active vibration control professor mike brennan institute of sound and vibration research university...

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