

acou

stic

inte

nsity

no contLMSDistr


Conclusions

Adaptive distributed Structures/SystemsAdaptive distributed Structures/Systems

Smart Electro-acoustical cellsSmart Electro-acoustical cells

Passive, semi-active or active ControlPassive, semi-active or active Control

Wave’s dispersion / Diffusion ControlWave’s dispersion / Diffusion Control

Developed ConceptsDeveloped Concepts

FEM Multiphysics ModellingFEM Multiphysics Modelling

MF range approach and broadband efficiencyMF range approach and broadband efficiency

Circuits SynthesisCircuits Synthesis

Toward the composite integration…Toward the composite integration…

ResultsResults

Application for more complex systemApplication for more complex system

LF / MF / HF ApproachLF / MF / HF Approach

Technological integration => Fusion ?Technological integration => Fusion ?

Hybride version including passive materialsHybride version including passive materials

FuturFutur

Experimental test on more complex systemsExperimental test on more complex systems

Experimental implementation of acoustic impedance control by a 2D network of distributed smart cells

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