Ative Control of an Automobile Suspension System for
Redution of Vibration and Noise
by
Kristen Lynn Clements
B.S., Mehanial Engineering (2002)
Massahusetts Institute of Tehnology
Submitted to the Department of Mehanial Engineering
in partial fulllment of the requirements for the degree of
Master of Siene in Mehanial Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2005
Massahusetts Institute of Tehnology 2005. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Mehanial Engineering
May 19, 2005
Certied by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Steven R. Hall
Professor of Aeronautis and Astronautis
Thesis Supervisor
Read by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Martin Culpepper
Rokwell International Assistant Professor of Mehanial Engineering
Thesis Reader
Aepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lallit Anand
Chairman, Graduate Department Committee
2
Ative Control of an Automobile Suspension System for Redution of
Vibration and Noise
by
Kristen Lynn Clements
Submitted to the Department of Mehanial Engineering
on May 19, 2005, in partial fulllment of the
requirements for the degree of
Master of Siene in Mehanial Engineering
Abstrat
A new method for ontrolling road noise transmitted through the suspension system of
an automobile was developed, using a Linoln LS automobile as the target vehile. In this
vehile, road surfae roughness generates vibrations that are transmitted into the automobile
primary through a single bushing (the point 4 bushing) on eah of the front suspension
ontrol arms.
An eletromagneti atuator was designed, built, and tested on a Linoln
LS with simulated road noise. The atuator applies a fore aross the point 4 bushing, in
response to aelerations of the vehile frame, just inboard of the bushing, with the goal
of reduing the net fores transmitted into the vehile frame, whih ultimately produe
unwanted interior noise. Several tonal ontrollers were developed, eah designed to operate
in a narrow frequeny band, and to eliminate ross member (frame) vibration just inside the
point 4 bushing. The tonal ontrollers were able to eliminate ross member vibration at the
desired frequeny.
Eliminating the ross member vibration resulted in modest redutions
in interior sound levels. A suessful vibration ontrol system (in this vehile) would need
to eliminate ross member vibrations over the frequeny range 100 to 200 Hz. However, a
broadband ontroller with this eletromagneti atuator system proved to be diult, due
to undesirable non-minimum phase dynamis.
Thesis Supervisor: Steven R. Hall
Title: Professor of Aeronautis and Astronautis
3
4
Aknowledgments
I would like to thank my advisor, Prof. Steven Hall, for his support and guidane, espeially
his patiene and willingness to explain onepts as many times as neessary. I also extend
many thanks to Dave Robertson for the use of his eletroni equipment, as well as his advie,
enouragement, and humor. Dik Perdihizzi helped me nd the various and sundry supplies
neessary for the ompletion of this projet. Don Weiner tried to teah me self-defense as
well as how to use the various mahines in the Gelb Laboratory. I am grateful to Prof. Martin
Culpepper for taking the time from his busy shedule to serve as a departmental reader for
my thesis.
Joe Shmidt of Ford provided muh of the automobile expertise neessary for this projet
and proured Sneezy and the Linoln LS used. Dieter Giese, also of Ford, was willing to
answer any question, no matter how trivial, that ame up during the ourse of my researh.
I also thank Dr. Joe Saleh, the Exutive Diretor of the Ford-MIT Alliane, and Kristin
and Steve Shondorf, also of the Ford-MIT Alliane, for their assistane with this projet.
Dr. Kyung-yeol Song helped get me started on this projet and was always willing to
try to answer any questions I had in the later stages. Jorge Feuhtwanger assisted with the
use of the eletroni disharge milling (EDM) mahine. Josh Chambers provided advie and
tehnial assistane.
I would also like to thank my friends: Chris for his endless omputer assistane, Christina
for stress relief and ookies, Rohan for help with all things MIT, Vitor for omputer hardware and editorial advie, and Zoa for onverting what I wrote into what I wanted to
say.
Finally, I want to thank my family for their ontinual support, partiularly my mother.
This work was sponsored by the Ford-MIT Alliane. Additional funding was provided
by Dean Isaa Colbert, MIT Dean for Graduate Students.
5
6
Contents
1 Introdution
9
1.1
Noise and Automobiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2
Previous Methods of Reduing Interior Noise
9
. . . . . . . . . . . . . . . . . .
10
. . . . . . . . . . . . . . . . . . . . . . . . . . .
10
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
1.3
Ative Suspension System Researh . . . . . . . . . . . . . . . . . . . . . . . .
11
1.4
Analysis of Ford Data
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
1.5
Overview
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
1.2.1
Interior Loudspeakers
1.2.2
Power Steering
2 Atuator Design
19
2.1
Problem Desription
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
2.2
Atuator Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.3
Piezoeletri vs. Eletromagneti Atuator . . . . . . . . . . . . . . . . . . . .
23
2.3.1
Piezoeletri Cerami Stak Atuator . . . . . . . . . . . . . . . . . . .
23
2.3.2
Eletromagneti Atuator
25
. . . . . . . . . . . . . . . . . . . . . . . . .
2.4
Eletromagneti Atuator Speiations
. . . . . . . . . . . . . . . . . . . . .
26
2.5
Atuator Amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3 Experimental Setup
29
3.1
Linoln LS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.2
Simulated Road Noise Exitation . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.3
Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
7
3.3.1
Aelerometers
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
3.3.2
Mirophones
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
3.3.3
Shaker Fore
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.4
Dynami Signal Analyzer
3.5
Eletroni Control Unit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4 Experimental Results
41
4.1
Open Loop Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
4.2
Tonal Controller
42
4.3
Expeted Performane
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.4
Closed Loop Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
4.5
Interior Sound Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
4.6
Summary
52
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Broadband Controller
57
5.1
Diulties with Broadband Control
. . . . . . . . . . . . . . . . . . . . . . .
5.2
Tonal Controllers at Various Other Frequenies
57
. . . . . . . . . . . . . . . . .
60
5.2.1
Tonal Control at 140 Hz . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5.2.2
Tonal Control at 160 Hz . . . . . . . . . . . . . . . . . . . . . . . . . .
61
5.2.3
Tonal Control at 180 Hz . . . . . . . . . . . . . . . . . . . . . . . . . .
63
6 Conlusion
69
A Calulation of Atuator Parameters
73
8
Chapter 1
Introdution
1.1 Noise and Automobiles
Unwanted noise is undesirable in many environments, among them the workplae, home
and automobile.
Automobile ustomers typially onsider a lak of interior noise to be a
desirable harateristi when purhasing a vehile. Interior road noise an be generated by
numerous soures throughout the automobile, with the engine being the major soure 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 that are transmitted though
the engine mounts to the frame [14℄. Other mehanial systems in the vehile, suh as the
power steering system [28℄, an also produe audible noise in the interior.
noises from outside the automobile an be heard inside the vehile.
Additionally,
Interior noise is also
aused by frame vibrations, whih are the result of tire ontat with various road surfaes
and potholes [33℄. This road-indued noise transmitted through the suspension system into
the frame is the soure of noise that will be primarily onsidered in this projet.
Undesired noise inside the abin of an automobile an range from merely annoying (making it more diult for passengers to listen to musi or to have a onversation) to dangerous
(preventing a driver from hearing important signals from outside the vehile, suh as an
emergeny siren). Constant noise on extended drives (even at low levels) an also redue
onentration and fatigue the driver [23℄.
9
For the reasons desribed above, a quieter automobile interior is highly desirable. Noise
redution an be aomplished through three general approahes. First, the soure of the
noise an be eliminated or redued.
Seond, the paths that the vibration follows an be
modied to redue the vibration transmission. Third, the sound at the user end of the path,
in this ase the interior of the automobile, an be modied to redue the apparent noise in
the interior of the vehile. However, many tehniques employed to redue interior noise an
also have a detrimental eet on other aspets of automobile performane.
For example,
the following parameters an be negatively impated by attempts to redue interior noise
by modifying the suspension system:
1. Handling. Handling is the pith and roll of the vehile body as a result of ornering
and braking maneuvers.
2. Road holding. Road holding is the ontat fore between the tires and the road.
3. Suspension travel. The allowable limit of suspension travel in any vehile design will
aet the performane ahievable from the suspension system.
4. Stati deetion resulting from variable payload. [12℄
The goal is to make the interior quieter without ompromising other faets of the automobile
performane.
1.2 Previous Methods of Reduing Interior Noise
Beause of onsumer preferenes for quieter ars, researhers and automobile ompanies
are always looking for new ways to redue interior noise, assuming that handling remains
omparable. Many of the details of the noise redution projets are onsidered proprietary
information. Presented here are desriptions of some of the non-proprietary researh eorts.
1.2.1
Interior Loudspeakers
One previous method that has been used to redue interior noise (aused by road-indued
noise) is plaing loudspeakers in the interior that anel road indued noise. This tehnique
10
an be employed if the soures of noise are known, and a orrelation between a reading at the
noise soure and the sound inside the vehile an be determined, so that the interior noise
an be predited. Interior loudspeakers an then be used to produe sound out of phase with
the noise, reduing interior sound levels. Using this method, Sutton and Elliott [31℄ were
able to redue low frequeny road-indued noise inside an automobile by approximately
7 dB. They plaed referene aelerometers on the wheel, suspension, and parts of the
frame that onstitute the road noise transmission paths. Then, the loudspeaker signal was
omposed of a linear ombination of the past and present referene aelerometer signals.
When this pratial road noise ontroller (developed at Lotus Engineering) was tested, noise
was redued roughly 7 dB at the major frequeny peaks in the range of 100 Hz to 200 Hz.
1.2.2
Power Steering
Another potential soure of noise is the power steering system. Pressure waves in the power
steering hoses ause uid noise. This noise an be redued some by adjusting the parameters
of the system, suh as the length of the hoses and the onguration of the omponents. One
study by Smid, Qatu, and Drew [28℄ used a Matlab simulation software program to determine
the optimal onguration for the hose, tuner, and tube in the power steering system. (Tuners
ome with some hoses and attenuate aousti waves in the uid.) They reated a model that
alulated the travel of the hydrauli pressure pulses (the soure of vibration and noise).
Smid, Qatu, and Drew found that the optimal length of hose is
pressure ripple, and the worst hose length is
1/2
1/4
of the wavelength of the
of the wavelength. Later researh in their
lab was onduted to optimize the other omponents of the power steering system.
1.3 Ative Suspension System Researh
Many automobile researhers have studied the benets of ative suspension systems over
their passive suspension ounterparts. [15, 16℄ Passive vehile suspensions, found on most
road vehiles, are designed with two ompeting requirements: good vibration isolation to
ensure ride omfort, and good steering fore transmission for vehile handling and safety.
Ative suspensions require additional power soures, but an allow improvements in both
11
ms
ks
bs
m us
kus
Figure 1-1: The ommonly used quarter ar model.
mus
is the unsprung mass (wheel mass),
sprung and unsprung mass, and
kus
ks
and
bs
ms
is the sprung mass (vehile mass),
are the spring and damper between the
is the tire stiness.
ride quality and vehile handling. Suspension system design onstraints inlude maximum
allowable relative displaements between the vehile body and unsprung mass omponents
(inluding wheels, bump stops, and protruding parts of the steering mehanism), overall
system robustness, reliability, weight, and ost. [16℄ Also, Hrovat's researh shows that, for a
quarter ar model (desribed below), an ative suspension system based on Linear Quadrati
optimal ontrol an substantially improve ride and handling performane when ompared
with the onventional passive suspensions. [16℄ However, LQ ontrollers do not neessarily
have good stability robustness properties.
For good ative suspension performane, and
robustness over all desirable ride harateristis, the passive suspension should be designed
with low stiness and damping. [32℄
To model vehile dynamis, many ative suspension system researhers 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 (ms ) representing the vehile mass, an unsprung
mass (mus ) representing the wheel mass, a spring (ks ) and damper (bs ) representing the
dynamis between the sprung and unsprung mass, and another spring (kus ) representing
the tire stiness. The ontat point between the tire and the ground is also allowed to move
in this model.
Also used are the half ar model [16℄ and the full ar model [16, 34, 13℄.
These models have similar omponents at eah wheel, but also allow for more ompliated
12
two or three dimensional motion.
A hydrauli atuator is the ommonly used atuator in ative suspension system researh.
[34, 3, 25, 21, 1℄ The hydrauli atuator used by Yamashita, Fujimori, Hayakawa, and Kimura
operates dierently at low and high frequenies. At low frequenies, where the servo valve
an follow the swithing of the input signal, the ow rate from the servo valve is onverted
to pressure by a hybrid gas spring and damping valve, and this pressure is used to atively
attenuate the body's vibration.
At high frequenies, where servo valve following is not
possible, the ylinder pressure is generated only by the gas spring and the damping valve.
This ensures the dynamis of the onventional suspension and the body's vibrations are
attenuated passively.
This atuator and its ontroller (designed using
H∞
methods [4℄)
were implemented both in shaking experiments and driving experiments. In both ases, the
vibrations were redued at frequenies lower than 8 Hz. Also in the driving experiments,
there was an improvement in handling with respet to maneuvering.
[34℄ A diulty in
using servo valves (with the hydrauli atuator) is that they are high ost items, and dirt
intolerant, so atuator maintenane ould be ompliated. [27℄
Nonlinear ontrol has also been used with hydrauli atuators (beause hydrauli atuators ome with assoiated nonlinear dynamis [25℄) to aommodate and improve the
tradeo between ride quality and suspension travel. [25, 21, 10℄ The added nonlinearities in
the ontroller make the suspension stier near its travel limits. In experiments by Lin and
Kanellakopoulos [21℄, a nonlinear ontroller was used to redue body aeleration by almost
70% and body travel by almost 80% as ompared to the passive suspension. The suspension
travel, however, is inreased slightly in ative designs. [21℄
1.4 Analysis of Ford Data
Prior to the start of the projet desribed here, engineers at Ford Motor Company had
performed dynamometer tests on a Linoln LS. They took vibration data on a dynamometer
with a oarse road surfae. Two aelerometers were plaed on the ontrol arm, one near
the spindle (near the wheel) and one near the ross member (near the point 4 bushing). [33℄
13
−4
4.5
x 10
Near cross member
Acceleration spectrum, Φ (g2/Hz)
4
Near spindle
3.5
3
2.5
2
1.5
1
0.5
0
0
200
400
600
800
1000
Frequency, f (Hz)
Figure 1-2: Aeleration spetrum measured by aelerometers plaed at two loations on the
ontrol arm, one near the ross member and one near the spindle. The thin line represents the
aeleration spetrum near the ross member and the thik line represents the aeleration
spetrum near the spindle. Note that for both aelerometer positions, virtually all of the
energy is between 100 Hz and 200 Hz, with a peak near 150 Hz.
Data ourtesy of Ford
Motor Company.
(See Setion 2.2 for a desription and photograph of these suspension omponents.)
Figure 1-2 shows the aeleration spetrum on a linear sale measured by the two aelerometers in the dynamometer test. The thin line represents the aeleration spetrum
for the aelerometer on the ross member (near the point 4 bushing) and the thik line represents the aeleration spetrum for the aelerometer near the spindle. The aeleration
spetrum learly shows that, for both aelerometers, almost all of the energy is between
100 Hz and 200 Hz, meaning that any atuator employed to redue this vibration would
likely only be required to operate near this frequeny range.
Figure 1-3 is the same data as in Figure 1-2, plotted on a logarithmi sale.
Again,
the thin line represents the aeleration spetrum from the aelerometer near the ross
member and the thik line represents the aeleration spetrum from the aelerometer
14
−3
10
Near cross member
−4
Near spindle
Acceleration spectrum, Φ (g2/Hz)
10
−5
10
−6
10
−7
10
−8
10
−9
10
−10
10
Figure 1-3:
0
200
400
600
Frequency, f (Hz)
800
1000
The same data from Ford as in Figure 1-2, plotted on a logarithmi sale.
The thin line shows the aeleration spetrum from the aelerometer plaed on the ontrol
arm near the ross member, and the thik line shows the aeleration spetrum from the
aelerometer plaed near the spindle. Again it is lear that there is a signiant peak around
150 Hz and that there is little energy at frequenies higher than 300 Hz. Data ourtesy of
Ford Motor Company.
near the spindle.
The sharp drop beginning at 200 Hz onrms the hypothesis that the
atuator would not be required to operate at higher frequenies. The aeleration spetrum
essentially goes to zero at frequenies higher than 400 Hz, so any atuator authority at
frequenies higher than 400 Hz would be unneessary and wasteful.
Figure 1-4 shows the umulative aeleration spetrum.
frequeny
f
The umulative spetrum at
is the total mean-square aeleration at frequenies of
f
and above. The thin
line represents the aeleration umulative spetrum for the aelerometer on the ontrol arm
near the ross member and the thik line represents the aeleration umulative spetrum
for the aelerometer on the ontrol arm near the spindle. On this umulative spetrum, the
previously observed peak at 150 Hz is learly seen as a large drop in energy. This suggests
that an atuator that ould redue the energy around the peak at 150 Hz, even without
15
0.045
Acceleration cumulative spectrum (g2)
Near cross member
0.04
Near spindle
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0
50
100
150
200
250
300
Frequency, f (Hz)
Figure 1-4: Cumulative aeleration spetrum of the data shown in Figure 1-2. The thin
line represents the aeleration umulative spetrum from the aelerometer near the ross
member, and the thik line represents the aeleration umulative spetrum from the aelerometer near the spindle. The resonane near 150 Hz is lear as a sharp drop o in the
umulative spetrum.
hanging the energy at any other frequenies, ould signiantly redue the total energy,
presumably also reduing the total sound. In other words, the frequenies around 150 Hz
are the highest energy, and therefore likely the loudest frequenies, so reduing the energy at
that frequeny would allow a redution in noise as well, assuming that reduing suspension
vibration does, in fat, redue interior noise.
1.5 Overview
The goal of this projet was to redue interior road-indued noise without negatively impating handling. Based on the assumption that reduing vibration of the ross member (frame)
will redue the interior abin noise, we designed a ontroller to redue the ross member
vibration in the frequeny range of 100 to 200 Hz.
16
Chapter 2 disusses the atuators we
onsidered using to provide the fores neessary to redue ross member vibration, and the
speiations of the eletromagneti atuator we hose. The eletromagneti atuator ats
aross the point 4 bushing to redue road noise vibration transmission. Chapter 3 desribes
the experimental setup: the Linoln LS, shaker, aelerometers, mirophone, dynami signal
analyzer, and eletroni ontrol unit we used for testing. Chapter 4 presents the experimental results we obtained using a tonal (narrowband) ontroller entered at 150 Hz. Both open
and losed loop vibration data is given, as well as the expeted ontroller performane and
losed loop sound levels. The diulties with broadband ontrol are disussed in Chapter 5,
along with additional tonal ontrollers, similar to the one disussed in Chapter 4, entered
at 140, 160, and 180 Hz.
Broadband ontrol proved to be diult due to two zeros in
the transfer funtion from the atuator to the ross member aelerometer, at 128 Hz and
184 Hz, giving the atuator no ontrol authority at those frequenies, and due to the large
non-minimum phase lag between 60 and 70 Hz.
diretions for further researh.
17
Chapter 6 disusses the onlusions and
18
Chapter 2
Atuator Design
This hapter desribes the atuator design proess. First, Setion 2.1 disusses the problem
desription, namely, reduing interior abin noise aused by road noise vibrations.
Then
the requirements on the atuator suh as required fore and displaement are desribed
(Setion 2.2).
Two dierent types of atuators, piezoeletri erami stak atuators and
eletromagneti atuators, are onsidered (Setion 2.3).
Finally, in Setion 2.4, the ele-
tromagneti atuator seleted for this projet is desribed, and the speiations for that
atuator are derived.
2.1 Problem Desription
The spei goal of this projet is to redue road noise that is transmitted through the
suspension system and frame of the automobile into the passenger ompartment, without
ompromising vehile handling. Bumps, potholes, and the general unevenness of the road all
vibrate the wheel as an automobile travels over road surfaes. The vibrations are then transferred through the ontrol arm, a rubber bushing, and into the frame, eventually reahing
the passenger ompartment, ausing undesired noise.
As disussed previously, there are three ommon approahes to the problem of noise
redution. Eliminating or reduing the noise at its soure is not pratial in this ase; the
roads annot be made perfetly smooth to prevent the wheel from vibrating.
Although
modifying the interior to redue noise has been explored by other researhers [31℄, it is
19
Figure 2-1: Photograph of the ontrol arm, ross member, and point 4 bushing, taken of
the front left suspension with the tire removed. The A shaped ontrol arm is towards the
bottom of the photograph. The ross member, the upside down U shaped part of the frame
over the bushing, is near the top. The visible bolt end is the bolt that goes through the
point 4 bushing.
outside the sope of this projet. Modifying the transmission path of the vibration is the
approah that we have employed here.
The geometry of the suspension system is shown in Figure 2-1. The ross member is a
strutural element of the frame, loated approximately on the axes of the front wheels, that
supports the engine. The ontrol arm is an A-shaped omponent of the suspension system.
It is onneted to the shok absorber, the wheel at the spindle, and to the frame through
two bushings, the point 3 the point 4 bushing. The point 3 bushing is the front bushing on
the ontrol arm onneting it to the frame, and the point 4 bushing is the rear bushing on
the ontrol arm, onneting the ontrol arm to the ross member.
Aording to tests onduted by Ford Motor Company, most of the road noise (and the
steering fores) is transmitted in a single dimension, parallel to the wheel's axis, through
the point 4 bushing [9℄. For noise redution purposes, a soft point 4 bushing is preferable.
A soft bushing would transmit less fore to the frame of the vehile, making the interior
quieter. However, softening this bushing has a negative impat on the vehile handling. A
20
sti bushing is superior for vehile handling, beause it better transmits the steering fores
to the wheels, so that the ar responds quikly and aurately to driver inputs.
Beause of the two opposing requirements for the point 4 bushing stiness soft for
noise redution and sti for vehile handling, a passive bushing is neessarily a ompromise.
However, the steering fore frequenies are on the order of a few hertz, and the road noise
vibration frequenies are on the order of a hundred hertz. Therefore, an ative bushing that
ats sti at low frequenies and soft at higher frequenies ould be used to reate a quieter
interior without negatively aeting vehile handling.
There are two approahes to reate this ative bushing. One ould begin with a physially
soft bushing, and use ative ontrol to stien it at low frequenies; or one ould begin with
a sti bushing, and use ative ontrol to soften it at higher frequenies. The low frequeny
fores assoiated 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 frequenies is quite large.
An example of the former approah (stiening at low
frequenies) is the work done at Bose Corporation.
The modular design added a linear
eletromagneti motor at eah wheel with a modied MPherson strut arrangement. [20℄
To demonstrate the ative suspension, a Bose modied Lexus LS400 was plaed atop a four
post shaker to simulate traveling down a rough road. From the outside, the wheels ould be
seen to be gyrating wildly, and from the inside, there was virtually no sense of motion. [6℄
Currently Bose is reduing the weight and seleting a manufaturer for the ative suspension
system. [20℄
On the other hand, using a sti bushing, the fores assoiated with road noise are muh
lower, on the order of 150 N (see Setion 2.2) and, as a result, muh less ontrol authority
is neessary to soften the bushing at higher frequenies. For this reason, our projet begins
with a sti bushing, and we then use ative ontrol to soften the bushing at frequenies from
100 Hz to 200 Hz.
21
2.2 Atuator Requirements
To begin atuator seletion, one must rst determine the design requirements of the system
during normal operation. The design parameters of this partiular system inlude bushing
displaement (required to ounterat displaements aused by road noise vibrations), fore
aross the bushing (that orresponds to the bushing displaement), atuator bandwidth,
and also the eets of shok loading.
As an be seen in Figure 1-4, almost all of the energy in the spetrum is near 150 Hz,
2
and the mean squared aeleration is 0.04 g . The rms aeleration is given by
σa = 0.2 g = 1.96 m/s2
(2.1)
Sine almost all the vibration ours at a frequeny of 150 Hz (ω
= 942 rad/s),
the rms
displaement is given by
σd ≈ σa /ω 2 = 2.5 µm
(2.2)
During normal exitation of the wheel, the rms point 4 bushing displaement is approximately
1 σd . 2.5 µm
under oarse road onditions. Allowing for
should be apable of at least 7.5
µm
3σ
motion, the atuator
of atuation. The fore that the atuator must be able
to provide is alulated by Hooke's Law,
f = kd
where
k
is the stiness of the point 4 bushing (about 20 kN/mm), and
displaement (7.5
µm).
d
is the required
Therefore, it is neessary for the atuator to generate at least 150 N
of fore.
As seen in Figure 1-2, the atuator will be required to ounterat disturbanes of frequenies between 100 Hz and 200 Hz.
Therefore, the large signal bandwidth must be at
least 200 Hz, meaning that the atuator must be apable of generating fores on the order of
150 N, up to 200 Hz in frequeny. However, to ensure that the phase lag in the atuator is
small, we would like the small signal bandwidth to be ten times larger than the large signal
22
bandwidth. The resulting required bandwidth for the atuator used here must be greater
than 2000 Hz.
The atuator must also be able to withstand shok loads, suh as that of a wheel hitting
a urb or a pothole, or those produed during sharp turns.
The entire vehile weighs
approximately 2000 kilograms; under normal onditions eah wheel supports 500 kilograms
(5000 N). During an extreme turn or hitting a pothole with most of the lateral fores reated
by the outer wheels, the fores might be as high as 10,000 N. Therefore, the atuator must
be able to withstand steering loads of approximately 10,000 N to the bushing. Equivalently,
the atuator must be able to withstand a bushing motion of 500
µm (0.5 mm) due to steering
loads, again alulated using the bushing stiness. The atuator would not be required to
ounterat these loads, but it must be able to bear them and ontinue to operate after the
loading is removed.
Beause the atuator must be able to withstand displaements muh larger then would
normally be produed by the atuator, the atuator should be ompliant, when ompared
to the stiness of the bushing. An atuator that is ompliant is eetively a fore atuator
rather than a displaement atuator. The ideal atuator for this projet should ommand
fore rather than displaement.
2.3 Piezoeletri vs. Eletromagneti Atuator
After determining the requirements on the atuator, two types of atuators were onsidered.
One is an atuator made from piezoeletri erami staks, one is an eletromagnet made
from steel laminations.
2.3.1
Piezoeletri Cerami Stak Atuator
One possible type of atuator is a piezoeletri erami stak atuator. This type of atuator
is an attrative option beause the piezoeletri material has a high energy density, approximately
80 kJ/m3 ,
and a high bandwidth. However, it may be diult to get the neessary
stroke, sine piezoeletri materials produe very small displaements, and very large fores.
Also, piezoeletri eramis staks have high osts, and may be prohibitively expensive.
23
The size of a typial piezoeletri erami stak, suh as model P-885.10 made by Physik
Instrumente (Auburn, Massahusetts), is
fore and 6.5
µm
displaement.
5 mm × 5 mm × 9 mm,
and it is apable of 800 N
A stak this size is on the order of $150.
[24℄ One of
these piezoeletri staks has more fore than is neessary for our needs, but not nearly
enough displaement.
Therefore, multiple staks and an ampliation mehanism an be
used to meet the atuator requirements. As a rough estimate (order of magnitude) of the
number of staks required, ompare the piezoeletri stak speiations with the atuator
requirements. The fore of a single stak is
The displaement is
500 µm/6.5 µm = 77
800 N/150 N = 5.3
times larger than we need.
times smaller than we need. Thus, even with an
ampliation mehanism to math the impedane of the material to the requirements, we
nd that we need at least 15 piezoeletri staks to ahieve enough fore and stroke.
The piezoeletri staks are too sti for this appliation.
fator must be hosen to math the stiness requirement.
Therefore, an ampliation
However, the displaements
and fores annot be modied separately (as assumed in the above estimation). A single
ampliation mehanism must be used to both amplify the displaement and redue the
fore. To make this piezoeletri material appropriate here, there must be some ampliation
mehanism. Consider a mehanism that amplies the atuator displaement by a fator of
A, so that the ratio of original to modied displaement is
1
A.
Then the ratio of original
to modied fore would be A, so that the ratio of original to modied stiness is
1/A2 .
If
the original atuator fore is 800 N, but the atuator is only required to provide 150 N of
fore, then A
= 5.3
for an ideal ampliation mehanism. Then 15 staks would be required
to ahieve the neessary stroke, and even more piezoeletri staks for a real (less eient)
ampliation mehanism.
Beause the driving requirement on the amount of neessary piezoeletri material is the
steering shok loads, not the higher frequeny atuation requirement, more than 15 staks
would be required for a piezoeletri atuator ating aross the point 4 bushing. At a ost
of around $150 eah, more than 15 staks is obviously far too many staks to make this
piezoeletri erami stak atuator feasible in this appliation.
A piezoeletri atuator ating aross the bushing is not feasible, but perhaps a piezoele-
24
tri atuator ould be employed in a dierent onguration. For example, pushing against
a proof mass may be a more pratial type of piezoeletri atuator.
At the operational
frequeny range, between 100 Hz and 200 Hz, the piezoeletri material would push against
the proof mass (whih ideally would not move) to displae the bushing. At the low frequenies of the steering shok loads, this type of atuator would push against and move the proof
mass, making it ompliant, and reduing the required number of piezoeletri staks. To
minimize the amount of piezoeletri material, the proof mass should have about the same
dynami stiness as the stiness of the point 4 bushing (20 kN/mm) at 100 Hz. The dynami
2
stiness of the proof mass is Mω , where M is the mass, and
ω
is the pertinent frequeny
(here 100 Hz). Setting the dynami stiness equal to 20 kN/mm results in a required proof
mass of approximately 50 kg. Unfortunately, a 50 kg proof mass added to the suspension
system is too large to be a feasible atuation solution. A smaller proof mass an be used, but
that would redue the eieny and require more piezoeletri material. A 5 kg proof mass
would be more appropriate in size, but would again require approximately 25 piezoeletri
staks, whih would be too ostly for feasibility. Although ative material atuators, suh
as piezoeletri ones, are attrative in some respets, they are probably impratial for this
appliation.
2.3.2
Eletromagneti Atuator
Another possible type of atuator is an eletromagneti atuator; with a xed element
(magneti ore), oil (exitation winding), and a movable element (armature). [19℄ Eletromagnets are used in many appliations, for example:
Solenoid atuators: aps, pneumati and hydrauli valves, slide valves, interloks
breaks.
Hammering atuators: riveting, punhing, stamping, hiseling mahines.
Turning magnets: throttle valves, ontrol valves (hydrauli, pneumati), material
support (for instane web of loth, paper), turnout in transport plants.
Swinging magnets, vibrators: eletri razors, massage apparatus, piston pumps,
25
swim pumps, diaphragm pumps, small ompressors, swing saws, vibrating hauling plants, osillating sieves, osillating tables, swinging and helial onveyors. [19℄
Eletromagneti atuators an be very ompliant; the gap between the rotor and the stator
allows for muh larger shok motion than the ontrol motion provided by the atuator.
Another benet is that eletromagneti tehnology is mature, ontributing to a redued
ost when ompared to the ost of ative materials.
After determining that an atuator
made of piezoeletri erami staks is not feasible, we hose to pursue development of an
eletromagneti atuator for the reasons outlined above.
2.4 Eletromagneti Atuator Speiations
The ore of an eletromagnet is made of steel laminations.
Steel is used beause of its
eletromagneti properties, but a solid steel ore is not as eient as a laminated ore. The
laminations redue eddy urrents that result from the indued magneti eld. Beause the
bandwidth of the atuator is proportional to the inverse of the time it takes for the eddy
urrents to settle, reduing the eddy urrents inreases the bandwidth of the eletromagnet.
The eletromagnet used here has 54 laminations that are eah 0.0185 inhes thik (0.47 mm),
for a total thikness of 2.5 m.
(Figure 2-2) The laminations were ut to shape by an
eletroni disharge milling (EDM) mahine.
The eletromagnet onsists of a stator, a rotor, and a 2 mm air gap separating the two.
The stator is the approximately irular side of the eletromagnet, and is onentri with
the point 4 bushing. It is bolted to the ross member and has a 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 irular side of the eletromagnet,
while maintaining the 2 mm air gap. These rounded edges allow the magnet to rotate about
the point 4 bushing bolt with the ontrol arm without altering the 2 mm air gap.
The
magneti rotor is approximately 15 m long, 8 m high, and 2.5 m thik. Figure 2-3 shows
the eletromagneti atuator in plae on the ar.
26
2 mm air gap
copper windings
laminated core with 2 poles laminated disk attached to cross member
attached to control arm
Figure 2-2: Diagram of the proposed eletromagneti atuator.
The fore produed by an eletromagnet is proportional to the square of the urrent in
the oil.
Therefore, to get an approximately sinusoidal fore, a large bias urrent plus a
sinusoidal urrent is required. For this eletromagnet, the rotor is wound with 120 turns of
opper wire. The maximum required urrent is 10 A plus the bias urrent.
2.5 Atuator Amplier
To supply the large urrents that are required for the eletromagneti atuator operation, a
substantial power supply and amplier were employed. The amplier used with the eletromagneti atuator is a brush type pulse width modulated servo amplier made by Advaned
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℄ Atuator urrent an be measured using the amplier's monitoring
port. A Hewlett Pakard (Palo Alto, California) power supply, model 6479C, was used to
provide the d power for the atuator amplier. The power supply an provide from 0-300 V
and 0-35 A of power.
To implement this eletromagneti atuator in a real ar, we learly annot use suh a
substantial power supply and amplier.
The atuator was designed to operate at around
27
Figure 2-3: A photograph of the eletromagnet bolted in plae to the ontrol arm and the
ross member.
42 V, whih is ompatible with the 42 V systems likely to be used in the near future. [5℄ In
addition, the total urrent requirements an be redued substantially by using a apaitor
in parallel with the eletromagnet.
28
Chapter 3
Experimental Setup
This hapter desribes the experimental testbed (the Linoln LS) used in this projet. In
partiular, we desribe the shaker used to indue vibrations in the testbed; the load ell
used to measure the fores generated by the shaker; the aelerometers used to measure
the testbed vibrations; the mirophone used to measure the interior abin sound; the signal
analyzer used as a virtual funtion generator, data reorder, and data analyzer; and the
eletroni ontrol unit used as D/A and A/D onverters, as well as an interfae to the
software ontroller.
3.1 Linoln LS
Experiments previously onduted by researhers at Ford Motor Company on the Linoln LS
led to the onlusion that most of the road noise vibrations are transmitted through the
point 4 bushing, a nding spei to this model.
[26℄ As desribed earlier, the point 4
bushing is the bushing that onnets the ontrol arm to the vehile frame.
Other Ford
vehiles did not exhibit the same major vibration pathway; any tehnique for noise redution
aomplished by this study may not apply to other Ford vehiles.
It is neessary to design a testbed setup in order to study the road noise transmitted
through the suspension system of a Linoln LS, with the goal of reduing this noise. In our
setup, road noise was simulated using a shaker to apply fores to the suspension. Sensors
were plaed on the ontrol arm and frame to measure the vibration levels, and in the vehile
29
Figure 3-1: The original testbed, a Linoln LS front end, is referred to as Sneezy.
interior to measure the sound. The testbed initially inluded the front suspension system
omponents, part of the vehile frame, and the front wheels and tires for support.
The
initial testbed was the front end of a Linoln LS provided by Ford, niknamed Sneezy, with
all neessary omponents forward of the steering olumn.
(Figure 3-1) Inluded were the
major parts of the frame and the entire suspension system. The body panels, engine, and
other omponents of the engine ompartment were not inluded. Due to the missing weight
of these omponents, the ride height was too high. We built a wooden box (loated in the
engine ompartment) to hold approximately 700 kg of lead briks to ahieve the orret ride
height. Beause the rear end of the ar was not present, a metal frame was welded to the
rear of the frame in order to properly position the testbed.
Sneezy was found to be an inadequate testbed; results obtained using Sneezy mathed
neither the expeted results nor the results from previous tests onduted by Ford.
To
onsider Sneezy an appropriate testbed, the transfer funtions obtained from Sneezy and
those from Ford's vehile modeling program should math, but they did not. The apparent resonane at 150 Hz from Ford's data was not present in experiments on Sneezy. (See
Figure 3-2.) The resonanes of Sneezy's transfer funtions are at higher frequenies. Additionally, the result from Ford that most of the vibrations are transmitted through the
point 4 bushing ould not be repliated on Sneezy.
30
Magnitude (dB)
−20
−40
−60
−80
0
150
300
400
500
600
700
800
900 1000
150
300
400 500 600
Frequency (Hz)
700
800
900 1000
Phase (degrees)
150
100
50
0
−50
0
Figure 3-2: The transfer funtion from the shaker exitation to the ross member aelerometer (data aquired with Sneezy).
No major peak is present near 150 Hz (ompare with
Figure 1-2).
After it was determined that the front end of the Linoln LS did not produe the same
results as an entire ar, Ford Motor Company provided a omplete, drivable 2001 Linoln LS.
Using the entire vehile, the vibration transmission paths and noise ould be studied in more
detail. Then eventually, we an design a ontroller to allow for a quieter drive without ompromising vehile handling. An additional advantage of using the entire Linoln LS is that it
would permit measurement of the interior sound levels, and allow testing of the hypothesis
that reduing the ross member vibration also redues the interior sound. Figure 3-3 shows
the new testbed (the entire Linoln LS).
The experimental setup using the Linoln LS is further outlined in Figures 3-4 and 3-5.
During the shaker or atuator transfer funtion identiation, the dynami signal analyzer
sends the driving signal to either the shaker or the atuator. (Figure 3-4) The solid line onneting the signal analyzer to the shaker box represents the onnetion that is present when
identifying the shaker transfer funtions. The dashed line onneting the signal analyzer to
31
Figure 3-3: The Linoln LS in plae in the Gerhard Neumann Hangar and Laboratory at
MIT.
the atuator represents the onnetion that is present when identifying the atuator transfer
funtions. The shaker is onneted in series with a load ell and a sting to the suspension, so
that when the shaker is being driven, the applied fore an be measured. Either the shaker
signal or the atuator signal an be used to indue vibration in the Linoln LS automobile.
Signals from the sensors on the automobile (the aelerometers and the mirophones) are
sent bak to the dynami signal analyzer and the eletroni ontrol unit's proessors, where
the signals are reorded and analyzed.
In the losed loop system (i.e., when the ontroller is present and operational), the
system funtions in a slightly dierent manner.
(See Figure 3-5.)
The dynami signal
analyzer still drives the shaker through a load ell to vibrate the ar, and the aelerometer
and mirophone signals are still sent bak to the signal analyzers and hardware eletroni
ontrol unit for analysis. The major dierene in the losed loop system is that the ontroller
is downloaded into the eletroni ontrol unit expansion box and used to drive the atuator.
32
shaker
load cell
Lincoln LS
actuator
accels
signal
analyser
Figure 3-4:
mics
electronic
control unit
The blok diagram outlines the experimental setup during either shaker or
atuator transfer funtion identiation. The signal analyzer drives either the shaker (solid
line) or the atuator (dashed line). Either the shaker or the atuator vibrates the Linoln LS.
The sensors on the automobile, both the aelerometers and the mirophones, measure the
vibration and return the signals to the signal analyzer and eletroni ontrol unit.
3.2 Simulated Road Noise Exitation
For the purposes of these experiments, it was not feasible to drive the Linoln LS on road
surfaes to measure and reord vibrations of the wheel and other suspension and frame
omponents, and the resulting sound in the interior of the automobile. Therefore, the road
noise vibrations had to be simulated in the laboratory.
To aomplish this simulation, a
shaker was attahed by a sting to the passenger side ontrol arm. (See Figure 3-6.)
The shaker used was a model 420 shaker, made by Ling Eletronis, In.
(Anaheim,
California). The shaker is an eletromagnet; urrent is supplied to the shaker (whih has a
permanent magnet armature), induing a magneti eld and a magneti fore. The shaker
is apable of providing up to 133 N of fore in a frequeny range of 0 to 7500 Hz and a
maximum aeleration of 118 g. The urrent required to produe 133 N of fore is 8.4 A
33
shaker
load cell
Lincoln LS
actuator
accels
signal
analyser
mics
electronic
control unit
Figure 3-5: The losed loop blok diagram represents the experimental setup during ontroller operation. The signal analyzer drives the shaker through a load ell to vibrate the
ar, and the aelerometers and mirophones measure the vibrations and send them bak to
the signal analyzer and eletroni ontrol unit. In this setup, the ontroller is downloaded
to the eletroni ontrol unit expansion box and drives the atuator.
rms. [22℄ The amplier used with the shaker is a Yorkville Audiopro 3400, a high eieny
stereo power amplier, made by Yorkville Sound, Toronto, Canada.
Vibration due to road roughness is simulated by the shaker, whih is attahed to the
ontrol arm by a sting. A load ell was plaed in series with the sting to measure the fore
applied. The sting is a slender aluminum rod with one end srewed into the load ell, whih
is in turn onneted to the shaker fae, and the other end srewed into the ontrol arm. The
sting is attahed to the ontrol arm at the point designated by the arrow in Figure 3-7. The
shaker pushes fore and aft on the sting, whih pushes fore and aft on the ontrol arm.
We also sometimes used an alternative method for mounting the shaker, by attahing the
shaker through the sting to a wheel lug bolt. The sting was srewed into a lug nut adaptor,
allowing the shaker to push on the wheel parallel to the wheel's axis. The vibrations resulting
34
Figure 3-6: A photograph of the shaker and sting in plae.
from this method of attahment were found not to be as representative a load ase as the
fore and aft exitation desribed above. Also, aording to Ford, the fore and aft exitation
results in vibrations in the vehile that are more representative of real-world vibrations. [26℄
3.3 Instrumentation
In order to measure and reord the vibration, vibration transmission through the frame, and
interior abin sound during experimentation, two types of sensors were used to instrument
the Linoln LS automobile.
Aelerometers were plaed in two loations to measure the
vibrations, one on the frame, and the other on the ontrol arm.
Also, a mirophone was
plaed in four dierent loations in the interior of the vehile to measure the sound level
throughout the automobile.
3.3.1
Aelerometers
To measure and reord the vibration of the relevant suspension omponents, two Endevo
(San Juan Capistrano, California) piezoeletri aelerometers were employed.
One was
plaed on eah side of the point 4 bushing, measuring the aeleration aross the bushing.
35
Figure 3-7: The arrow points to the spot on the ontrol arm to whih the sting is attahed.
The photograph is taken from the front, looking aft at the right front wheel.
Table 3.1: Additional Endevo piezoeletri aelerometer speiations
Serial Number
EL89
EL92
Charge Sensitivity
96.8 pC/g
97.1 pC/g
Capaitane
2743 pF
2698 pF
Max. Transverse Sensitivity
0.4%
2.0%
The plaement of the aelerometers is shown in Figure 3-8.
The small metal ylinders
attahed to ables are the aelerometers. The aelerometer above the point 4 bushing in
the piture is attahed to the ross member, and will be referred to as the ross member
aelerometer.
The aelerometer below and to the left in the piture is attahed to the
ontrol arm, and will be referred to as the ontrol arm aelerometer.
The aelerometers used were Endevo model 7701-100.
The frequeny range of the
aelerometers is 20 Hz to 5 kHz. The serial numbers for the ross member and ontrol arm
aelerometers are EL89 and EL92, respetively. Additional speiations for the aelerometers are shown in Table 3.1. [7℄ Endevo laboratory harge ampliers, model 2721B, were
used to ondition the aelerometer signals. The harge ampliers an be adjusted for the
36
Figure 3-8:
A photograph showing the plaement of the two aelerometers.
The ross
member aelerometer is the aelerometer loated above the point 4 bushing. The ontrol
arm aelerometer is loated below and to the left of the point 4 bushing.
harge sensitivity of eah aelerometer, as well as the desired gain (V/g). The frequeny
range of the harge ampliers is 3 Hz and 10 kHz. The output has a maximum voltage of
10.0 V peak, and a maximum urrent of 2.0 mA. [8℄
3.3.2
Mirophones
The mirophone on a sound level meter was used to measure the sound at eah of four
positions in the interior of the Linoln LS. The 1982 Preision sound level meter and analyzer
was made by GenRad (now IET Labs, In., Westbury, New York). The range of this sound
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 soures of noise in the vehile interat, ausing a large number of nodes
and antinodes.
At the nodes, the sound waves are out of phase and anel eah other's
magnitude; and at the antinodes the pressure waves are in phase and the magnitudes add
together. However, the entire distribution is not pertinent, only the sound levels in the areas
37
(a)
(b)
()
Figure 3-9: The rst mirophone position is loated at the driver's left ear.
The seond
mirophone position is at the reetion of this position at the front passenger's right ear
(a). The third mirophone position is loated at the right (passenger side) rear passenger's
right ear (b). The fourth mirophone position is loated in the enter of the driver's seat at
approximately hin level ().
where the driver or any passengers would be able to hear the transmitted road noise are
signiant for this projet, and the mirophone positions were hosen to measure the sound
in these areas.
The rst mirophone position is at the driver's left ear. (See Figure 3-9(a).) The seond
mirophone position is at the front passenger's right ear, a reetion of the rst mirophone
position, as shown in Figure 3-9(a).
The third mirophone position is at the right rear
passenger's right ear. (See Figure 3-9(b).) The fourth and nal mirophone position (Figure 3-9(b)) is at approximately the enter of the seat, at the driver's hin level. The rst and
third positions (driver's ear and rear passenger's ear) are similar to the standard positions
38
that Ford uses when measuring sound levels. The other two positions were hosen to obtain
a better idea of the sound distribution throughout the interior of the automobile.
3.3.3
Shaker Fore
A load ell was plaed between the sting and the shaker fae to measure and reord the fores
applied by the shaker to the automobile through the sting. The fore measurement provides
more detailed information about the load ase than what an be dedued from the shaker
input signal voltage.
The load ell used is model SM-50 made by Interfae (Sottsdale,
Arizona). It an measure fores up to 200 N. At 200 N of fore the deetion is 0.08 mm
and the natural frequeny is 1550 Hz. [18℄
3.4 Dynami Signal Analyzer
The dynami signal analyzer serves many funtions. It ats as a virtual funtion generator,
data reorder, and a data analyzer. The dynami signal analyzer used here onsists of two
Siglab model 20-42 signal analyzers and the assoiated software, made by Spetral Dynamis
(San Jose, California). Eah signal analyzer unit has a 20 kHz bandwidth, 4 input hannels,
and 2 output hannels, for a total of 8 input hannels and 4 output hannels. [29℄
The dynami signal analyzer was used as a funtion generator to provide the required
sinusoidal signals to drive the shaker or the eletromagneti atuator, depending on the
experiment. The software virtual funtion generator supplied the neessary signals sent out
through a D/A onverter and the output hannels. The two output hannels an independently supply two dierent exitation signals for use during the testing. Eah hannel an
output 20 mA and 10 V maximum with an available optional DC oset. [29℄
The signal analyzers also have analog to digital onverters, whih were used to aquire
and reord the various aelerometer, mirophone, and load ell signals.
The two signal
analyzer units were time synhronized, allowing simultaneous reording of eight dierent
signals. The voltage range for eah input hannel is adjustable from
[29℄
39
±
20 mV to
±
10 V.
The dynami signal analyzer was also used for simple data analysis, and to display
the sensor signals, simple transfer funtions, and the oherene of the estimated transfer
funtion. The available analysis funtions (other than oherene) inlude time history, autospetrum, transfer funtion, ross-spetrum, auto-orrelation, ross-orrelation, and impulse
response. [29℄ Cheking the oherene was espeially important to ensure that the signals
were of a high enough signal-to-noise ratio to trust the results. The reorded signals were
also exported to Matlab, to allow for more extensive analysis.
3.5 Eletroni Control Unit
The signal analyzers have analog to digital and digital to analog onverters that an be
used to transfer the shaker and atuator driving signals, as well as to aquire the sensor
signals. Another piee of hardware, the eletroni ontrol unit, made by dSPACE In (Novi,
Mihigan), was used for the ontroller signals.
The eletroni ontrol unit onsists of an
expansion box (model PX10) and two I/O ds1003 proessor boards mounted in the expansion
box. The ontrol feedbak signals (aelerometer and mirophone signals) were brought into
the omputer using this eletroni ontrol unit.
This eletroni ontrol unit has, among
other things, hardware A/D and D/A onverters.
It was also used as the interfae for
the software ontroller. The ontroller was assembled in the Matlab modeling appliation
Simulink, and then downloaded and run from this eletroni ontrol unit.
An assoiated
program alled Control Desk works with the eletroni ontrol unit, and allows some of the
ontrol parameters to be hanged while the ontroller is operating. This feature allowed us
to ne-tune some of the ontroller parameters, without the need to reompile the ontrollers.
40
Chapter 4
Experimental Results
This hapter presents and explains the experimental data taken on the Linoln LS. First
is the baseline data, the open loop transfer funtions from the shaker and atuator to
the ross member and ontrol arm aelerometers, in Setion 4.1. Next (Setion 4.2), the
design of tonal ontrollers is disussed. This is followed by the expeted performane. Both
the predited performane from the Bode plot of the ontroller transfer funtion and the
performane omparison of the alulated theoretial transfer funtion to the measured
experimental transfer funtion (showing that the experimental results math the predited
theory) is desribed. Finally, the losed loop data is presented, inluding the losed loop
vibration (Setion 4.4) and the interior sound levels (Setion 4.5).
4.1 Open Loop Results
The initial baseline results are the open loop transfer funtions. The two exitation inputs
are the shaker (desribed in Setion 3.2) and the atuator (desribed in Setion 2.4). The
two important open loop outputs are the ross member aelerometer and the ontrol arm
aelerometer (desribed in Setion 3.3.1). Figure 4-1 shows the open loop transfer funtion
from the shaker input to the ross member (thin line) and ontrol arm (thik line) aelerometer outputs. Clearly, both the ross member aelerometer and ontrol arm aelerometer
transfer funtions are quite modal. Also, the 150 Hz peak that was present in the data from
Ford (Figure 1-2) is diult to observe in the measured ross member aelerometer transfer
41
2
Magnitude
10
0
10
−2
10
1
2
Phase (degrees)
10
10
3
10
0
−1000
−2000
−3000
−4000
1
10
cross member
control arm
2
10
Frequency (Hz)
3
10
Figure 4-1: Open loop transfer funtions from the shaker to the ross member (thin line)
and ontrol arm (thik line) aelerometers. Both transfer funtions are quite modal. The
150 Hz peak that was present in the data from Ford (Figure 1-2) is also diult to observe.
funtion.
Figure 4-2 shows the open loop transfer funtions from the atuator exitation
to both the ross member (thin line) and ontrol arm (thik line) aelerometers. Again,
both of the open loop transfer funtions are quite modal.
Control ould be diult due
to the many modes present in the ross member aelerometer transfer funtion, as well as
the large phase roll-o present in the ross member transfer funtion. The diulties with
broadband ontrol will be desribed further in Setion 5.1.
4.2 Tonal Controller
After examining the open loop transfer funtion from the atuator to the ross member
aelerometer, the form and details of the ontroller must be determined.
Beause the
transfer funtions from the shaker to the aelerometers and also from the atuator to the
aelerometers are highly modal (Figure 4-2), the design of a broadband ontroller that has
good performane ould be diult. It is simpler to rst develop a tonal ontroller, then
42
2
Magnitude
10
0
10
−2
10
1
Phase (degrees)
10
2
3
10
10
cross member
control arm
500
0
−500 1
10
2
10
Frequency (Hz)
3
10
Figure 4-2: Open loop transfer funtions from the atuator to the ross member (thin line)
and ontrol arm (thik line) aelerometers. Both transfer funtions are very modal, whih
ould make ontrol diult. Also the ross member aelerometer transfer funtion has a
signiant phase roll-o that an ause problems with ontrol.
broaden the eetive frequeny range one the simpler tonal ontroller is funtional. This
tonal ontroller will demonstrate whether ontrol is eetive, i.e., if reduing ross member
vibration redues interior noise.
The tonal ontroller will be a feedbak ontroller. Here, the logial variable to be fed
bak is the ross member aeleration. In the unmodied bushing, with no atuator, road
noise vibration is transmitted aross the point 4 bushing. The atuator added to the system
will be used to supply a fore that anels the road noise vibration the ross member
aeleration will be fed bak into the ontroller and driven to zero. If the vibration of the
ross member an be redued, then the sounds in the interior aused by that vibration should
also be redued.
The tonal ontroller employed here is designed to eliminate the ross member vibration
at a single frequeny. The initial frequeny onsidered was 150 Hz, hosen beause it falls
in the range of highest amplitude in the vibration spetrum, as shown in Figure 1-2.
43
The form of the ontroller used here is from a methodology known as higher harmoni
ontrol (HHC) originally designed to redue heliopter vibrations, developed by Hall and
Wereley [11℄. Their ontinuous time HHC ompensator is
2k(as + bΩ)
s2 + (Ω)2
K(s) =
(4.1)
where
a=
b=
Re[G(jΩ)]
(4.2)
|G(jΩ)|2
Im[G(jΩ)]
(4.3)
|G(jΩ)|2
1
k=
T
and
T
(4.4)
is the desired the settling time of the losed loop system. In this ase,
(in rad/s) of the harmoni to be redued, is
Ω = 2π × 150 Hz,
and
Ω, the frequeny
G(jΩ)
is the transfer
funtion from the atuator to the ross member aelerometer evaluated at 150 Hz.
This ontroller (Equation 4.1) eliminates vibrations at the frequeny
innite there.
funtion
The onstants,
G(jΩ),
a = −0.099
and
b = 0.2732,
Ω
beause
K
is
determined from the transfer
generally result in good phase margins at the rossover frequenies, just
above and below 150 Hz. However, it is sometimes neessary to adjust
a and b to give better
phase margins at one of the two rossover frequenies (above or below
Ω).
4.3 Expeted Performane
Classial ontrol theory ditates that for the most basi feedbak ontrol system, suh as
the one shown in Figure 4-3, the losed loop transfer funtion is given by
H(s) =
where
K(s)G(s)
1 + K(s)G(s)
(4.5)
H(s) represents the losed loop transfer funtion from r to y , G(s) is the plant transfer
funtion, and
K(s)
represents the ontroller transfer funtion. In Figure 4-3, the input or
44
r
e
+
u
y
K(s)
G(s)
-
Figure 4-3: Classial ontrol theory blok diagram.
r
e
is the input (also alled the referene signal),
and
y
G(s) is the plant, K(s) is the ontroller,
u is the ontrol signal,
is the error signal,
is the output signal.
d
0
e
+
u
+
K(s)
G(s)
-
y
+
Figure 4-4: Disturbane rejetion blok diagram. The signals are the same signals desribed
in Figure 4-3.
referene signal,
r,
is the ommand signal. The error signal,
e,
the dierene between the
referene signal and the output, is also the ontroller input. The ontrol signal,
output from the ontroller. The output signal,
y,
u,
is the
is the measurement of interest.
In disturbane rejetion problems (Figure 4-4), suh as this one, the input referene
signal is set to zero, sine the desired output,
to
y,
y,
is zero.
The transfer funtion from
d
whih measures the attenuation of the disturbane by the ontroller, is alled the
sensitivity transfer funtion, and is given by
S(s) =
1
1 + G(s)K(s)
(4.6)
The Linoln LS system is only slightly more ompliated than the standard disturbane
rejetion system desribed above, beause the disturbane signal,
to the plant
tion, making
G(s)
w,
does not add diretly
output. The disturbane signal is modied by the shaker transfer fun-
d = wGw (s)
the signal diretly added to the plant output. A blok diagram
representing the signiant parts of the Linoln LS system is shown in Figure 4-5.
45
Gw (s)
w
Gw(s)
d
0
u
+
+
K(s)
Ga(s)
-
y
+
Gw (s)
Ga (s) is the atuator transfer funtion, K(s) is the ontroller
signal into the shaker, u is the ontrol signal, and y is the
Figure 4-5: Blok diagram representing the pertinent parts of the Linoln LS system.
is the shaker transfer funtion,
transfer funtion,
w
is the
measurement signal.
represents the shaker transfer funtion,
ontroller transfer funtion,
w
Ga (s)
is the atuator transfer funtion,
is the signal into the shaker,
u
K(s)
is the
is the ontrol signal, and
y
is
the measured ross member aeleration. The referene signal in this ase, as in the disturbane rejetion ase, is zero beause the ontroller is supposed to rejet the shaker vibration
disturbane. The frational attenuation due to ontrol in this senario is
Tyd =
1
1 + K(s)Ga (s)
(4.7)
and the losed loop transfer funtion from the shaker to the aelerometer is
Tyw =
Gw (s)
1 + K(s)Ga (s)
(4.8)
Some of the harateristis of the expeted performane an be seen in the Bode plot of
the atuator to ross member aelerometer transfer funtion times the ontroller transfer
funtion,
Ga (s)K(s).
(See Figure 4-6.) Clearly, the Bode plot shows that there is a large
gain at 150 Hz, and lower gains at frequenies farther away from 150 Hz. Also, the Bode plot
shows that there are two rossover frequenies, 147 Hz and 153 Hz. First, onsider the lower
rossover frequeny, at 147 Hz. At this frequeny, the phase is -67 degrees. This rossover is
obviously stable, with a phase margin of 113 degrees. The seond rossover, at 153 Hz, has
46
Magnitude
0
10
−5
10
1
2
10
3
10
10
Phase (degrees)
1000
500
0
1
2
10
Figure 4-6: Bode plot of
10
Frequency (Hz)
Ga (s)K(s),
3
10
the atuator to ross member aelerometer transfer
funtion times the ontroller transfer funtion.
There is a large gain at 150 Hz, and two
rossovers, one at 147 Hz and the other at 153 Hz, with orresponding phases of -67 and 72
degrees.
a orresponding phase of 72 degrees. Again, the rossover is stable, and the phase margin
is 108 degrees. This Bode plot demonstrates that the ontroller designed above should be
stable and attenuate disturbanes at frequenies near 150 Hz and have little eet elsewhere.
The expeted performane demonstrated by the Bode plot is shown in Figure 4-7. Consider the losed loop transfer funtion from the shaker to the ross member aelerometer
of the ontroller used here.
The measured experimental transfer funtion should losely
resemble the transfer funtion alulated from theory. Figure 4-7 shows a omparison of experimental and predited results. The experimental losed loop transfer funtion from the
shaker exitation to the ross member aelerometer is measured using the signal analyzer,
and is represented by the thin line.
The thik line represents the theoretial losed loop
transfer funtion alulated using Equation 4.8. The experimental and theoretial results
are similar, although the bandwidth of the experimental transfer funtion is narrower than
the theoretially alulated transfer funtion bandwidth. This is likely due to the data pro-
47
Magnitude (dB, g/V)
0
−20
−40
−60
−80
100
125
150
175
200
150
Frequency (Hz)
175
200
Phase (degrees)
0
−200
−400
−600
100
Experimental
Calculated
125
Figure 4-7: Experimental and alulated transfer funtions from the shaker exitation to
the ross member aelerometer.
The thin line is the experimentally determined transfer
funtion and the thik line is the alulated transfer funtion based on ontrol theory. The
theoretial alulated transfer funtion and the experimental transfer funtion math losely.
essing done on the experimental data. The signal analyzer aquires the experimental data
at a nite rate, and it also averages several streams of data. The lose math between the
experimental and theoretial transfer funtions indiates that the experimental ontroller
does what it was expeted to do, and the ross member vibration is signiantly redued
near 150 Hz.
4.4 Closed Loop Vibration
The purpose of the tonal ontroller is to eliminate ross member vibration over a narrow
band of frequenies. As a result, the magnitude of the transfer funtion from the shaker to
the ross member aelerometer should derease signiantly at 150 Hz when the ontrol
loop is losed. This drop an be seen by omparing the open loop transfer funtion from
the shaker to the ross member aelerometer and the losed loop transfer funtion from
48
Magnitude (dB, g/V)
0
−20
−40
Phase (degrees)
100
150
−100
175
200
Open Loop
Closed Loop
−200
−300
100
Figure 4-8:
125
125
150
Frequency (Hz)
175
200
Open and losed loop transfer funtions from the shaker to the ross mem-
ber aelerometer. The thin line shows the open loop transfer funtion and the thik line
shows the losed loop transfer funtion. At 150 Hz the ross member vibration dereases
dramatially, as expeted.
the shaker to the ross member aelerometer. (Figure 4-8) The thin line is the open loop
transfer funtion and the thik line is the losed loop transfer funtion. As expeted, the ross
member vibrations (open and losed loop transfer funtions) are similar at all frequenies,
exept at those around 150 Hz, where the vibration goes to nearly zero.
The vibration
derease extends for only a few hertz on either side of 150 Hz, roughly 148 Hz to 152 Hz.
Unlike the ross member vibration, the magnitude of the ontrol arm vibration at 150 Hz
would not be expeted to derease 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
aelerometer. A ontroller that redues the aeleration on one side of the bushing (ross
member) is not expeted to redue the aeleration on the other side of the bushing (ontrol
arm). Figure 4-9 shows the open (thin line) and losed loop (thik line) transfer funtions
from the shaker to the ontrol arm aelerometer. No signiant dierene is seen between
the open loop ontrol arm vibration and the losed loop vibration at 150 Hz. There is a level
49
Magnitude (dB, g/V)
Phase (degrees)
0
−10
−20
−30
100
125
150
175
200
Open Loop
Closed Loop
0
−200
−400
−600
100
125
150
Frequency (Hz)
175
200
Figure 4-9: Open and losed loop transfer funtions from the shaker to the ontrol arm
aelerometer.
The thin line is the open loop transfer funtion and the thik line is the
losed loop transfer funtion. As expeted, there is no signiant derease in vibration at
150 Hz. At 142 Hz, there is a derease in the magnitude of vibration.
shift upwards of magnitude of vibration at frequenies above 150 Hz, probably due to small
experimental dierenes. Also, there is a derease of roughly 6 dB in the magnitude of the
vibration at 142 Hz. This result is diult to explain. With the addition of the ontroller
(losed loop), the only part of the loop that hanges is the eet of the ontroller on ontrol
arm vibration. Therefore, we would expet the ontrol arm vibration to hange only when
the ontroller signal is large, but without a more detailed examination of the ontrol arm
transfer funtions, it is diult to predit what eet the ontroller would have. However,
how the ontrol arm vibration hanges is not very important, assuming that ontrol arm
vibrations are not extreme, sine it is only the frame vibrations that we are about.
50
4.5 Interior Sound Levels
We know that most of the road vibrations are transmitted into the frame through the point 4
bushing [9℄, and these road vibrations result in inreased interior abin noise. Therefore, we
assume that using the tonal ontroller to eliminate the ross member (frame) vibration near
the point 4 bushing will redue the sound in the interior of the vehile.
In the modeling
tests onduted by Ford, all fores aross the point 4 bushing were removed and the interior
sound was measured.
the bushing.
The sound dereased signiantly when there was no fore aross
This result points to the elimination of ross member vibration as a logial
approah to ounterat the road noise indued fores aross the bushing, beause it would
leave the net fore aross the bushing nearly zero.
In our test setup, the sound level meter mirophone was positioned at the four loations
desribed in Setion 3.3.2. Sound was reorded at eah loation, and ompared to the sound
without the ontroller in operation. The open loop (thin line) and losed loop (thik line)
transfer funtions from the shaker to the mirophone are shown in Figure 4-10 (rst mirophone position, Figure 3-9(a)), Figure 4-11 (seond mirophone position, Figure 3-9(a)),
Figure 4-12 (third mirophone position, Figure 3-9(b)), and Figure 4-13 (fourth mirophone
position, Figure 3-9()).
If the assumption that reduing ross member vibration redues interior sound is orret, then magnitude of the mirophone signals at eah loation should derease when the
ontroller is turned on. We do see redutions in sound level, ranging from 2.4 dB at the rst
mirophone position, to an almost negligible redution at the seond mirophone position,
but the redutions were not as large as we had hoped.
Although we did not reord the vibration levels at other loations on the ar, we did
notie that when we felt the hood, front fenders, et., there was a signiant redution
of vibration levels under losed loop ontrol.
Nevertheless, the interior abin sound level
redution was small.
There are a few possible onlusions from these results. It is possible that the statement
that most of the road noise vibrations are transmitted laterally through the point 4 bushing
is inorret.
Or, it is oneivable that our experimental setup introdued a new sound
51
Magnitude (dB)
10
0
−10
−20
−30
Phase (degrees)
−40
100
125
150
175
200
Open Loop
Closed Loop
0
−500
−1000
100
125
150
Frequency (Hz)
175
200
Figure 4-10: Open and losed loop transfer funtions from the shaker to the rst mirophone
position. The thin line is the open loop transfer funtion and the thik line is the losed
loop transfer funtion. Notie that there is a small redution (about 2.4 dB) in sound level
at 150 Hz.
transmission path not previously observed, or that our setup does not aurately represent
driving onditions. Future researh would need to be done to disover why we were able to
signiantly redue ross member vibrations without reduing interior sound levels muh.
4.6 Summary
In this hapter, we presented the experimental results for a tonal ontroller.
Although a
broadband ontroller is neessary to signiantly attenuate sound levels over the 100 to
200 Hz band, the use of a tonal ontroller allows us to determine whether a losed loop
redution in ross member aeleration redues interior sound levels.
We had hoped for
a bigger sound redution, but we did show that eliminating ross member vibration does
redue the sound somewhat (up to 2.4 dB at one loation). Although we do not have data
desribing the loations of the aousti nodes, we observed by moving the mirophone around
52
Magnitude (dB)
10
5
0
−5
−10
−15
100
125
150
175
200
Phase (degrees)
200
Open Loop
Closed Loop
0
−200
−400
−600
100
125
150
Frequency (Hz)
175
200
Figure 4-11: Open and losed loop transfer funtions from the shaker to the seond mirophone position. The thin line is the open loop transfer funtion and the thik line is the
losed loop transfer funtion. No signiant dierene in the sound level at 150 Hz is seen
at this mirophone position.
the vehile interior near the driver, that the node loations hanged when the ontrol loop
was losed. A more detailed study of the entire sound distribution in the interior is required
to determine how muh the sound levels are redued, or if the sound pressure distribution
is merely hanged without a net redution in overall sound levels.
Additionally, this tonal ontroller was expeted to eliminate ross member vibration in
the losed loop ase and have little eet on the ontrol arm vibration, and the experimental
results show the ontroller did behave generally as expeted. The results also show that,
as expeted, the tonal ontroller was stable when implemented. In addition, it was important to see that the measured experimental transfer funtions losely math the alulated
theoretial transfer funtion to show that the ontroller works as it was expeted.
53
Magnitude (dB)
10
0
−10
−20
−30
100
125
150
175
200
Phase (degrees)
0
Open Loop
Closed Loop
−200
−400
−600
−800
100
125
150
Frequency (Hz)
175
200
Figure 4-12: Open and losed loop transfer funtions from the shaker to the third mirophone
position. The thin line is the open loop transfer funtion and the thik line is the losed
loop transfer funtion. Note the small (roughly 0.75 dB) derease in sound level at 150 Hz
at this mirophone position.
54
Magnitude (dB)
0
−10
−20
−30
100
125
150
175
200
Phase (degrees)
200
Open Loop
Closed Loop
0
−200
−400
−600
−800
100
125
150
Frequency (Hz)
175
200
Figure 4-13: Open and losed loop transfer funtions from the shaker to the fourth mirophone position. The thin line is the open loop transfer funtion and the thik line is the
losed loop transfer funtion. A derease in sound level of approximately 1 dB is seen at
150 Hz at this mirophone position
55
56
Chapter 5
Broadband Controller
After the tonal ontroller, the next logial step to redue interior noise in the Linoln LS is
a broadband ontroller. We would like the ontroller to operate over the range of 100 Hz
to 200 Hz, but the tonal ontroller only has eet over a range of a few hertz. It turns out
that a broadband ontroller is diult to design and implement for this partiular hoie
of atuator.
Setion 5.1 disusses these diulties.
Seondly, to show redution of ross
member aeleration at other frequenies (other than 150 Hz), Setion 5.2 desribes several
dierent tonal ontrollers similar to the one designed in Setion 4.2, but entered at other
frequenies, namely 140 Hz, 160 Hz, and 180 Hz. We use these tonal ontrollers to determine
if reduing ross member vibration at eah frequeny is eetive at reduing interior noise.
5.1 Diulties with Broadband Control
The rst step in designing a broadband ontroller is to examine the pertinent transfer
funtion, in this ase the transfer funtion from the atuator exitation to the ross member
aelerometer vibration. (See Figure 5-1.) We would like the broadband ontroller to at
over the range 100 to 200 Hz. As an be seen in the Bode plot, the magnitude plot is quite
modal, but is generally steadily inreasing over this range.
The ideal ontrol open loop
transfer funtion would be a broad peak with rossovers below 100 Hz and above 200 Hz.
This would attenuate the noise in this range, and have little eet at other frequenies. It
would not be diult to design a suh a ontroller that would atten the transfer funtion
57
2
Magnitude
10
0
10
−2
10
−4
10
0
1
Phase (degrees)
10
2
10
3
10
10
1000
500
0
0
1
10
2
10
3
10
10
Frequency (Hz)
Figure 5-1:
Bode plot of the transfer funtion from the atuator exitation to the ross
member aelerometer vibration. The transfer funtion is modal, but generally inreasing
in the signiant range.
and then add a broad peak that extends from 100 Hz to 200 Hz.
transfer funtion attened by adding stable poles and zeros.
Figure 5-2 shows the
In this Bode plot, it is also
lear that there are two zeros in the frequeny range we are interested in, at 128 Hz and
184 Hz. Due to these two zeros, this atuator has no authority at 128 Hz and 184 Hz; we
will not be able to aet the ross member vibration at these frequenies with this atuator
alone.
Another purpose of the attened transfer funtion is to show if there is the presene of
non-minimum phase lag. Beause phase is related to the slope of the Bode magnitude plot
in a minimum phase system, a minimum phase system that has a perfetly at magnitude
would also have at phase.
In pratial appliations, a minimum phase system with an
approximately at magnitude plot will have roughly at phase. If the system is not minimum
phase, the exess phase lag will be learly seen.
broadband ontrol.
Exess phase lag auses diulty with
Non-minimum phase lag an be aused by time delays in the system
58
−2
Magnitude
10
−3
10
−4
10
−5
10
0
Phase (degrees)
10
1
2
10
10
3
10
1000
500
0
0
10
1
2
10
10
3
10
Frequency (Hz)
Figure 5-2:
Bode plot of the attened transfer funtion from the atuator to the ross
member aelerometer.
The transfer funtion was attened by adding stable poles and
zeros (minimum phase poles and zeros). There are two zeros in the range of interest (100 to
200 Hz), at 128 Hz and 184 Hz. These zeros mean that this atuator has no ontrol authority
at those frequenies. Also, there is a large amount of non-minimum phase at roughly 30 Hz,
as well as a signiant amount between 60 and 70 Hz.
and right hand plane zeros, and tends to make a system less stable.
As an be seen in
Figure 5-2, there is a large amount of exess phase lag at roughly 30 Hz. The non-minimum
phase lag here would not ause too many problems to a ontroller ating around 100 Hz,
but there is also a signiant amount of non-minimum phase between 60 and 70 Hz that
would ause problems with a ontroller ating at 100 Hz (the lower end of the frequeny
range we are interested in). If the broadband ontroller is to at at frequenies as low at
100 Hz, there would have to be a rossover near the loation of this exess phase lag.
In summary, with this partiular atuator and sensor (aelerometer) pair, an eetive
broadband ontroller would be diult, if not impossible, to design.
There is no way to
get around the fat that this atuator has no ontrol authority around 128 Hz and 184 Hz,
and the atuator annot attenuate the ross member vibration at those frequenies. The
59
non-minimum phase lag is also a problem for broadband ontrol, but this problem may
be overome by a arefully designed broadband ontroller that has the rossover frequeny
above the non-minimum phase lag (above 70 Hz). These broadband ontroller diulties,
however, are ontingent on this partiular atuator, sensor, and plant system. It is possible
that a dierent atuator design may make it easier to design a broadband ontroller for this
system.
5.2 Tonal Controllers at Various Other Frequenies
To show that we ould get ross member vibration and interior sound redution at various
frequenies (other than 150 Hz), we implemented three other tonal ontrollers, very similar
to the ontroller designed in Setion 4.2, but at dierent frequenies. These ontrollers show
that ontrol (and noise attenuation) is possible at multiple frequenies.
5.2.1
Tonal Control at 140 Hz
The tonal ontroller entered at 140 Hz is similar to the tonal ontroller entered at 150 Hz
designed in Setion 4.2, with
a = −0.2382 and b = −0.1663.
The ontroller should eliminate
the vibration of the ross member around 140 Hz. Figure 5-3 shows the open loop transfer
funtion (thin line) from the shaker to the ross member aelerometer as well as the losed
loop transfer funtion (thik line) with the tonal ontroller at 140 Hz.
As expeted and
similar to the results from the tonal ontroller at 150 Hz, the ross member vibration drops
signiantly around 140 Hz, in the range of 137 to 145 Hz.
in Figure 5-4.
The interior sound is shown
Figure 5-4(a) shows the open loop (thin line) and losed loop (thik line)
transfer funtions from the shaker to the rst mirophone position. Figure 5-4(b) shows the
same transfer funtions from the shaker to the third mirophone position. As an be seen,
there is a derease of about 6.5 dB in interior sound at the rst mirophone position and
about 2 dB at the third mirophone position. There is little hange in the interior sound at
other frequenies with this tonal ontroller.
The tonal ontroller entered at 140 Hz has similar results as the tonal ontroller entered
at 150 Hz. Both eliminate ross member vibration at the frequeny of interest, and redue
60
Magnitude (dB, g/V)
0
−20
−40
100
110
120
130
140
150
160
170
180
190
200
Phase (degrees)
300
Open Loop
Closed Loop
200
100
0
100
110
120
130
140 150 160
Frequency (Hz)
170
180
190
200
Figure 5-3: Open and losed loop transfer funtion from the shaker to the ross member
aelerometer with the tonal ontroller entered at 140 Hz. Notie the signiant drop in
ross member vibration in the range 137 to 145 Hz, entered at 140 Hz.
the interior sound by a small amount over a small frequeny range.
5.2.2
Tonal Control at 160 Hz
The tonal ontroller entered at 160 Hz, with
a = −0.0249 and b = 0.28945,
is also similar to
the tonal ontrollers entered at 140 Hz and 150 Hz. The ross member vibration at 160 Hz
should be eliminated, as seen in Figure 5-5. The open loop transfer funtion from the shaker
to the ross member aelerometer is the thin line and the losed loop transfer funtion is
the thik line. Clearly, the ross member vibration is eliminated at 160 Hz (between 153 Hz
and 170 Hz), as expeted. There is, however, an inrease in vibration in the frequeny range
136 to 153 Hz. This inrease in vibration is due to the poor phase margin in that range. (See
Figure 5-6) This tonal ontroller ould be improved by adjusting
a and b
in Equation 4.1 to
give better phase margins.
In Figure 5-7, Figure 5-7(a) shows the open loop (thin line) and losed loop (thik
61
Magnitude (dB)
10
0
−10
−20
−30
100
110
120
130
140
150
160
170
180
190
200
Phase (degrees)
200
Open Loop
Closed Loop
0
−200
−400
−600
100
110
120
130
140 150 160
Frequency (Hz)
170
180
190
200
160
170
180
190
200
140 150 160
Frequency (Hz)
170
180
190
200
(a)
Magnitude (dB)
10
0
−10
−20
Phase (degrees)
−30
100
110
120
130
140
150
200
0
−200
−400
100
Open Loop
Closed Loop
110
120
130
(b)
Figure 5-4: Open and losed loop transfer funtions from the shaker to the mirophone for a
tonal ontroller entered at 140 Hz. At the rst mirophone position, (a), there is a derease
in interior sound of about 6.5 dB near 140 Hz (at 136.5 Hz) and almost no hange at other
frequenies. At the third mirophone position, (b), there is a minor derease of roughly 2 dB
in sound near 140 Hz (at 137 Hz) with little hange in sound at other frequenies.
62
Magnitude (dB, g/V)
0
−20
−40
100
110
120
130
140
150
160
170
180
190
200
Phase (degrees)
300
Open Loop
Closed Loop
200
100
0
100
110
120
130
140 150 160
Frequency (Hz)
170
180
190
200
Figure 5-5: Open and losed loop transfer funtion from the shaker to the ross member
aelerometer with the tonal ontroller entered at 160 Hz. As expeted, there is a large
derease in ross member vibration entered at 160 Hz, and between 153 and 170 Hz. There
is also an inrease in vibration between 136 and 153 Hz due to poor phase margin.
(See
Figure 5-6.)
line) transfer funtions from the shaker to the rst mirophone position, and Figure 5-7(b)
shows the open and losed loop transfer funtions from the shaker to the third mirophone
position. A small redution (3.1 dB at the rst mirophone position and 2 dB at the third
mirophone position) in interior sound an be seen, with only minor hanges in sound at
other frequenies.
The results from the tonal ontroller entered at 160 Hz are very similar to the results
from both the 140 Hz and 150 Hz tonal ontrollers. At 160 Hz, the ross member vibration
is eliminated and there is a small redution in sound.
5.2.3
Tonal Control at 180 Hz
Again, the tonal entered at 180 Hz is similar in design to the other tonal ontrollers previously desribed, with
a = −0.0249
and
b = 0.28945.
63
The open loop (thin line) and losed
40
Magnitude (dB)
20
0 dB
0
6 dB
3 dB
−20
−40
−360
−270
−180
Phase (degrees)
−90
0
Figure 5-6: Nihols plot of the transfer funtion from the atuator to the ross member
aelerometer times the ontroller transfer funtion from 100 to 200 Hz. The low frequenies
start in the bottom middle of the plot and the high frequenies end at the bottom right. The
plot line touhes the 17.4 dB ontour (innermost ontour) at 147 Hz, explaining why the
vibration transfer funtion from Figure 5-5 inreases approximately 17 dB around 147 Hz.
loop (thik line) transfer funtions from the shaker to the ross member aelerometer are
shown in Figure 5-8.
Unlike the previous tonal ontrollers, the tonal ontroller entered
at 180 Hz does not eliminate the ross member vibration, it only dereases it by a small
amount. This an be explained by the zero at 184 Hz, as disussed in Setion 5.1. The tonal
ontroller at 180 Hz is lose enough to the zero for the atuator to have only a little ontrol
authority at 180 Hz. Also, due to the lak of ontrol authority at 180 Hz, we do not expet
the sound to be redued at 180 Hz. (See Figure 5-9.) The open loop (thin line) and losed
loop (thik line) transfer funtions from the shaker to the rst mirophone position (Figure 5-9(a)) and the third mirophone position (Figure 5-9(b)) show that the sound atually
inreases, 2.1 dB and 1.9 dB, respetively. The lak of ontrol authority explains the lak
of sound redution.
The results from the tonal ontroller entered at 180 Hz are dierent from the results
64
Magnitude (dB)
10
0
−10
−20
−30
100
110
120
130
140
150
160
170
180
190
200
Phase (degrees)
200
Open Loop
Closed Loop
0
−200
−400
−600
100
110
120
130
140 150 160
Frequency (Hz)
170
180
190
200
160
170
180
190
200
140 150 160
Frequency (Hz)
170
180
190
200
(a)
Magnitude (dB)
10
0
−10
−20
−30
−40
Phase (degrees)
100
110
120
130
140
150
200
0
−200
−400
Open Loop
Closed Loop
−600
−800
100
110
120
130
(b)
Figure 5-7: Open and losed loop transfer funtions from the shaker to the mirophone for a
tonal ontroller entered at 160 Hz. At the rst mirophone position, (a), there is a roughly
3.1 dB derease in interior sound at 160 Hz and little hange at other frequenies. At the
third mirophone position, (b), there is a minor derease of roughly 2 dB in sound at 160 Hz
with only a little hange in sound at other frequenies.
65
Magnitude (dB, g/V)
10
5
0
160
170
180
190
200
Phase (degrees)
100
Open Loop
Closed Loop
50
0
160
170
180
Frequency (Hz)
190
200
Figure 5-8: Open and losed loop transfer funtion from the shaker to the ross member
aelerometer with the tonal ontroller entered at 180 Hz. There is only a small derease in
ross member vibration at 180 Hz, and almost no hange in vibration at other frequenies.
from the other tonal ontrollers due to the lak of ontrol authority at 180 Hz. The ross
member vibration dereases only slightly, and the sound at 180 Hz does not derease at all.
66
Magnitude (dB)
5
0
−5
−10
Phase (degrees)
−15
160
170
180
200
190
200
Open Loop
Closed Loop
150
100
50
0
160
170
180
Frequency (Hz)
190
200
180
190
200
180
Frequency (Hz)
190
200
(a)
Magnitude (dB)
0
−10
−20
Phase (degrees)
−30
160
170
300
200
100
0
160
Open Loop
Closed Loop
170
(b)
Figure 5-9:
Open and losed loop transfer funtions from the shaker to the mirophone
for a tonal ontroller entered at 180 Hz.
At the rst mirophone position, (a), there
is no derease in interior sound at 180 Hz, there is a slight inrease (2.1 dB). At the third
mirophone position, (b), again there is no derease in sound at 180 Hz, and a small inrease
in sound (1.9 dB).
67
68
Chapter 6
Conlusion
The aim of this study was to attempt to redue the interior abin noise of an automobile
without ompromising vehile handling by using an ative suspension system.
In passive
suspensions, typially used in prodution vehiles, reduing interior noise and improving
handling are ompeting goals, and reduing noise typially redues handling quality. With
an ative suspension, however, it may be possible to redue noise while maintaining good
vehile handling.
In a passive suspension system, the point 4 bushing must have onstant properties at all
frequenies. A soft point 4 bushing is good for noise redution purposes beause it damps
road noise vibrations and makes the ride quieter.
For vehile handling purposes, on the
other hand, a sti bushing is more eetive. A sti bushing allows drive fores, suh as the
steering fores, to be transmitted without attenuation. A passive suspension system annot
be both sti at the drive fore frequenies and soft at vibration frequenies.
An ative
suspension system, however, allows the point 4 bushing to have variable harateristis at
dierent frequenies. At the low frequenies assoiated with drive fores (on the order of
a few Hz) it is possible to make the bushing sti, while at the higher road noise vibration
frequenies, the bushing an be more soft. To implement this ative suspension system, we
designed and built an eletromagneti atuator that ats aross the point 4 bushing.
A broadband ontroller ating over the frequeny range 100 to 200 Hz would be required
to implement this system in an atual automobile. To simplify the system for our preliminary
69
studies, we began with a tonal ontroller entered at 150 Hz to eliminate ross member
vibration.
The eet of this tonal ontroller extended for only a few hertz on either side
of 150 Hz, but was intended to demonstrate our ability to redue ross member vibration
and to show that reduing vibration leads to a redution in interior noise. We also designed
similar tonal ontrollers entered at 140 Hz, 160 Hz, and 180 Hz.
Our experiments determined that eah of the tonal ontrollers has a small frequeny
band at whih it is eetive at rejeting the disturbane aused by shaker vibration. Also,
eah of the tonal ontrollers (with the exeption of the tonal ontroller entered at 180 Hz)
signiantly redued ross member vibration. The tonal ontroller entered at 180 Hz proved
ineetive at rejeting the shaker disturbane, due to the lose proximity of a zero in the
transfer funtion from the atuator to the ross member aelerometer (further explanation
below).
Although the ross member vibration at the pertinent frequeny was redued to
nearly zero for eah of the 140 Hz, 150 Hz, and 160 Hz ontrollers, the interior abin sound
levels did not derease as muh as we had hoped. The sound levels did derease somewhat
(a few deibels at most of the mirophone loations), but we had hoped for dereases on the
order of 6 to 10 deibels.
Designing a broadband ontroller turned out to be more diult than antiipated for
several reasons. The transfer funtion from the atuator to the ross member aelerometer
(Figure 5-1) has two zeros in the frequeny range of interest (100 to 200 Hz):
one zero
at 128 Hz and one at 184 Hz. At the frequenies where the transfer funtion is zero, the
eletromagneti atuator used in this projet has no ontrol authority.
No ontroller an
be designed with this partiular atuator that would allow us to attenuate ross member
vibration at 128 Hz and 184 Hz.
The zero at 184 Hz explains why the tonal ontroller
entered at 180 Hz was not eetive at attenuating ross member vibration. Additionally,
the exess phase lag (Figure 5-2) between 60 and 70 Hz would make it diult to design a
stable ontroller with a rossover below 100 Hz.
Our studies demonstrated that it is possible to redue ross member vibration at various
frequenies with the eletromagneti atuator used here, although the atuator has no ontrol
authority at 128 Hz and 184 Hz. We also found that eliminating ross member vibration at
70
a partiular frequeny redues interior sound, albeit by a small amount.
The redution in sound level was not as enouraging as we had hoped, but it may be
explained by examining our assumptions.
Some of the assumptions made in this projet
appear to have perhaps been not entirely orret. One assumption that may not have been
orret is the one suggested by Ford [9℄, that most of the road noise vibration is transmitted
laterally (parallel to the wheel axis) through the point 4 bushing. Given the experimental
data presented here, it is unlear whether this assumption was orret. One possibility is
that although most vibration may initially be transmitted through the point 4 bushing, our
ontroller modies the vibration transmission and reates other paths.
This may explain
why the magnitude of the sound redution is not as great as we had hoped.
Another assumption vital to this projet was that reduing the frame vibration at the
ross member would lead to a redution in interior abin noise.
This was a reasonable
assumption; reduing the amount of road noise that is transmitted through the point 4
bushing would redue the vibration of the ross member, and reduing the ross member
vibration would be expeted to redue the interior abin noise aused by road noise vibration.
Again, it is unlear if this assumption was orret. The road noise vibration transmission
paths ould have been modied by the addition of the atuator, resulting in the transmission
of road noise into the interior abin through pathways other than those involving the ross
member.
Further studies are needed to resolve the diulties with broadband ontrol desribed
above. We would rst need to determine whether broadband ontrol is possible, despite the
two zeros in the frequeny range of interest and the exess phase lag. Seond, if broadband
ontrol proved impossible, we would need to determine whether the diulties were spei
to the eletromagneti atuator used here. It is possible that a dierent type of atuator,
or a dierent onguration of the eletromagnet, would make broadband ontrol possible.
Additional researh is also required to determine why we were unable to redue interior
sound levels as muh as we had hoped. Determining the exat noise transmission paths using
our atuator ould determine if and how the vibration paths had hanged, giving lues as
to why our studies were only partially suessful.
71
72
Appendix A
Calulation of Atuator Parameters
This appendix inludes the alulation of all important atuator parameters.
First, we
desribe the atuator size and shape, as well as the required air gap between the rotor and
that stator. Then, we dene some of the material properties of the steel laminations that
will be neessary in the later alulations. Next we use the required fore (determined in
Setion 2.2) to alulate the magneti eld, the magneti ux, and the magnetizing fore.
Then we alulate the relutane and use it (along with the magneti ux) to alulate
the number of amp-turns required for this magneti atuator.
Finally, we alulate the
estimated power required to operate the eletromagnet.
Geometry of Atuator
The atuator (Figure 2-3) is omposed of a irular side (the stator), onentri with the
point 4 bushing, whih ats as a magneti return path, and a U-shaped side (the rotor)
wound with the urrent arrying oil, attahed to the ontrol arm. The radius of the stator
is 5 m, large enough so that when the ontrol arm rotates about the point 4 bushing,
the magnet does not interfere with any of the automobile omponents near the bushing.
The ends of the rotor are rounded so that they onform to the urvature of the irular
side of the eletromagnet while maintaining the air gap. The size of the rotor is set both
by the required eletromagneti eld required, and by the free spae available near the
ontrol arm.
The length (L) of the magneti ore is
73
L = 30 m = 0.30 m,
making a U-
shape that is approximately 15 m long and 8 m wide.
(2.5 m)2 = 0.000625 m 2 .
An air gap (g
The ross setional area is
= 2 mm = 2 × 10−3 m)
A=
is neessary to separate
the eletromagneti rotor and stator, and allow for some relative motion aross the point 4
bushing. At least 2 mm is required so that the two sides of the magnet stay separated during
normal operation of the atuator.
Material Properties
Several material properties are required to alulate the atuator parameters suh as the
magneti permeability of ore. The permeability of the ore is
µ = κm µ0
where
µ0 = 4π × 10−7 N/A2
is the permeability of free spae and
(A.1)
κm = 8000
is the magneti
permeability of steel. Then the permeability of the ore is
µ = κm µ0 = 0.0101 N /A2
(A.2)
Atuator Fore
The total fore required is given by
Ftotal = 2F = 150 N
where
F
(A.3)
is the fore in the air gap, beause the magneti eld goes through two faes, eah
leg of the U. Therefore, the fore in the gap is
F = 75 N
74
(A.4)
The magneti eld required to produe this fore is
B=
where
F
is the fore in the gap,
µ0
r
2µ0 F
= 0.5492 T
A
(A.5)
A
is the permeability of the gap (air), and
is the ross
setional area at the gap. Then, the total magneti ux through any surfae is dened by
Φ=
Z
B dA = BA cos θ = 3.432 × 10−4 Wb
(A.6)
if the magneti eld has a onstant magnitude and diretion, as in this ase, where
the magneti ux,
B
is the magneti eld,
A
is the ross setional area, and
θ
Φ
is
is the angle
between the normal to the surfae and the diretion of the magneti eld (zero in this ase).
Finally, the magnetizing fore is
H=
where
µ
B
= 0.68 Oe = 54.374 A/m
µ
is the magneti permeability, and
B
(A.7)
is the magneti eld, both from above.
Relutane
The relutane of the ore is
Rc =
where
L
is the length of the ore,
µ
L
= 47, 525 A /Wb
µA
is the permeability of the ore, and
(A.8)
A
is the ross
setional area of the ore. Similarly, the relutane of gap is
Rg =
g
= 2, 550, 000 A /Wb
µ0 A
75
(A.9)
where
g
is the length of the air gap,
µ0
is the permeability air, and
A
is the ross setional
area gap at the ore. Then the total relutane,
R = Rc + 2Rg = 5, 140, 000 A /Wb
(A.10)
is the relutane of the ore plus the relutane of eah air gap.
Required Amp-Turns
The magnetomotive fore,
M,
required to produe the desired eld strength in the gap is
given by
M = ΦR = N I = 1764 amp-turns
where
Φ
is the magneti ux,
turns, and
I
R is the
N
total relutane,
is the urrent in the oil.
NI
(A.11)
is the number of urrent arrying
is the number of amp-turns required for the
magnet. As a result, the magnet has 120 turns and 15 A urrent.
Estimate of Power Required
The length of the turns is the length of one side of the magnet (L
radius of the oil is approximately
thikness of the oil (t
= 1.25 m).
r = 2.4 m,
= 15 m).
The average
the thikness of the ore plus half of the
But the volume of the oils is not ompletely lled with
opper, so we assume a volume lling eieny
η
of approximately
η = 0.7.
Then the ross
setion of the oil is
A = ηLt = 13.125 m2
where
L
is the length of the eletromagneti oil, and
t
(A.12)
is the thikness of the oil.
The
irumferene of the oil is
l = 2πr = 15.1 m
where
r
(A.13)
is the average radius of the oil.
The resistivity of opper is
ρ = 1.673 × 10−8 Ωm.
76
The resistane of the oil (if it were
only one turn) is given by
R1 =
where
ρ
is the resistivity of opper,
l
ρl
= 1.9 µΩ
A
is the irumferene of the oil, and
(A.14)
A
is the ross
setion of the oil. Then the estimated power in a one-turn oil is
P =
where
NI
is the total urrent and
power in an
N -turn
R1
1
(N I)2 R1 = 3.0 W
2
(A.15)
is the resistane of a one-turn oil. The estimated
oil is
P =
1 2
1
I R = I 2 (N 2 R1 ) = 3.0 W
2
2
whih is the same as the power in a one-turn oil.
77
(A.16)
78
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