Active control of an automobile suspension system for reduction of vibration and noise

(1)

Redu tion of Vibration and Noise

by

Kristen Lynn Clements

B.S., Me hani alEngineering (2002)

Massa husetts Institute of Te hnology

Submitted tothe Departmentof Me hani al Engineering

in partialfulllmentof the requirements for the degree of

Master of S ien e inMe hani al Engineering

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

June 2005

Author...

Departmentof Me hani al Engineering

May 19,2005

Certied by...

Steven R.Hall

Professor of Aeronauti s and Astronauti s

Thesis Supervisor

Read by...

Martin Culpepper

Ro kwell International AssistantProfessor of Me hani al Engineering

Thesis Reader

A epted by...

LallitAnand

(2)

(3)

Vibration and Noise

by

KristenLynn Clements

Submitted tothe Department of Me hani al Engineering

on May19,2005, inpartialfulllment ofthe

requirementsfor thedegree of

Master ofS ien e inMe hani al Engineering

Abstra t

A new method for ontrolling road noise transmitted through the suspension system of

an automobile was developed, using a Lin oln LS automobile asthetarget vehi le. In this

vehi le,roadsurfa eroughnessgeneratesvibrationsthataretransmittedintotheautomobile

primary through a single bushing (the point 4 bushing) on ea h of the front suspension

ontrol arms. An ele tromagneti a tuator was designed, built, and tested on a Lin oln

LS with simulated roadnoise. The a tuator applies a for e a ross the point 4 bushing, in

response to a elerations of the vehi le frame, just inboard of the bushing, with the goal

of redu ing the net for es transmitted into the vehi le frame, whi h ultimately produ e

unwanted interiornoise. Several tonal ontrollerswere developed,ea h designed to operate

inanarrowfrequen yband,andtoeliminate rossmember(frame)vibrationjustinsidethe

point4bushing. Thetonal ontrollerswereabletoeliminate rossmembervibration atthe

desired frequen y. Eliminating the ross member vibration resulted in modest redu tions

ininterior sound levels. A su essfulvibration ontrol system(in this vehi le) wouldneed

to eliminate ross member vibrations overthe frequen y range 100 to 200 Hz. However, a

broadband ontroller with this ele tromagneti a tuator system proved to be di ult, due

to undesirable non-minimumphase dynami s.

Thesis Supervisor: Steven R.Hall

(4)

(5)

Iwouldliketothankmyadvisor,Prof.StevenHall,forhissupportandguidan e,espe ially

his patien eand willingness to explain on epts asmanytimes as ne essary. I alsoextend

manythankstoDaveRobertsonfortheuseofhisele troni equipment,aswellashisadvi e,

en ouragement,andhumor. Di kPerdi hizzihelpedmendthevariousandsundrysupplies

ne essary for the ompletion of this proje t. DonWeiner tried to tea h me self-defenseas

wellashowtousethevariousma hinesintheGelbLaboratory. IamgratefultoProf.Martin

Culpepperfor takingthetimefromhis busys hedule toserve asadepartmental reader for

mythesis.

JoeS hmidtofFordprovidedmu hoftheautomobileexpertisene essaryforthisproje t

and pro ured Sneezy and the Lin oln LS used. Dieter Giese, also of Ford, was willing to

answeranyquestion,nomatterhowtrivial, that ameupduringthe ourseofmyresear h.

Ialso thankDr.JoeSaleh, theEx utive Dire torof theFord-MIT Allian e,andKristin

and Steve S hondorf, alsoof the Ford-MIT Allian e,for their assistan ewiththis proje t.

Dr. Kyung-yeol Song helped get me started on this proje t and was always willing to

tryto answeranyquestions Ihadinthe later stages. JorgeFeu htwanger assistedwiththe

useoftheele troni dis hargemilling(EDM)ma hine. JoshChambersprovidedadvi eand

te hni al assistan e.

Iwouldalsoliketothankmyfriends: Chrisforhisendless omputerassistan e,Christina

for stressreliefand ookies,Rohan for helpwithallthings MIT,Vi torfor omputer

hard-ware and editorial advi e, and Zoa for onverting what I wrote into what I wanted to

say.

Finally,Iwant to thankmy familyfor their ontinual support,parti ularly my mother.

This work was sponsored by the Ford-MIT Allian e. Additional funding was provided

(6)

(7)

1 Introdu tion 9

1.1 NoiseandAutomobiles . . . 9

1.2 Previous Methodsof Redu ing Interior Noise . . . 10

1.2.1 Interior Loudspeakers . . . 10

1.2.2 Power Steering . . . 11

1.3 A tiveSuspensionSystem Resear h . . . 11

1.4 Analysisof Ford Data . . . 13

1.5 Overview . . . 16

2 A tuator Design 19 2.1 ProblemDes ription . . . 19

2.2 A tuator Requirements. . . 22

2.3 Piezoele tri vs. Ele tromagneti A tuator . . . 23

2.3.1 Piezoele tri Cerami Sta kA tuator. . . 23

2.3.2 Ele tromagneti A tuator . . . 25

2.4 Ele tromagneti A tuator Spe i ations . . . 26

2.5 A tuator Amplier . . . 27

3 Experimental Setup 29 3.1 Lin oln LS. . . 29

3.2 Simulated Road NoiseEx itation . . . 33

(8)

3.3.2 Mi rophones . . . 37

3.3.3 ShakerFor e . . . 39

3.4 Dynami Signal Analyzer . . . 39

3.5 Ele troni Control Unit . . . 40

4 Experimental Results 41 4.1 Open Loop Results . . . 41

4.2 TonalController . . . 42

4.3 Expe tedPerforman e . . . 44

4.4 ClosedLoop Vibration . . . 48

4.5 Interior SoundLevels . . . 51

4.6 Summary . . . 52

5 Broadband Controller 57 5.1 Di ultieswithBroadband Control . . . 57

5.2 TonalControllersat Various Other Frequen ies . . . 60

5.2.1 TonalControl at 140 Hz . . . 60

6 Con lusion 69

(9)

Introdu tion

1.1 Noise and Automobiles

Unwanted noise is undesirable in many environments, among them the workpla e, home

and automobile. Automobile ustomers typi ally onsider a la k of interior noise to be a

desirable hara teristi when pur hasing a vehi le. Interior road noise an be generated by

numerous sour es throughout the automobile, with the engine being the major sour e of

noise [30℄. Generated engine noise is transmitted to the interior of the ar both as sound

that radiates from the engine ompartment and as vibrations thatare transmitted though

theengine mounts to the frame [14℄. Other me hani al systems inthe vehi le, su h asthe

power steering system [28 ℄, an also produ e audible noise in the interior. Additionally,

noises from outside the automobile an be heard inside the vehi le. Interior noise is also

aused byframe vibrations, whi h are theresult of tire onta t withvarious road surfa es

and potholes[33 ℄. Thisroad-indu ednoise transmitted throughthesuspension systeminto

theframe isthe sour e ofnoise thatwill beprimarily onsidered inthis proje t.

Undesirednoiseinsidethe abinofanautomobile anrangefrommerelyannoying

(mak-ingitmoredi ultforpassengerstolistentomusi ortohavea onversation)to dangerous

(preventing a driver from hearing important signals from outside the vehi le, su h as an

emergen y siren). Constant noise on extended drives (even at low levels) an also redu e

(10)

redu tion an be a omplished through three general approa hes. First, the sour e of the

noise an be eliminated or redu ed. Se ond, the paths that the vibration follows an be

modiedtoredu ethevibrationtransmission. Third,thesoundattheuserendofthepath,

inthis asethe interiorof the automobile, an be modiedto redu e theapparent noisein

theinteriorofthevehi le. However,manyte hniques employed to redu einteriornoise an

also have a detrimental ee t on other aspe ts of automobile performan e. For example,

the following parameters an be negatively impa ted by attempts to redu e interior noise

by modifyingthesuspensionsystem:

1. Handling. Handling is the pit h and roll of the vehi lebodyas a result of ornering

and brakingmaneuvers.

2. Road holding. Roadholding is the onta t for e between thetires andtheroad.

3. Suspension travel. The allowable limit of suspension travelin any vehi le design will

ae t the performan e a hievable fromthe suspensionsystem.

4. Stati dee tionresulting from variable payload. [12℄

Thegoalistomaketheinteriorquieterwithout ompromisingotherfa etsoftheautomobile

performan e.

1.2 Previous Methods of Redu ing Interior Noise

Be ause of onsumer preferen es for quieter ars, resear hers and automobile ompanies

are always looking for new ways to redu e interior noise, assuming that handling remains

omparable. Manyof the details of thenoise redu tion proje ts are onsidered proprietary

information. Presentedherearedes riptionsofsomeofthenon-proprietaryresear heorts.

1.2.1 Interior Loudspeakers

One previous method that hasbeen used to redu e interior noise ( aused by road-indu ed

(11)

noise sour e and the soundinside thevehi le an be determined, sothatthe interior noise

anbepredi ted. Interiorloudspeakers anthenbeusedtoprodu esoundoutofphasewith

the noise, redu ing interior sound levels. Using this method, Sutton and Elliott [31℄ were

able to redu e low frequen y road-indu ed noise inside an automobile by approximately

7 dB. They pla ed referen e a elerometers on the wheel, suspension, and parts of the

frame that onstitute theroadnoise transmission paths. Then, theloudspeaker signalwas

omposed of a linear ombination of the past and present referen e a elerometer signals.

Whenthispra ti alroadnoise ontroller(developedatLotusEngineering)wastested,noise

wasredu ed roughly7 dBatthemajor frequen y peaks intherangeof 100 Hz to200 Hz.

1.2.2 Power Steering

Anotherpotentialsour e ofnoiseisthepowersteeringsystem. Pressurewavesinthepower

steeringhoses auseuidnoise. Thisnoise anberedu edsomebyadjustingtheparameters

ofthesystem,su hasthelengthofthehosesandthe ongurationofthe omponents. One

studybySmid,Qatu,andDrew[28 ℄usedaMatlabsimulationsoftwareprogramtodetermine

theoptimal ongurationforthehose,tuner,andtubeinthepowersteeringsystem. (Tuners

omewithsomehosesandattenuatea ousti wavesintheuid.) They reatedamodelthat

al ulated the travel of the hydrauli pressure pulses (the sour e of vibration and noise).

Smid,Qatu,andDrewfoundthattheoptimallengthofhoseis

1/4

ofthewavelengthofthe pressure ripple,and theworst hose length is

1/2

of thewavelength. Laterresear hin their labwas ondu ted to optimize theother omponentsof thepower steering system.

1.3 A tive Suspension System Resear h

Many automobile resear hers have studied the benets of a tive suspension systems over

their passive suspension ounterparts. [15 , 16 ℄ Passive vehi le suspensions, found on most

road vehi les, are designed with two ompeting requirements: good vibration isolation to

ensure ride omfort, and good steering for e transmission for vehi le handling and safety.

(12)

m

s

k

s

us

b

s

Figure 1-1: The ommonlyused quarter ar model.

m

s

is the sprungmass (vehi le mass),

m

us

is theunsprung mass(wheel mass),

k

s

and

b

s

arethe spring and damperbetween the sprungand unsprung mass,and

k

us

isthe tire stiness.

ride quality and vehi le handling. Suspension systemdesign onstraints in lude maximum

allowable relative displa ements between the vehi lebodyand unsprung mass omponents

(in luding wheels, bump stops, and protruding parts of the steering me hanism), overall

systemrobustness,reliability,weight,and ost. [16 ℄Also,Hrovat'sresear hshowsthat,fora

quarter armodel(des ribedbelow),ana tivesuspensionsystembasedonLinearQuadrati

optimal ontrol an substantially improve ride and handling performan e when ompared

withthe onventional passive suspensions. [16 ℄ However, LQ ontrollers do not ne essarily

have good stability robustness properties. For good a tive suspension performan e, and

robustness overalldesirable ride hara teristi s, the passivesuspension shouldbedesigned

withlowstiness anddamping. [32 ℄

To model vehi le dynami s, many a tive suspension system resear hers use the one or

two degree of freedom quarter ar models. [15, 16 , 32, 3 , 25, 21 , 10, 1℄ (See Figure 1-1.)

This model onsists of a sprung mass (

m

s

) representing the vehi le mass, an unsprung mass (

m

us

) representing the wheel mass, a spring (

k

s

) and damper (

b

s

) representing the dynami s between the sprung and unsprung mass, and another spring (

k

us

) representing thetire stiness. The onta tpointbetween thetireandthegroundisalsoallowedtomove

in this model. Also used are the half ar model [16℄ and the full ar model [16, 34, 13 ℄.

(13)

Ahydrauli a tuatoristhe ommonlyuseda tuatorina tivesuspensionsystemresear h.

[34 ,3 ,25 ,21,1℄Thehydrauli a tuatorusedbyYamashita,Fujimori,Hayakawa,andKimura

operatesdierently at low and high frequen ies. At low frequen ies, where theservo valve

an followthe swit hingof the inputsignal, theowrate fromtheservo valveis onverted

to pressure bya hybrid gasspring and damping valve, andthis pressure isusedto a tively

attenuate the body's vibration. At high frequen ies, where servo valve following is not

possible,the ylinder pressure isgenerated only by thegas spring and thedamping valve.

This ensures the dynami s of the onventional suspension and the body's vibrations are

attenuated passively. This a tuator and its ontroller (designed using

H

_∞

methods [4 ℄) wereimplementedbothinshakingexperimentsanddrivingexperiments. Inboth ases,the

vibrations were redu ed at frequen ies lower than 8 Hz. Also in the driving experiments,

there was an improvement in handling with respe t to maneuvering. [34 ℄ A di ulty in

using servo valves (with the hydrauli a tuator) is that they arehigh ost items, and dirt

intolerant, soa tuator maintenan e ouldbe ompli ated. [27℄

Nonlinear ontrol has also been used with hydrauli a tuators (be ause hydrauli

a -tuators ome with asso iated nonlinear dynami s [25 ℄) to a ommodate and improve the

tradeobetween ridequalityand suspensiontravel. [25,21,10℄Theaddednonlinearitiesin

the ontroller make thesuspension stier nearits travellimits. Inexperiments byLin and

Kanellakopoulos[21℄,anonlinear ontrollerwasusedto redu ebodya elerationbyalmost

70%andbodytravelbyalmost80%as omparedtothepassivesuspension. Thesuspension

travel, however, isin reased slightly ina tive designs. [21℄

1.4 Analysis of Ford Data

Prior to the start of the proje t des ribed here, engineers at Ford Motor Company had

performeddynamometertestsonaLin oln LS.Theytookvibrationdataonadynamometer

with a oarse road surfa e. Two a elerometers were pla ed on the ontrol arm, one near

(14)

0

200

400

600

800 1000

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5 x 10

−4

Frequency, f (Hz)

Acceleration spectrum,

Φ

(g

2 /Hz)

Near cross member

Near spindle

Figure1-2: A elerationspe trummeasuredbya elerometerspla edattwolo ationsonthe

ontrolarm,onenearthe rossmemberandonenearthespindle. Thethinlinerepresentsthe

a eleration spe trumnearthe rossmember andthe thi kline represents thea eleration

spe trum nearthe spindle. Note that for both a elerometer positions, virtually all of the

energy is between 100 Hz and 200 Hz, with a peak near 150 Hz. Data ourtesy of Ford

MotorCompany.

(SeeSe tion 2.2for a des riptionand photograph ofthese suspension omponents.)

Figure 1-2 shows the a eleration spe trum on a linear s ale measured by the two

a - elerometers in the dynamometer test. The thin line represents the a eleration spe trum

forthea elerometer onthe rossmember(nearthepoint4bushing)andthethi kline

rep-resents thea eleration spe trum for the a elerometer near the spindle. The a eleration

spe trum learly shows that, for both a elerometers, almost all of the energy is between

100 Hz and 200 Hz, meaning that any a tuator employed to redu e this vibration would

likely only be required tooperate nearthis frequen yrange.

Figure 1-3 is the same data as in Figure 1-2, plotted on a logarithmi s ale. Again,

the thin line represents the a eleration spe trum from the a elerometer near the ross

(15)

0

200

400

600

800 1000

10 −10

10 −9

10 −8

10 −7

10 −6

10 −5

10 −4

10 −3

Frequency, f (Hz)

Acceleration spectrum,

Φ

(g

2 /Hz)

Near cross member

Near spindle

Figure 1-3: The same data from Ford as in Figure 1-2, plotted on a logarithmi s ale.

Thethinlineshows thea elerationspe trumfromthea elerometer pla edonthe ontrol

arm near the ross member, and the thi k line shows the a eleration spe trum from the

a elerometerpla ednearthespindle. Againitis learthatthereisasigni antpeakaround

150 Hz and that there is little energy at frequen ies higher than 300 Hz. Data ourtesy of

Ford MotorCompany.

near the spindle. The sharp drop beginning at 200 Hz onrms the hypothesis that the

a tuator wouldnotberequiredtooperateat higherfrequen ies. Thea elerationspe trum

essentially goes to zero at frequen ies higher than 400 Hz, so any a tuator authority at

frequen ieshigher than 400 Hz wouldbeunne essaryand wasteful.

Figure 1-4 shows the umulative a eleration spe trum. The umulative spe trum at

frequen y

f

is the total mean-square a eleration at frequen ies of

f

and above. The thin linerepresentsthea eleration umulativespe trumforthea elerometeronthe ontrolarm

near the rossmember and the thi kline represents the a eleration umulative spe trum

forthea elerometeronthe ontrolarmnearthespindle. Onthis umulativespe trum,the

previously observed peakat 150 Hz is learly seen asa large drop inenergy. Thissuggests

(16)

0

50

100

150

200

250

300

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045 Frequency, f (Hz)

Acceleration cumulative spectrum (g

2 )

Near cross member

Near spindle

Figure 1-4: Cumulative a eleration spe trum of the data shown in Figure 1-2. The thin

line represents thea eleration umulative spe trumfromthe a elerometer nearthe ross

member, and the thi k line represents the a eleration umulative spe trum from the

a - elerometer nearthe spindle. Theresonan e near150 Hz is lear asa sharpdrop ointhe

umulative spe trum.

hanging the energy at any other frequen ies, ould signi antly redu e the total energy,

presumably also redu ing the total sound. In other words, the frequen ies around 150 Hz

arethehighestenergy,andthereforelikelytheloudestfrequen ies,soredu ingtheenergy at

thatfrequen y wouldallowaredu tion innoiseaswell, assumingthatredu ing suspension

vibration does,infa t, redu einterior noise.

1.5 Overview

Thegoalofthisproje twastoredu einteriorroad-indu ednoisewithoutnegatively

impa t-inghandling. Basedontheassumptionthatredu ingvibrationofthe rossmember(frame)

will redu e the interior abin noise, we designed a ontroller to redu e the ross member

(17)

spe i ations ofthe ele tromagneti a tuator we hose. The ele tromagneti a tuator a ts

a rossthepoint4bushing toredu eroad noisevibration transmission. Chapter3des ribes

theexperimentalsetup: theLin olnLS,shaker,a elerometers,mi rophone, dynami signal

analyzer,andele troni ontrolunitweusedfortesting. Chapter4presentsthe

experimen-talresultsweobtainedusingatonal(narrowband) ontroller enteredat150Hz. Bothopen

and losed loop vibration dataisgiven, aswell astheexpe ted ontroller performan e and

losedloopsoundlevels. Thedi ultieswithbroadband ontrolaredis ussedinChapter5,

along withadditional tonal ontrollers, similar to theone dis ussedin Chapter4, entered

at 140, 160, and 180 Hz. Broadband ontrol proved to be di ult due to two zeros in

thetransfer fun tion from the a tuator to the ross membera elerometer, at 128 Hz and

184 Hz, givingthe a tuator no ontrol authorityat thosefrequen ies, and due to the large

non-minimum phase lag between 60 and 70 Hz. Chapter 6 dis usses the on lusions and

(18)

(19)

A tuator Design

This hapter des ribesthea tuator designpro ess. First,Se tion 2.1dis ussestheproblem

des ription, namely, redu ing interior abin noise aused by road noise vibrations. Then

the requirements on the a tuator su h as required for e and displa ement are des ribed

(Se tion 2.2). Two dierent types of a tuators, piezoele tri erami sta k a tuators and

ele tromagneti a tuators, are onsidered (Se tion 2.3). Finally, in Se tion 2.4, the

ele -tromagneti a tuator sele ted for this proje t is des ribed, and the spe i ations for that

a tuator arederived.

2.1 Problem Des ription

The spe i goal of this proje t is to redu e road noise that is transmitted through the

suspension system and frame of the automobile into the passenger ompartment, without

ompromisingvehi lehandling. Bumps,potholes,andthegeneralunevennessoftheroadall

vibratethewheelasanautomobiletravelsoverroadsurfa es. Thevibrationsarethen

trans-ferred through the ontrol arm, a rubberbushing, and into the frame,eventually rea hing

thepassenger ompartment, ausing undesirednoise.

As dis ussed previously, there are three ommon approa hes to the problem of noise

redu tion. Eliminating or redu ing the noise at its sour e is not pra ti al inthis ase; the

roads annot be made perfe tly smooth to prevent the wheel from vibrating. Although

(20)

the front left suspension with the tire removed. The A shaped ontrol arm is towards the

bottomofthe photograph. The rossmember,theupsidedown Ushapedpartoftheframe

over the bushing, is near the top. The visible bolt end is the bolt that goes through the

point4 bushing.

outside the s ope of this proje t. Modifying the transmission path of the vibration is the

approa h thatwe have employed here.

The geometry of the suspension systemis shownin Figure2-1. The rossmember is a

stru tural elementoftheframe,lo atedapproximatelyon theaxes ofthefrontwheels,that

supports theengine. The ontrol armisan A-shaped omponent of thesuspension system.

It is onne ted to thesho k absorber, the wheel at the spindle, and to the frame through

two bushings,the point3 the point 4 bushing. Thepoint3 bushingis thefrontbushing on

the ontrol arm onne ting itto theframe, and thepoint 4 bushingis therear bushing on

the ontrol arm, onne tingthe ontrol armto the rossmember.

A ording to tests ondu ted byFord MotorCompany, mostof theroad noise (andthe

steering for es) is transmitted in a single dimension, parallel to the wheel's axis, through

thepoint 4 bushing [9℄. For noise redu tion purposes, a soft point 4 bushing ispreferable.

A soft bushing would transmit less for e to the frame of the vehi le, making the interior

(21)

to the wheels,sothatthe arrespondsqui klyand a uratelyto driverinputs.

Be ause of the two opposing requirements for the point 4 bushing stiness soft for

noiseredu tionandstifor vehi lehandling,apassivebushingisne essarilya ompromise.

However, the steering for e frequen iesare on the orderof a few hertz, and theroad noise

vibrationfrequen iesareontheorderofahundredhertz. Therefore,ana tivebushingthat

a ts stiat lowfrequen ies andsoft athigher frequen ies ould be usedto reate a quieter

interiorwithout negatively ae ting vehi lehandling.

Therearetwoapproa hesto reatethisa tivebushing. One ouldbeginwithaphysi ally

softbushing,and usea tive ontrol to stienitat low frequen ies; orone ould beginwith

a stibushing,and usea tive ontrol to soften itat higher frequen ies. Thelow frequen y

for es asso iated with handling are omparable to the weight of the ar (approximately

20,000 N), and therefore the amount of ontrol authority required to stien the bushing

at those frequen ies is quite large. An example of the former approa h (stiening at low

frequen ies) is the work done at Bose Corporation. The modular design added a linear

ele tromagneti motor at ea h wheel with a modied M Pherson strut arrangement. [20 ℄

To demonstratethea tive suspension,aBosemodiedLexus LS400 waspla ed atopa four

postshakertosimulatetraveling downarough road. Fromtheoutside,thewheels ouldbe

seen to be gyrating wildly,and from theinside, there wasvirtually no sense ofmotion. [6℄

CurrentlyBoseisredu ingtheweightandsele tingamanufa turer forthea tivesuspension

system. [20℄

Onthe otherhand,usingastibushing,the for esasso iatedwithroadnoisearemu h

lower, onthe order of 150 N (see Se tion 2.2) and,as a result, mu h less ontrol authority

isne essaryto soften thebushing at higherfrequen ies. For this reason,our proje tbegins

withastibushing,andwethenusea tive ontroltosoftenthebushingatfrequen iesfrom

(22)

To begina tuator sele tion,onemustrst determinethedesignrequirements ofthesystem

during normaloperation. The design parameters of this parti ular systemin lude bushing

displa ement (required to ountera t displa ements aused byroad noise vibrations), for e

a ross the bushing (that orresponds to the bushing displa ement), a tuator bandwidth,

and alsothe ee ts ofsho kloading.

As an be seen in Figure 1-4, almost all of the energy in thespe trum is near 150 Hz,

and themeansquareda eleration is0.04g

2

. The rms a elerationisgiven by

σ

a

= 0.2

g

= 1.96

m

/

s

2

(2.1)

Sin e almost all the vibration o urs at a frequen y of 150 Hz (

ω = 942

rad

/

s), the rms displa ement is given by

σ

d

≈ σ

a

/ω

2 = 2.5 µ

m (2.2)

During normal ex itation of the wheel, the rms point 4 bushing displa ement is

approxi-mately

1 σ

d

.

2.5 µ

m under oarse road onditions. Allowing for

3 σ

motion, thea tuator shouldbe apableof atleast7.5

µ

mofa tuation. Thefor ethatthea tuatormustbeable to provide is al ulated byHooke'sLaw,

f = kd

where

k

is the stiness of the point 4 bushing (about 20 kN/mm), and

d

is the required displa ement (7.5

µ

m). Therefore,itisne essaryforthea tuatortogenerate atleast150N of for e.

As seen in Figure 1-2, the a tuator will be required to ountera t disturban es of

fre-quen ies between 100 Hz and 200 Hz. Therefore, the large signal bandwidth must be at

least200Hz,meaningthatthea tuator mustbe apableofgeneratingfor esontheorderof

150 N,up to 200 Hz infrequen y. However, to ensure thatthephaselag inthea tuator is

(23)

than 2000 Hz.

Thea tuator mustalsobeabletowithstand sho kloads,su hasthatofawheelhitting

a urb or a pothole, or those produ ed during sharp turns. The entire vehi le weighs

approximately 2000 kilograms;undernormal onditions ea hwheelsupports 500 kilograms

(5000N).Duringanextremeturnorhittingapotholewithmostofthelateralfor esrea ted

by theouterwheels, the for es might beashigh as10,000N. Therefore,thea tuator must

beableto withstandsteeringloadsofapproximately10,000 Ntothebushing. Equivalently,

thea tuatormustbeabletowithstandabushingmotionof500

µ

m(0.5mm)duetosteering loads, again al ulated using the bushing stiness. The a tuator would not be required to

ountera t these loads,but itmust be ableto bearthem and ontinue to operate afterthe

loading isremoved.

Be ause the a tuator must be able to withstand displa ements mu h larger thenwould

normally be produ ed by thea tuator, thea tuator should be ompliant, when ompared

to thestinessof thebushing. Ana tuator that is ompliant isee tively a for ea tuator

rather than a displa ement a tuator. The ideal a tuator for this proje t should ommand

for erather than displa ement.

2.3 Piezoele tri vs. Ele tromagneti A tuator

Afterdeterminingtherequirementsonthea tuator,twotypesofa tuatorswere onsidered.

One is an a tuator made from piezoele tri erami sta ks, one is an ele tromagnet made

fromsteel laminations.

2.3.1 Piezoele tri Cerami Sta k A tuator

Onepossibletypeofa tuatorisapiezoele tri erami sta ka tuator. Thistypeofa tuator

isanattra tive optionbe ausethe piezoele tri material hasahighenergy density,

approx-imately

80

kJ

/

m

3

,and a highbandwidth. However, itmaybedi ult to getthene essary

stroke,sin epiezoele tri materialsprodu everysmalldispla ements,andverylargefor es.

(24)

Instrumente (Auburn, Massa husetts), is

5

mm

× 5

mm

× 9

mm , and itis apable of 800 N for e and 6.5

µ

m displa ement. A sta k this size is on the order of $150. [24 ℄ One of these piezoele tri sta ks has more for e than is ne essary for our needs, but not nearly

enough displa ement. Therefore, multiple sta ks and an ampli ation me hanism an be

used to meet the a tuator requirements. As a rough estimate (order of magnitude) of the

numberof sta ks required, ompare the piezoele tri sta kspe i ations withthea tuator

requirements. The for e of a single sta k is

800

N

/150

N

= 5.3

times larger than we need. The displa ement is

500 µ

m

/6.5 µ

m

= 77

times smaller than we need. Thus, even with an ampli ation me hanism to mat h the impedan e of the material to the requirements, we

nd thatwe need at least15piezoele tri sta ksto a hieve enough for eandstroke.

The piezoele tri sta ks are too sti for this appli ation. Therefore, an ampli ation

fa tor must be hosen to mat h the stiness requirement. However, the displa ements

and for es annot be modied separately (as assumed in the above estimation). A single

ampli ation me hanism must be used to both amplify the displa ement and redu e the

for e. Tomakethispiezoele tri materialappropriatehere,theremustbesomeampli ation

me hanism. Consider a me hanism thatamplies the a tuator displa ement bya fa tor of

A, so that the ratio of original to modied displa ement is

1

A

. Then the ratio of original

to modied for e would be A,so thatthe ratio of original to modied stinessis

1/

A

2

. If

the original a tuator for e is 800 N, but thea tuator is only required to provide 150 N of

for e,thenA

= 5.3

for anidealampli ationme hanism. Then15sta kswouldberequired to a hieve the ne essarystroke,and even more piezoele tri sta ksfor a real(less e ient)

ampli ation me hanism.

Be ausethedrivingrequirementontheamount ofne essarypiezoele tri materialisthe

steering sho kloads, not thehigher frequen y a tuation requirement, more than 15 sta ks

would be required for a piezoele tri a tuator a ting a rossthe point 4 bushing. At a ost

of around $150 ea h, more than 15 sta ks is obviously far too many sta ks to make this

piezoele tri erami sta ka tuator feasible inthisappli ation.

(25)

piezoele -a proof mass may be a more pra ti al type of piezoele tri a tuator. At the operational

frequen yrange, between100 Hzand200 Hz,thepiezoele tri material wouldpushagainst

theproofmass(whi hideally wouldnotmove)todispla e thebushing. Atthelow

frequen- iesofthesteeringsho kloads,thistypeofa tuatorwouldpushagainstandmovetheproof

mass, making it ompliant, and redu ing the required number of piezoele tri sta ks. To

minimize the amount of piezoele tri material,the proofmassshould have about the same

dynami stinessasthestinessofthepoint4bushing(20kN/mm)at100Hz. Thedynami

stiness of the proof massis M

ω

2

, where M is themass, and

ω

is thepertinent frequen y (here100 Hz). Settingthedynami stiness equalto 20kN/mm resultsinarequired proof

mass of approximately 50 kg. Unfortunately, a 50 kg proof mass added to the suspension

systemistoolargetobeafeasiblea tuationsolution. Asmallerproofmass anbeused,but

thatwouldredu ethe e ien y andrequiremorepiezoele tri material. A5 kgproofmass

would be more appropriate in size, but wouldagain require approximately 25 piezoele tri

sta ks,whi h would be too ostly for feasibility. Although a tive material a tuators, su h

aspiezoele tri ones, areattra tive insome respe ts,they areprobablyimpra ti al for this

appli ation.

2.3.2 Ele tromagneti A tuator

Another possible type of a tuator is an ele tromagneti a tuator; with a xed element

(magneti ore), oil(ex itation winding),and amovableelement (armature). [19℄

Ele tro-magnetsareused inmanyappli ations, for example:

Solenoida tuators: aps,pneumati andhydrauli valves,slidevalves,interlo ks

breaks.

Hammering a tuators: riveting,pun hing, stamping, hiseling ma hines.

Turningmagnets: throttlevalves, ontrolvalves(hydrauli ,pneumati ),material

support(forinstan e web of loth,paper), turnout intransportplants.

(26)

ing plants, os illating sieves, os illating tables, swinging and heli al

onvey-ors. [19℄

Ele tromagneti a tuators anbevery ompliant;thegapbetween therotorand thestator

allows for mu h larger sho k motion than the ontrol motion provided by the a tuator.

Another benet is that ele tromagneti te hnology is mature, ontributing to a redu ed

ost when ompared to the ost of a tive materials. After determining that an a tuator

made of piezoele tri erami sta ks is not feasible, we hose to pursue development of an

ele tromagneti a tuator for thereasonsoutlinedabove.

2.4 Ele tromagneti A tuator Spe i ations

The ore of an ele tromagnet is made of steel laminations. Steel is used be ause of its

ele tromagneti properties, butasolidsteel oreisnotase ientasalaminated ore. The

laminations redu e eddy urrentsthat resultfrom theindu ed magneti eld. Be ausethe

bandwidth of the a tuator is proportional to the inverse of the timeit takes for the eddy

urrentsto settle,redu ing theeddy urrentsin reasesthebandwidthoftheele tromagnet.

Theele tromagnetusedherehas54laminationsthatareea h0.0185in hesthi k(0.47mm),

for a total thi kness of 2.5 m. (Figure 2-2) The laminations were ut to shape by an

ele troni dis hargemilling (EDM)ma hine.

The ele tromagnet onsistsof astator, arotor, anda 2mmair gap separatingthetwo.

The stator is the approximately ir ular side of the ele tromagnet, and is on entri with

thepoint 4 bushing. Itis bolted to the rossmemberand hasa radius of 5 m. The rotor

is roughly U-shaped, and is bolted to the ontrol arm. The ends of the rotor arms are

rounded so that they onform to the urvature of the ir ular side of the ele tromagnet,

whilemaintainingthe2mmairgap. Theseroundededgesallowthemagnet torotateabout

the point 4 bushing bolt with the ontrol arm without altering the 2 mm air gap. The

magneti rotor isapproximately 15 mlong,8 mhigh, and2.5 mthi k. Figure2-3shows

(27)

laminated core with 2 poles

attached to control arm

laminated disk attached to cross member

2 mm air gap

copper windings

Figure2-2: Diagramof theproposedele tromagneti a tuator.

The for e produ ed by anele tromagnet isproportional to thesquare of the urrent in

the oil. Therefore, to get an approximately sinusoidal for e, a large bias urrent plus a

sinusoidal urrent is required. For this ele tromagnet, therotor iswoundwith120 turns of

opperwire. The maximumrequired urrent is10 A plusthebias urrent.

2.5 A tuator Amplier

To supplythe large urrentsthatarerequired fortheele tromagneti a tuator operation, a

substantialpowersupplyandamplierwereemployed. Theamplier usedwiththe

ele tro-magneti a tuatorisabrushtypepulsewidthmodulatedservoampliermadebyAdvan ed

Motion Controls (Montville, New Jersey), model 100A40. It requires a DC power supply

between 80 V and 400 V. The amplier is apable of

±

100 A peak urrent and

±

50 A ontinuous urrent. [2℄ A tuator urrent an be measured using theamplier's monitoring

port. A Hewlett Pa kard (Palo Alto, California) power supply, model 6479C, was used to

providethed powerforthea tuatoramplier. Thepowersupply anprovidefrom0-300V

and 0-35A ofpower.

To implement this ele tromagneti a tuator in a real ar, we learly annot use su h a

(28)

rossmember.

42V,whi h is ompatible withthe42 Vsystemslikelyto be usedinthenearfuture. [5℄In

addition, the total urrent requirements an be redu ed substantially by using a apa itor

(29)

Experimental Setup

This hapter des ribes the experimental testbed (the Lin oln LS) used in this proje t. In

parti ular, we des ribe the shaker used to indu e vibrations in the testbed; the load ell

used to measure the for es generated by the shaker; the a elerometers used to measure

thetestbedvibrations; themi rophone usedtomeasuretheinterior abinsound; thesignal

analyzer used as a virtual fun tion generator, data re order, and data analyzer; and the

ele troni ontrol unit used as D/A and A/D onverters, as well as an interfa e to the

software ontroller.

3.1 Lin oln LS

Experimentspreviously ondu tedbyresear hersatFordMotorCompanyontheLin olnLS

led to the on lusion that most of the road noise vibrations are transmitted through the

point 4 bushing, a nding spe i to this model. [26 ℄ As des ribed earlier, the point 4

bushing is the bushing that onne ts the ontrol arm to the vehi le frame. Other Ford

vehi lesdidnotexhibitthesamemajorvibrationpathway; anyte hniquefornoiseredu tion

a omplished bythis study maynot apply to otherFord vehi les.

It is ne essary to design a testbed setup in order to study the road noise transmitted

throughthe suspensionsystemofa Lin oln LS,withthegoal ofredu ing thisnoise. Inour

setup, road noise was simulated using a shaker to apply for es to the suspension. Sensors

(30)

interior to measure the sound. The testbed initially in luded the front suspension system

omponents, part of the vehi le frame, and the front wheels and tires for support. The

initial testbedwasthefrontend ofa Lin oln LSprovided byFord,ni knamed Sneezy,with

all ne essary omponents forward of the steering olumn. (Figure 3-1) In luded were the

major parts of the frame and the entire suspension system. The body panels, engine, and

other omponentsofthe engine ompartment werenotin luded. Dueto themissingweight

of these omponents, theride height wastoo high. We built a wooden box (lo ated inthe

engine ompartment)toholdapproximately700 kgofleadbri kstoa hievethe orre tride

height. Be ause the rear end of the arwasnot present, a metalframe was welded to the

rearof theframe inorderto properlypositionthe testbed.

Sneezy was found to be an inadequate testbed; results obtained using Sneezy mat hed

neither the expe ted results nor the results from previous tests ondu ted by Ford. To

onsider Sneezy an appropriate testbed, the transfer fun tions obtained from Sneezy and

those from Ford's vehi le modeling program should mat h, but they did not. The

appar-ent resonan e at 150 Hz from Ford's datawas not present inexperiments on Sneezy. (See

Figure 3-2.) The resonan es of Sneezy's transfer fun tions are at higher frequen ies.

Ad-ditionally, the result from Ford that most of the vibrations are transmitted through the

(31)

0

150

300

400

500

600

700

800

900 1000

−80

−60

−40

−20

Magnitude (dB)

0

150

300

400

500

600

700

800

900 1000

−50

0

50

100

150 Frequency (Hz)

Phase (degrees)

Figure3-2: Thetransferfun tionfromtheshakerex itationtothe rossmember

a elerom-eter (data a quired with Sneezy). No major peak is present near 150 Hz ( ompare with

Figure1-2).

After itwasdetermined thatthe front endof theLin oln LS didnot produ e the same

resultsasanentire ar,FordMotorCompanyprovideda omplete,drivable2001Lin olnLS.

Usingtheentirevehi le,thevibrationtransmissionpathsandnoise ouldbestudiedinmore

detail. Theneventually,we andesign a ontrollerto allowforaquieter drive without

om-promisingvehi lehandling. AnadditionaladvantageofusingtheentireLin olnLSisthatit

would permitmeasurement ofthe interior soundlevels,and allowtestingof thehypothesis

thatredu ing the rossmembervibration also redu estheinteriorsound. Figure3-3shows

thenewtestbed (theentire Lin oln LS).

The experimental setupusing theLin oln LSis furtheroutlined inFigures 3-4and 3-5.

During the shaker or a tuator transfer fun tion identi ation, thedynami signal analyzer

sendsthedrivingsignaltoeithertheshakerorthea tuator. (Figure3-4)Thesolidline

on-ne tingthesignalanalyzerto theshakerboxrepresentsthe onne tionthatispresentwhen

(32)

MIT.

thea tuatorrepresentsthe onne tionthatispresentwhenidentifyingthea tuatortransfer

fun tions. Theshakeris onne tedinserieswithaload ellandastingtothesuspension,so

thatwhen theshakerisbeingdriven,theapplied for e an bemeasured. Either theshaker

signalor the a tuator signal an be usedto indu evibration intheLin oln LS automobile.

Signals from the sensors on the automobile (the a elerometers and the mi rophones) are

sent ba kto thedynami signalanalyzer andtheele troni ontrol unit'spro essors,where

thesignals arere orded andanalyzed.

In the losed loop system (i.e., when the ontroller is present and operational), the

system fun tions in a slightly dierent manner. (See Figure 3-5.) The dynami signal

analyzerstill drivestheshakerthrough aload ellto vibratethe ar,and thea elerometer

and mi rophone signals are still sent ba k to thesignal analyzers and hardware ele troni

ontrolunitforanalysis. Themajordieren einthe losedloopsystemisthatthe ontroller

(33)

accels

mics

shaker

signal

analyser

actuator

Lincoln LS

electronic

control unit

load cell

Figure 3-4: The blo k diagram outlines the experimental setup during either shaker or

a tuator transferfun tion identi ation. The signalanalyzerdriveseithertheshaker(solid

line)orthea tuator(dashedline). Eithertheshakerorthea tuatorvibratestheLin olnLS.

Thesensors on the automobile,both thea elerometers andthemi rophones, measurethe

vibration and returnthe signals to thesignalanalyzer andele troni ontrol unit.

3.2 Simulated Road Noise Ex itation

For thepurposes of these experiments, it was not feasible to drive the Lin oln LS on road

surfa es to measure and re ord vibrations of the wheel and other suspension and frame

omponents, and theresulting soundinthe interior oftheautomobile. Therefore,theroad

noise vibrations had to be simulated in the laboratory. To a omplish this simulation, a

shakerwasatta hedbya stingto thepassenger side ontrol arm. (SeeFigure3-6.)

The shaker used was a model 420 shaker, made by Ling Ele troni s, In . (Anaheim,

California). The shakerisan ele tromagnet; urrent is suppliedto theshaker(whi h hasa

permanent magnet armature),indu ing amagneti eld and a magneti for e. The shaker

is apable of providing up to 133 N of for e in a frequen y range of 0 to 7500 Hz and a

(34)

electronic

control unit

Lincoln LS

accels

mics

shaker

actuator

signal

analyser

load cell

Figure 3-5: The losed loop blo k diagram represents the experimental setup during

on-troller operation. The signal analyzer drives theshaker through a load ell to vibrate the

ar,andthea elerometersandmi rophones measurethevibrationsandsendthemba kto

the signalanalyzer and ele troni ontrol unit. In this setup, the ontroller isdownloaded

to the ele troni ontrol unitexpansion boxand drivesthea tuator.

rms. [22 ℄ Theamplier usedwiththeshakerisaYorkville Audiopro 3400,ahighe ien y

stereopoweramplier, madebyYorkvilleSound, Toronto, Canada.

Vibration due to road roughness is simulated by the shaker, whi h is atta hed to the

ontrol armbya sting. A load ell waspla ed inseries withthesting to measurethefor e

applied. Thestingisaslenderaluminumrodwithoneend s rewedinto theload ell,whi h

isinturn onne tedto theshakerfa e,andtheotherends rewedintothe ontrolarm. The

stingisatta hedtothe ontrol armatthepointdesignatedbythearrowinFigure3-7. The

shakerpushesforeand aft on thesting, whi h pushesforeand aft onthe ontrol arm.

Wealsosometimesusedanalternativemethodformountingtheshaker,byatta hingthe

shakerthroughthe sting toawheellugbolt. Thesting wass rewed intoalugnutadaptor,

(35)

from this method of atta hment were found not to be as representative a load ase asthe

foreandaft ex itationdes ribedabove. Also,a ordingtoFord, theforeandaft ex itation

resultsinvibrationsinthevehi lethataremorerepresentativeofreal-worldvibrations. [26 ℄

3.3 Instrumentation

Inordertomeasureandre ordthevibration,vibrationtransmissionthroughtheframe,and

interior abinsound during experimentation, two types ofsensors were usedto instrument

the Lin oln LS automobile. A elerometers were pla ed in two lo ations to measure the

vibrations, one on the frame, and the other on the ontrol arm. Also, a mi rophone was

pla ed in four dierent lo ations in the interior of the vehi le to measure the sound level

throughout the automobile.

3.3.1 A elerometers

To measure and re ord the vibration of the relevant suspension omponents, two Endev o

(San Juan Capistrano, California) piezoele tri a elerometers were employed. One was

(36)

Thephotograph is taken fromthefront, looking aftat theright frontwheel.

Table 3.1: Additional Endev o piezoele tri a elerometer spe i ations

Serial Number EL89 EL92

Charge Sensitivity 96.8pC/g 97.1pC/g

Capa itan e 2743 pF 2698 pF

Max. Transverse Sensitivity 0.4% 2.0%

The pla ement of the a elerometers is shown in Figure 3-8. The small metal ylinders

atta hed to ables arethe a elerometers. The a elerometer above thepoint 4bushing in

the pi ture is atta hed to the ross member, and will be referred to as the ross member

a elerometer. The a elerometer below and to the left in the pi ture is atta hed to the

ontrol arm, andwill bereferredto asthe ontrol arma elerometer.

The a elerometers used were Endev o model 7701-100. The frequen y range of the

a elerometersis20Hzto 5kHz. Theserialnumbers forthe rossmemberand ontrol arm

a elerometersareEL89andEL92,respe tively. Additionalspe i ationsforthe

a elerom-eters are shownin Table 3.1. [7 ℄ Endev o laboratory harge ampliers, model 2721B, were

(37)

membera elerometer isthe a elerometer lo ated above thepoint 4bushing. The ontrol

arma elerometer islo atedbelow andto theleft ofthepoint 4bushing.

harge sensitivity of ea h a elerometer, as well as thedesired gain (V/g). The frequen y

range of the harge ampliers is3 Hz and 10 kHz. Theoutput has a maximumvoltage of

10.0V peak,and a maximum urrent of 2.0mA. [8℄

3.3.2 Mi rophones

The mi rophone on a sound level meter was used to measure the sound at ea h of four

positionsintheinterioroftheLin olnLS.The1982Pre isionsoundlevelmeterandanalyzer

wasmadebyGenRad(nowIETLabs, In .,Westbury,NewYork). Therangeof thissound

level meter is 30 dB to 130 dB rms (150 dB peak). [17℄ The sound level distribution

throughout the interior of the automobile is quite modal. The sound waves from all of

the numerous sour es of noise in the vehi le intera t, ausing a large number of nodes

and antinodes. At the nodes, the sound waves are out of phase and an el ea h other's

magnitude; and at theantinodes the pressure wavesare in phase and themagnitudes add

(38)

( )

Figure 3-9: The rst mi rophone position is lo ated at the driver's left ear. The se ond

mi rophone position is at the ree tion of this position at the front passenger's right ear

(a). Thethird mi rophone positionis lo ated attheright (passenger side) rearpassenger's

right ear(b). Thefourthmi rophone positionislo atedinthe enterofthedriver'sseat at

approximately hinlevel( ).

where the driver or any passengers would be able to hear the transmitted road noise are

signi ant for thisproje t, andthemi rophonepositionswere hosento measurethesound

inthese areas.

Therstmi rophone positionisat thedriver's leftear. (SeeFigure3-9(a).) These ond

mi rophonepositionisatthefront passenger'srightear,aree tionoftherstmi rophone

position, as shown in Figure 3-9(a). The third mi rophone position is at the right rear

passenger's right ear. (See Figure 3-9(b).) The fourthand nalmi rophone position

(Fig-ure3-9(b))isatapproximatelythe enteroftheseat,atthedriver's hinlevel. Therstand

(39)

abetter ideaof thesounddistribution throughout theinteriorof theautomobile.

3.3.3 Shaker For e

Aload ellwaspla edbetweenthestingandtheshakerfa etomeasureandre ordthefor es

appliedbytheshakertotheautomobilethroughthesting. Thefor emeasurementprovides

more detailed information about the load ase than what an be dedu ed from the shaker

input signal voltage. The load ell used is model SM-50 made by Interfa e (S ottsdale,

Arizona). It an measure for es up to 200 N. At 200 N of for e the dee tion is 0.08 mm

and the natural frequen yis 1550 Hz. [18 ℄

3.4 Dynami Signal Analyzer

Thedynami signalanalyzerservesmanyfun tions. Ita tsasavirtual fun tion generator,

datare order, and a dataanalyzer. The dynami signal analyzer usedhere onsistsof two

Siglabmodel20-42signalanalyzersandtheasso iatedsoftware,madebySpe tralDynami s

(SanJose,California). Ea hsignalanalyzerunithasa20kHzbandwidth, 4input hannels,

and 2output hannels, fora total of 8input hannels and 4output hannels. [29℄

The dynami signal analyzer was used asa fun tion generator to provide the required

sinusoidal signals to drive the shaker or the ele tromagneti a tuator, depending on the

experiment. Thesoftwarevirtual fun tiongeneratorsuppliedthene essarysignalssentout

through a D/A onverter and the output hannels. The two output hannels an

indepen-dently supply two dierent ex itationsignals for useduring the testing. Ea h hannel an

output20 mAand 10V maximumwithan available optionalDCoset. [29 ℄

The signal analyzersalso have analog to digital onverters, whi h were used to a quire

and re ord the various a elerometer, mi rophone, and load ell signals. The two signal

analyzer units were time syn hronized, allowing simultaneous re ording of eight dierent

signals. The voltage range for ea h input hannel is adjustable from

±

20 mV to

±

10 V. [29 ℄

(40)

the sensor signals, simple transfer fun tions, and the oheren e of the estimated transfer

fun tion. Theavailableanalysisfun tions(otherthan oheren e)in ludetimehistory,

auto-spe trum,transferfun tion, ross-spe trum,auto- orrelation, ross- orrelation,andimpulse

response. [29 ℄ Che king the oheren e wasespe iallyimportant to ensure that the signals

were of a highenough signal-to-noise ratio to trust the results. The re orded signals were

also exportedto Matlab, to allowfor more extensive analysis.

3.5 Ele troni Control Unit

The signal analyzers have analog to digital and digital to analog onverters that an be

used to transfer the shaker and a tuator driving signals, as well as to a quire the sensor

signals. Anotherpie eofhardware,theele troni ontrolunit,madebydSPACEIn (Novi,

Mi higan), was used for the ontroller signals. The ele troni ontrol unit onsists of an

expansionbox(modelPX10)andtwoI/Ods1003pro essorboardsmountedintheexpansion

box. The ontrolfeedba ksignals(a elerometerandmi rophonesignals)werebroughtinto

the omputer using this ele troni ontrol unit. This ele troni ontrol unit has, among

other things, hardware A/D and D/A onverters. It was also used as the interfa e for

the software ontroller. The ontroller was assembled in the Matlab modeling appli ation

Simulink, and then downloaded and run from this ele troni ontrol unit. An asso iated

program alledControl Deskworkswiththeele troni ontrol unit, andallowssome ofthe

ontrol parameters to be hanged whilethe ontroller is operating. Thisfeature allowed us

(41)

Experimental Results

This hapter presents and explains the experimental data taken on the Lin oln LS. First

is the baseline data, the open loop transfer fun tions from the shaker and a tuator to

the ross member and ontrol arm a elerometers, in Se tion 4.1. Next (Se tion 4.2), the

designof tonal ontrollersisdis ussed. Thisisfollowedbytheexpe tedperforman e. Both

the predi ted performan e from the Bode plot of the ontroller transfer fun tion and the

performan e omparison of the al ulated theoreti al transfer fun tion to the measured

experimental transferfun tion (showing thatthe experimental results mat h thepredi ted

theory) is des ribed. Finally, the losed loop data is presented, in luding the losed loop

vibration (Se tion4.4) andthe interior soundlevels(Se tion 4.5).

4.1 Open Loop Results

The initial baseline results aretheopen loop transferfun tions. The two ex itation inputs

are theshaker (des ribed in Se tion 3.2) and the a tuator (des ribed in Se tion 2.4). The

two important open loop outputs arethe rossmembera elerometer and the ontrol arm

a elerometer (des ribedinSe tion3.3.1). Figure4-1showstheopenlooptransferfun tion

fromtheshakerinputtothe rossmember(thinline)and ontrolarm(thi kline)

a elerom-eter outputs. Clearly,both the rossmember a elerometer and ontrol arma elerometer

transferfun tionsarequitemodal. Also,the150Hzpeakthatwaspresent inthedatafrom

(42)

10

1

10

2

10

3

10 −2

10

0

10

2 Magnitude

10

1

10

2

10

3 −4000

−3000

−2000

−1000

0 Phase (degrees)

Frequency (Hz)

cross member

control arm

Figure 4-1: Open loop transfer fun tions from the shaker to the ross member (thin line)

and ontrol arm (thi kline) a elerometers. Both transfer fun tionsare quitemodal. The

150 Hzpeakthatwaspresent inthedatafromFord(Figure 1-2)isalsodi ultto observe.

fun tion. Figure 4-2 shows the open loop transfer fun tions from the a tuator ex itation

to both the ross member (thin line) and ontrol arm (thi k line) a elerometers. Again,

both of the open loop transfer fun tions are quite modal. Control ould be di ult due

to themany modespresent inthe rossmembera elerometer transferfun tion,aswell as

thelarge phase roll-o present inthe rossmembertransfer fun tion. Thedi ulties with

broadband ontrol will be des ribed further inSe tion5.1.

4.2 Tonal Controller

After examining the open loop transfer fun tion from the a tuator to the ross member

a elerometer, the form and details of the ontroller must be determined. Be ause the

transfer fun tionsfrom the shakerto thea elerometers and also from the a tuator to the

a elerometersarehighlymodal(Figure4-2), thedesign ofabroadband ontrollerthathas

(43)

10

1

10

2

10

3

10 −2

10

0

10

2 Magnitude

10

1

10

2

10

3 −500

0

500 Phase (degrees)

Frequency (Hz)

cross member

control arm

Figure4-2: Open looptransferfun tionsfrom thea tuator tothe rossmember(thinline)

and ontrol arm (thi kline)a elerometers. Both transferfun tionsarevery modal, whi h

ould make ontrol di ult. Also the rossmember a elerometer transfer fun tion has a

signi ant phase roll-o that an auseproblems with ontrol.

broaden the ee tive frequen y range on ethe simpler tonal ontroller is fun tional. This

tonal ontroller will demonstrate whether ontrolis ee tive,i.e., ifredu ing rossmember

vibration redu es interiornoise.

The tonal ontroller will be a feedba k ontroller. Here, the logi al variable to be fed

ba k isthe ross membera eleration. In theunmodiedbushing, with no a tuator, road

noisevibrationistransmitteda rossthepoint4bushing. Thea tuatoraddedtothesystem

will be used to supply a for e that an els the road noise vibration the ross member

a eleration will be fed ba k into the ontroller and driven to zero. If the vibration of the

rossmember anberedu ed,thenthesoundsintheinterior ausedbythatvibrationshould

also be redu ed.

The tonal ontroller employed hereis designed toeliminate the rossmember vibration

at a singlefrequen y. The initial frequen y onsidered was 150 Hz, hosen be ause itfalls

(44)

ontrol (HHC) originally designed to redu e heli opter vibrations, developed by Hall and

Wereley [11 ℄. Their ontinuous timeHHC ompensator is

K(s) =

2k(as + bΩ)

s

2 _{+ (Ω)}

2

(4.1) where

a =

Re

[G(jΩ)]

|G(jΩ)|

2

(4.2)

b =

Im

[G(jΩ)]

|G(jΩ)|

2

(4.3)

k =

1 T

(4.4)

and

T

isthedesiredthesettlingtimeofthe losedloopsystem. Inthis ase,

Ω

,thefrequen y (in rad/s) of the harmoni to be redu ed, is

Ω = 2π × 150

Hz , and

G(jΩ)

is the transfer fun tion fromthea tuator to the rossmembera elerometer evaluatedat 150 Hz.

This ontroller (Equation 4.1) eliminates vibrations at the frequen y

Ω

be ause

K

is innite there. The onstants,

a = −0.099

and

b = 0.2732

, determined from the transfer fun tion

G(jΩ)

, generally result in good phase margins at the rossover frequen ies, just aboveandbelow150Hz. However,itissometimesne essarytoadjust

a

and

b

togivebetter phasemargins at one ofthe two rossoverfrequen ies(above or below

Ω

).

4.3 Expe ted Performan e

Classi al ontrol theory di tates that for the most basi feedba k ontrol system, su h as

theone showninFigure4-3, the losed loop transferfun tion isgiven by

H(s) =

K(s)G(s)

1 + K(s)G(s)

(4.5)

where

H(s)

representsthe losedlooptransferfun tionfrom

r

to

y

,

G(s)

istheplanttransfer fun tion, and

K(s)

represents the ontroller transfer fun tion. In Figure 4-3, theinput or

(45)

G(s)

u

e

r

₊

-K(s)

y

Figure4-3: Classi al ontroltheoryblo kdiagram.

G(s)

istheplant,

K(s)

isthe ontroller,

r

is the input(also alled the referen esignal),

e

is theerror signal,

u

is the ontrol signal, and

y

isthe outputsignal.

G(s)

u

e

+

-K(s)

y

+

0 d

Figure4-4: Disturban ereje tionblo kdiagram. Thesignalsarethesamesignalsdes ribed

inFigure4-3.

referen e signal,

r

,is the ommand signal. The error signal,

e

, thedieren e between the referen e signal and the output, is also the ontroller input. The ontrol signal,

u

, is the outputfrom the ontroller. Theoutput signal,

y

,isthemeasurement of interest.

In disturban e reje tion problems (Figure 4-4), su h as this one, the input referen e

signal is set to zero, sin e the desired output,

y

, is zero. The transfer fun tion from

d

to

y

, whi h measures the attenuation of the disturban e by the ontroller, is alled the sensitivity transfer fun tion,and isgiven by

S(s) =

1 1 + G(s)K(s)

(4.6)

TheLin oln LS systemisonly slightlymore ompli atedthanthestandard disturban e

reje tion systemdes ribed above, be ause the disturban e signal,

w

, does not add dire tly to theplant

G(s)

output. The disturban e signal is modied by the shakertransfer fun -tion, making

d = wG

w

(s)

the signaldire tly added to the plant output. A blo k diagram representing the signi ant parts of theLin oln LS systemis shown in Figure 4-5.

G

w

(s)

(46)

u

+

-K(s)

y

+

0 G (s)

G (s)

a

w

d

Figure4-5: Blo kdiagramrepresentingthepertinentpartsoftheLin olnLSsystem.

G

w

(s)

istheshakertransferfun tion,

G

a

(s)

isthea tuatortransferfun tion,

K(s)

isthe ontroller transfer fun tion,

w

is the signal into the shaker,

u

is the ontrol signal, and

y

is the measurement signal.

representsthe shakertransfer fun tion,

G

a

(s)

isthe a tuator transferfun tion,

K(s)

isthe ontroller transferfun tion,

w

isthe signalinto theshaker,

u

is the ontrol signal,and

y

is themeasured rossmembera eleration. Thereferen esignalinthis ase,asinthe

distur-ban ereje tion ase, iszerobe ausethe ontroller issupposedtoreje ttheshakervibration

disturban e. The fra tionalattenuation dueto ontrol inthis s enariois

T

yd

=

1 1 + K(s)G

a

(s)

(4.7)

and the losed looptransfer fun tionfrom the shakerto thea elerometer is

T

yw

=

G

w

(s)

1 + K(s)G

a

(s)

(4.8)

Some ofthe hara teristi s oftheexpe tedperforman e an be seenintheBode plotof

the a tuator to ross member a elerometer transferfun tion times the ontroller transfer

fun tion,

G

a

(s)K(s)

. (See Figure 4-6.) Clearly, the Bode plot shows that there is a large gainat150Hz,andlowergainsatfrequen iesfartherawayfrom150Hz. Also,theBodeplot

showsthattherearetwo rossoverfrequen ies,147 Hzand153 Hz. First, onsiderthelower

rossoverfrequen y,at147Hz. Atthisfrequen y,thephaseis-67degrees. This rossoveris

(47)

10

1

10

2

10

3

10 −5

10

0 Magnitude

10

1

10

2

10

3

0

500 1000

Phase (degrees)

Frequency (Hz)

Figure 4-6: Bode plot of

G

a

(s)K(s)

, the a tuator to ross member a elerometer transfer fun tion times the ontroller transfer fun tion. There is a large gain at 150 Hz, and two

rossovers, one at147 Hzand theother at153 Hz,with orrespondingphasesof-67and 72

degrees.

a orresponding phase of 72 degrees. Again, the rossoveris stable, and thephase margin

is 108 degrees. This Bode plot demonstrates that the ontroller designed above should be

stableandattenuatedisturban esatfrequen iesnear150Hzandhavelittleee telsewhere.

Theexpe tedperforman edemonstrated bytheBodeplotis showninFigure4-7.

Con-sider the losed loop transferfun tion from the shaker to the ross member a elerometer

of the ontroller used here. The measured experimental transfer fun tion should losely

resemblethe transferfun tion al ulatedfromtheory. Figure4-7showsa omparison of

ex-perimental and predi ted results. The experimental losed loop transferfun tion from the

shakerex itationto the rossmembera elerometer ismeasuredusing thesignalanalyzer,

and is represented by the thin line. The thi k line represents the theoreti al losed loop

transfer fun tion al ulated using Equation 4.8. The experimental and theoreti al results

aresimilar, although thebandwidth of theexperimental transferfun tion is narrowerthan

(48)

pro-100

125

150

175

200 −80

−60

−40

−20

0 Magnitude (dB, g/V)

100

125

150

175

200 −600

−400

−200

0 Frequency (Hz)

Phase (degrees)

Experimental

_Calculated

Figure 4-7: Experimental and al ulated transfer fun tions from the shaker ex itation to

the ross member a elerometer. The thin line is the experimentally determined transfer

fun tion and the thi kline is the al ulated transferfun tion basedon ontrol theory. The

theoreti al al ulatedtransferfun tionandtheexperimentaltransferfun tionmat h losely.

essingdone on the experimental data. The signalanalyzera quires theexperimentaldata

at a nite rate, and italso averages several streams of data. The lose mat h between the

experimental and theoreti al transfer fun tions indi ates that the experimental ontroller

does what it was expe ted to do, and the ross member vibration is signi antly redu ed

near150 Hz.

4.4 Closed Loop Vibration

The purpose of the tonal ontroller is to eliminate ross member vibration over a narrow

band offrequen ies. Asa result, themagnitudeof thetransferfun tion from theshakerto

the ross member a elerometer should de rease signi antly at 150 Hz when the ontrol

loop is losed. This drop an be seen by omparing the open loop transfer fun tion from

(49)

100

125

150

175

200 −40

−20

0 Magnitude (dB, g/V)

100

125

150

175

200 −300

−200

−100

Frequency (Hz)

Phase (degrees)

Open Loop

Closed Loop

Figure 4-8: Open and losed loop transfer fun tions from the shaker to the ross

mem-bera elerometer. The thin line shows the open loop transfer fun tion and the thi k line

shows the losed loop transfer fun tion. At 150 Hz the ross member vibration de reases

dramati ally, asexpe ted.

theshaker to the ross membera elerometer. (Figure 4-8) The thin line is theopen loop

transferfun tionandthethi klineisthe losedlooptransferfun tion. Asexpe ted,the ross

member vibrations (open and losed loop transfer fun tions) aresimilar at all frequen ies,

ex ept at those around 150 Hz, where the vibration goes to nearly zero. The vibration

de reaseextends for onlya fewhertz oneitherside of 150Hz, roughly148 Hz to 152Hz.

Unlikethe rossmembervibration,themagnitudeofthe ontrolarmvibrationat150Hz

would not be expe ted to de rease when the ontrol loop is losed. The ontrol arm

a - elerometer is on the opposite side of the point 4 bushing, relative to the ross member

a elerometer. A ontroller thatredu es the a eleration on one side of thebushing ( ross

member)isnotexpe tedtoredu ethea elerationontheothersideofthebushing( ontrol

arm). Figure4-9 shows theopen (thin line) and losed loop (thi k line) transferfun tions

from theshakerto the ontrol arm a elerometer. Nosigni ant dieren e isseen between

(50)

100

125

150

175

200 −30

−20

−10

0 Magnitude (dB, g/V)

100

125

150

175

200 −600

−400

−200

0 Frequency (Hz)

Phase (degrees)

Open Loop

Closed Loop

Figure 4-9: Open and losed loop transfer fun tions from the shaker to the ontrol arm

a elerometer. The thin line is the open loop transfer fun tion and the thi k line is the

losed loop transfer fun tion. As expe ted, there is no signi ant de rease in vibration at

150 Hz. At 142Hz, thereis ade rease inthe magnitudeof vibration.

shiftupwardsofmagnitude ofvibrationat frequen iesabove 150Hz,probablydueto small

experimentaldieren es. Also, thereis a de reaseof roughly6 dBinthemagnitude ofthe

vibration at 142 Hz. This result isdi ult to explain. Withthe addition of the ontroller

( losedloop),the onlypartoftheloopthat hangesistheee t ofthe ontroller on ontrol

arm vibration. Therefore, we would expe tthe ontrol armvibration to hange only when

the ontroller signal is large, but without a more detailed examination of the ontrol arm

transferfun tions, itis di ult to predi t what ee t the ontroller wouldhave. However,

how the ontrol arm vibration hanges is not very important, assuming that ontrol arm