active vibration control professor mike brennan institute of sound and vibration research university...
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ACTIVE VIBRATION CONTROL
Professor Mike Brennan
Institute of Sound and Vibration ResearchUniversity of Southampton, UK
Active Vibration ControlWHY ?
• Structures become lighter
• Space and weight constraints
Actuators Sensors
ControlledStructure
Controller
Active Vibration Control
• Active control strategies
• Semi-active/adaptive-passive control changing damping changing stiffness changing mass tunable vibration neutralisers
• Fully-active control where to place the control force feedforward control feedback control control of waves
Active Vibration Control
Control strategy Disturbance Physical objective
Deterministic Random Globalcontrol
Blockingstructuralpath
Local ControlFeedback Feedforward
Semi-active Fully-active
Active Vibration Control
m
k c
m
k c
m
k c
fp fp fp fs
Passive Semi-active /Adaptive-passive Fully- active
• Passive – Mass, stiffness and damping (quantity and distribution) fixed at the design stage
• Fully-active – Dynamic forces applied to the system to minimise the response
• Semi-active / Adaptive-passive
– Stiffness and/or damping properties changed to adjust internal dynamic forces to minimise the response
SEMI-ACTIVE / ADAPTIVE-PASSIVE VIBRATION CONTROL
Semi-Active / Adaptive-Passive Vibration Control
Strategies
• Change Stiffness – low frequencies (air spring)
• Change mass – high frequencies ??
m
k c
f
• Change damping – resonance (hydraulics, electro / magneto rheological fluids
frequency
|Dis
plac
emen
t/for
ce|
stiffnesscontrolled
mass controlled
dampingcontrolled
high damping
low damping
ADAPTIVE DAMPING
Electro / Magneto -Rheological Fluids
• micron sized, polarizable particles in oil
What do they do?
• Newtonian in absence of applied field
• develop yield strength when field applied
What are they ?
ER fluids respond to electric field
MR fluids respond to magnetic field
Basic ER/MR Device Configurations
hydraulic controlsservo valves dampersshock absorbersactuators
clutches and brakeschucking/locking devices dampersbreakaway devicesstructural composites
Direct Shear Mode
force velocity
N
S
applied magnetic field
E
Valve Mode
flow
pressure
N
S
applied magnetic field applied electric field
Typical MR Fluid Behaviour at 25°C
Sh
ear
Str
ess
(kP
a)
0
20
40
60
80
100
120
0 25 50 75 100
Shear Strain Rate (sec-1
)
0 kA/m
80 kA/m
160 kA/m
240 kA/m
Bingham Model
Total damping = Viscous Damping + Coulomb Damping
Constant Due to MR effect
Magneto-Rheological Fluids - Applications
Ride Mode Switch
MR Fluid Damper
Sensor/Controller
Magneto-Rheological Fluids - Applications
Seat
Sensor
Controller
SpringControllable shock absorber
Road input
Acceptable motion transmitted
Off-stateRandompattern
On-State Ordered pattern
Single Degree of Freedom System -
Heavy Duty Vehicle Suspended Seats
• off-highway, construction and agricultural vehicles • class 8 trucks ("eighteen wheelers")• buses
Magneto-Rheological Fluids - Applications
• Seismic excitation
Nihon-Kagaku-Miraikan
National Museum of Emerging Science and Innovation
Opened July, 2001
Tokyo, Japan
2 30-ton MR dampers installed between 3rd and 5th floors
Dong Ting Lake BridgeHunan Province, PRC
• Wind excitation
ADAPTIVE STIFFNESS
mT
Change in Stiffness
Table systems
mA
pneumatic isolators
Stiffness of a pneumatic spring = 2PA
V
where P = pressure in the pneumatic spring A = cross-sectional area of the bellows V = air volume = ratio of specific heats
…………………..(1)
Change in Stiffness
Consider a single mass on a pneumatic spring
m
k
The natural frequency is given by:
n
k
m………………………….(2)
Substituting for k from (1) gives:
2
n
PA
VmBut PA=F=mg, therefore:
n
gA
V• Thus provided that the area and volume remain constant, then the natural frequency is independent of the mass
• Normally designed to have a natural frequency of 1Hz
Change in Stiffness – shape memory alloys
When the memory metal is pulled apart, it deforms. When placed into hot water, the metal "remembers" its original shape, and again forms the letters ICE.
Memory metal is a nickel-titanium alloy
This piece has been formed into the letters ICE, heat-treated, and cooled.
Change in Stiffness – shape memory alloys
Soft
Stiff
Stiffness increasesWith temperature
Change in Stiffness – shape memory alloys
• Material whose Young’s modulus changes with temperature
Composite panel
}
Embedded SMA wires
• Activating the fibres (by passing a current through them and hence causing a temperature change) causes local stiffening and hence the natural frequencies can be shifted to avoid troublesome excitation frequencies.
Variable Stiffness Civil Engineering
TUNABLE VIBRATION ABSORBERS
j tf Fe
j tx Xe
structure
Tunable Vibration Absorbers
The Vibration Absorber – What does it do?
m
k c
frequency
X
F
Tuned Vibration Absorber
X
F
frequency
Tunable Vibration Absorbers
Some Terminology
X
F
frequency
Natural frequency
• Absorber: Tuned to suppress the response at a troublesome resonance frequency
frequency
X
F
Forcing frequency
• Neutraliser: Tuned to suppress the response at a troublesome forcing frequency
The Absorber – some key parameters
m
k c
F X
ma
kaca
Mass ratio 0.1am
mOptimum Damping
3
30.17
8 1opt
frequency
X
F
Location of absorbers
Land-Mark TowerYokohama
ma
kaca
m
k c
F X
Tunable Vibration Absorbers
an
a
k
m
Land-Mark Tower YokohamaLargest building in Japan (earthquake zone)
ma
kaca
m
k c
Acvtive Tunable Vibration Absorbers
K
Λ
+_
Relative displacementz(t) measured using a stroke transducer
Measured value of z(t)
Desired value of z(t)
Computer model of second order system with variable natural frequencyAnd damping ratio
( )sf t
• A secondary force fs(t) is used to “tune” a vibration absorber
Tunable Vibration Absorbers
63rd floor of the Citicorp Centre, New York City
Citicorp Centre New York City
frequency
X
F
Forcing frequency
X
F
2
Tunable Vibration Neutralisers
Change damping
XF
Change stiffness
frequency
2
4t
t
ma
kaca
mFX
at
a
k
m am
m
XF
frequency
Some Important ParametersTunable Vibration Neutralisers
Pneumatically Controlled Vibration Neutraliser (50-100Hz)
22Stiffness =
PA
V
ratio of specific heats for air
pressure in the bellows
effective cross-sectional area of the bellows
volume of the bellows
P
A
V
Too muchdamping
Beam-Type Neutraliser
excitation
L
neq
k
m eq em m m
effective mass of the beam
3
3EIk
LChange E, I or L
k m
Beam-Type Neutraliser
3
18
u
l
h
d
h=distance between beamsd=thickness of one beam
35% change in natural frequency
Servo motor
Beam-Type Neutraliser
Shape Memory Alloy Beam-Like Neutraliser
shaker
neutralisershape memory alloy wires
impedance head
Change in Stiffness – Shape Memory Alloys
Change in Stiffness – shape memory alloys
Elastic modulus changes from 40 to 59 MPa Hysteresis of about 10°C
Temperature
Em
Ea
Cooling Heating
Soft
Stiff
Stiffness increasesWith temperature
Shape Memory Alloy Beam-Like Neutraliser
Coldstate
Hot state
Frequency [Hz]
Fo
rce
/Ve
loc
ity
[Ns
/m]
ma
ka ca
mFV
Shape Memory Alloy Beam-Like NeutraliserSteady-State Experimental Results
63.9 Hz 77.6 Hz+17.5%
Temperature below 35°C Temperature above 67°C
-10
0
10
20
30
40
50
20 40 60 80 100 120 140 160 180 200
20
30
40
50
60
70
80
90
100
Frequency [Hz]
Tem
pera
ture
[ C
]
FRF - Impedance [dB]
-10
00
10
1010
10
10
20
20
20
20
20
30
30
30
4040
40
5050
0
Shape Memory Alloy Beam-Like Neutraliser
tem
pera
ture
(ºC
)
frequency (Hz)
increasing temperature
natural frequency
-5
0
5
10
15
20
25
30
35
40
45
50
20 40 60 80 100 120 140 160 180 200
20
30
40
50
60
70
80
90
Frequency [Hz]
Tem
pera
ture
[ C
]
FRF - Impedance [dB]
0
000
10
10
10
10
2020
20
2020
30
30
4040
5050
50
30
10
20
Shape Memory Alloy Beam-Like Neutraliser
tem
pera
ture
(ºC
)
frequency (Hz)
decreasing temperature
natural frequency
Performance
0 20 40 60 80 100 120 140 160 180 200-1
0
1
Time [sec]
Cos
ine
cos( )
0 20 40 60 80 100 120 140 160 180 2000
5
10
Time [sec]C
urre
nt [A
]
0 20 40 60 80 100 120 140 160 180 200-1
0
1
Time [sec]
D[c
os(
)]
Time
co
s()
D[c
os
()]
I
0 20 40 60 80 100 120 140 160 180 200-1
-0.5
0
0.5
1
Time [sec]
Acc
eler
atio
n m
1 [?V
?]
0 20 40 60 80 100 120 140 160 180 200-1
-0.5
0
0.5
1
Time [sec]
Acc
eler
atio
n m
2 [?V
?]
Time
V(H
os
t)V
(TV
A)
• Good performance also with the real ATVA• No oscillation around the equilibrium point• Constant excitation frequency 59Hz from amb
Change in natural frequency by shape change
mass
Host structure
Low natural frequency
mass
Host structure
Change curvature
High natural frequency
Curved beams
Change in stiffness by change in curvature
ph
s u
2
3
2non-dimensional stiffness
puEI hs s
Adaptive Neutraliser using shape change
natural frequency: 39 Hz - 50 Hz
Adaptive Neutraliser using shape control
-300 -200 -100 0 100 200 300 400 500-30
-20
-10
0
10
20
30
40
50
% in
crea
se in
tune
d fr
eque
ncy
voltage (volts, dc)
predicted
measured (low force amplitude)
Control
ma
kaca
mfx
y
Y
X
n
Adjust stiffness so that natural frequency=forcing frequency
Large steps Large steps
small steps
Control Algorithm
The controller updates the output current every Tn seconds
en is the evaluation of cosΦ at the nth time step
The current at the (n+1)th time step:
P: Constant of the non-linear proportional part D: Constant of the derivative part
3 51n n n n n nI I e e e dP D
Control
Measure phase angle and set cos 0
cosx y
X Y
cosx X t cosy Y t
0
1dt cos
Tx y x y X Y
T
ma
ka ca
mfx
y
Frequency sweep test
input/output board
voltage amplifier electrodynamic
shaker
ATVA
PCvariable frequency harmonic excitation signal
amplifier
amplifier
accelerometers
2a1a
controller output
3 51 , cosn n n n n n nV V P e e e De e
Adaptive Neutraliser using shape control
amplifier
Frequency sweep test – NO CONTROL P-D CONTROL
0 2 4 6 8 10 12 14 16 18 20
-10
0
10
time (s)
2ac
cele
rati
on
(m
/s)
0 2 4 6 8 10 12 14 16 18-1
0
1
time (s)
cos(
ph
ase)
20
0 2 4 6 8 10 12 14 16 18 2035
40
45
50
55
time (s)
freq
uen
cy (
Hz)
38 Hz
52 Hz2 Hz/s
t at 0 V
Boeing CH - 47C
Three adaptive self-tuning absorbers (neutralisers) are installed and tuned to the blade passage frequency of approximately 11 Hz
Upper chamber
Lower chamber
DecouplerPrimary rubber
Rubber bellows
Inertia track
Hydraulic engine mount
High damping at low frequencies Low damping at high frequencies
Hydraulic engine mount
Amplitude sensitive device Damping peaks at a low frequency which is controlled by the mass of
the fluid in the inertia track and stiffness of the rubber elements Increased stiffness at high frequencies
stiff
ness
dam
ping
Adaptive hydraulic engine mount
dam
ping
m
Engine side
Structure side
Effective length of inertia
track is adjusted in real-time
Freudenburg active engine mount
actuator
working reservoir
outer reservoir
balancereservoir
bellowsrubberelement
diaphragm
At low frequencies (<20Hz) the mount behaves as a conventional hydromount
At high frequencies the inertia of the fluid is high decoupling the working and balance reservoirs
At high frequencies the
generated forces are in
anti-phase with the dynamic
forces generated by the engine
Combined active noise/engine mount system
Combined active noise/engine mount system
Engine speed (RPM)
dB
re
20
μP
a
Drivers position 3rd gear acceleration
Active mount driven with a piezo actuator
Cha
ssis
acc
eler
atio
n (d
B)
Engine speed (RPM)
FULLY-ACTIVE VIBRATION CONTROL
FEEDFORWARD CONTROL OF VIBRATION
• Used where it is possible to get advance information on the vibration to be controlled
eg. To control machinery vibration which is generally periodic in nature
Mechanical system
Controller
++
Excitation Response
Fully-Active Systems – where to place the secondary force? - SDOF example
m
k c
receiver
pF
X
sF
m
k c
receiver
pF
X
sF
m
k c
receiver
pF
X
sF
(1) Secondary source applied to source
(2) Secondary source applied to receiver
(3) Secondary source applied between source and receiver
Where to apply the secondary force to bring the receiver to rest with a minimum applied force?
Fully-Active Systems – where to place the secondary force? - SDOF example
m
k c
receiver
pF
X
sF
(1) Secondary source applied to source
( ) ( )s pF F
Fully-Active Systems – where to place the secondary force? - SDOF example
m
k c
receiver
pF
X
sF
(2) Secondary source applied to receiver
2
( ) ( )s p
k j cF F
k m j c
Or in non-dimensional terms as
2
1 2( ) ( )
1 2s p
jF F
j
where
n
2
c
mk n
k
m
Fully-Active Systems – where to place the secondary force? - SDOF example
2
( ) ( )s p
k j cF F
m
Or in non-dimensional terms as
2
1 2( ) ( )s p
jF F
m
k c
receiver
pF
X
sF
(3) Secondary source applied between source and receiver
Fully-Active Systems – where to place the secondary force? - SDOF example
10-1
100
101
10-2
10-1
100
101
102
s
p
F
F
Force applied to the receiver
Force applied to the source
Force applied between the receiver and the source
Application of ACSR to the Westland/Agusta EH101 Helicopter.
Active Control of Structural Response (Westlands, 1989)
Active Control of Rotor Vibration
rotor
fuselage
Hydraulic actuators
• Active control at rotor blade passing frequency at about 18 Hz + harmonics
• Feedforward control
ACSRACSR - Actuator Installation for Production EH101
•sa
Steel downtube
CompositeCompliantElement
TitaniumLug End
ACSR Actuator
Hydraulic Supply
Main GearboxInstallation
Fwd
Support Strut/ACSR ActuatorAssembly
FEEDBACK CONTROL OF VIBRATION• Used where it is not possible to get advance information on the vibration to be controlled
Often used to control random vibration
Mechanical system
Controller
++
Disturbance
Response
Feedback Control of a Single-degree-of-freedom System
2
( )
( )
X j k j c
Y j k m jM cK C
X
Y
c
m H(j)
k Fs
equipment
actuator
controller
vibrating base
accelerometer Can feed back displacement, velocity or acceleration
Feedback gains
Closed-loop response is given by
2( ) K CH j j M
Feedback Control of a Single-degree-of-freedom System – base excitation
• Constant gain feedback control
Non-dimensional frequency
dB
X
YX
Y
c
m H(j)
k fs
equipment
actuator
controller
vibrating base
accelerometer
Open-Loop FRF – Nyquist Plots (simulations)
No high-pass filter One high-pass filter
All are unconditionally stable Velocity feedback isthe “most” stable
Active Vibration Isolation – Feedback Control
Equipment
Controller
Baseplate
Primary shaker
Secondary shaker
Electromagnetic actuator - relatively low forces and large displacements
ve
Vin
ev
Power Amplifier
H
Signal conditioner
+ Amplifier + Integrator + Highpass filter (1 Hz)
base
equipment
•Objective To isolate the delicate piece of equipment using active vibration control
The Control Problem
11
22
33
44
0 0 0
0 0 0( )
0 0 0
0 0 0
H
Hs
H
H
HDecentralisedControl
imag
inar
yreal
Stability of the Decentralised Control System (measurements)
1 2det + ( ) ( ) 1 ( ) 1 ( ) ......j j j j I G H
Stability criterion: None of the eigenvalues i should encirclethe Nyquist point (-1,0) as varies from – infinity to +infinity
Performance of the Decentralised Control System (measurements)
1( ) + ( ) ( ) ( )j j j j
y I G H d
Overall Performance
• Decentralised velocity feedback control
• Electromagnetic actuators in parallel with resilient mounts
• Feedback of absolute velocity in 4 local loops
• Analogue controller – still effective if one channel fails
Example: Feedback (displacment) control of circular saw vibrations (Ellis and Mote, 1979)
Example: Ride comfort improvement o an aircraft(Sensburg et al, 1980)
Frequency (Hz)
Discomfort due to fuselage bendingMode at 9 Hz
Velocity feedback to the taileron9Hz vibration reduced by 2/3
Flexural waves in a beam
j tFe
power power
Active control of waves in beams
Equivalent block diagram
Active control of waves in beams
Frequency (Hz)
PS
D a
t er
ror
sens
or (
dB)
Poor performance at low frequenciesbecause of noise and presence of near field wave
Poor performance at high frequenciesbecause of highgroup velocity causing causalityproblems
Concluding Remarks
• Active control of vibration is being used as an alternative to passive control in many different applications
• Weight /space constraints
• Novelty factor
• Many more current and potential applications:
• Dynamic control of large space structures
• Flutter control in aircraft
• Vibration isolation
• Vibration control of rotating machines
References
• C.R. FULLER, S.J. ELLIOTT and P.A. NELSON 1996. Active Control of Vibration. Academic Press
• P.A. NELSON and S.J. ELLIOTT 1992. Active Control of Sound. Academic Press
• C.H. HANSEN and S.D. SNYDER 1997 Active Control of Noise and Vibration. E & F.N. Spon
• R.L. CLARK, W.R. SAUNDERS and G.P. GIBBS 1998. Adaptive Structures. Wiley Interscience
• A.V. SRINIVASAN and D. MICHAEL McFARLAND 2001. Smart Structures. Cambridge University Press