-

Sang-Myeong Kim

UNESP @ Ilha Solteira

2013

Vibration Modeling, Measurement and Control

ACTIVE VIBRATION CONTROL 2/3

II. Damping Control of Vibrating Systems

The topics coveredThe topics covered

Active Control of S&V General Feedback Control

Feedforward State-Space-based Modern Control

Classical Feedback Control

2. EDA (Electrical Dynamic Absorber)1. PID, Lead-Lags, Notch filters

ContentsContentsI. Principle

Background & Concept

II. Application Examples

1. Active Vibration Isolation (IEEE TCST 2008)

2. Transducer Damping (JSV1 2011)

3. Multi-Modal Control (SMS1 2011)

4. PPF v.s. NPF (SMS2 2011)

5. Broadband Vibration Control (SMS3 2011)

6. Non-collocated Control (JSV2 2013)

7. Time Delay Control (SMS4 2013)

8. Vibration Control of a Flexible Manipulator (SMS5 2013)

III. Potential Applications

1.B

ackground

2.W

hat and Why E

DA

?

3.D

esign Rule

I. Prin

ciple

Background:Background: Mechanical Damper Mechanical Damper v.sv.s.. Mechanical Dynamic Vibration AbsorberMechanical Dynamic Vibration Absorber

ca

F

v

F

v

Parallel Form

ca

ka

ma

F

v

Serial Form 10-1

100

101

-40

-20

0

20

Frequency (Hz)V

eloc

ity (

dB)

10-1

100

101

-40

-20

0

20

Frequency (Hz)

Vel

ocity

(dB

)

Contributor

-Hartog (1947)

Background: Background: Mechanical Damper Mechanical Damper v.sv.s.. Mechanical Dynamic Vibration AbsorberMechanical Dynamic Vibration Absorber

a aZ c

1 1

1

a a a

a jj m c k

Z

10-1

100

101

10-1

100

101

Frequency (Hz)

Impe

danc

e

ca

F

v ka

ma

10-1

100

101

-40

-20

0

20

Frequency (Hz)

Vel

ocity

(dB

)

OriginalDamperDVA ca

F

v

Equivalent Form

Background: Mechanical Damper Background: Mechanical Damper v.sv.s. Mechanical Dynamic Vibration Absorber. Mechanical Dynamic Vibration Absorber

Tools Damper Dynamic Absorber

Performance Broadband Device Narrowband Device

Mechanism Narrowband Skyhook Damper

Advantage • ?• Installation (ex. Vehicles)• Vibration Isolation & Transmission

Frequency Ratio

Transm

issibility

1

1

AmplificationRegion

IsolationRegion

25 %10 %2 %

m

k c

v1

v2

Examples of DVAExamples of DVA

• Simple cantilever form

• Automobiles

• Buildings

break engine

Examples of DVAExamples of DVA

• Harmonic Dampers for Engines • Helmholz Resonator

Suction Resonator

Muffler

Piezo Actuator Electromagnetic Actuator

Background:Background: PassivePassive Electrical Dynamic AbsorberElectrical Dynamic Absorber

C R L

v

F

F v

F vms

Background:Background: EEllectrical Damper (ED) ectrical Damper (ED) v.sv.s.. Electrical DElectrical Dynamic ynamic AAbsorberbsorber (EDA)(EDA)

Fv

- H

FC

Mechanical System

Controller

Response

Disturbance

Control Force

aH c

ca

F

v

Equivalent Model

ED EDA

Contributor

-Karnopp et. Al. (1974)

Development of Development of Electrical Dynamic Absorber (EDA)Electrical Dynamic Absorber (EDA)

)( jH

u

FsF

Electrical Damper

acjH )( G(j)

-H(j)

d

e

10-1

100

101-40

-30

-20

-10

0

10

20

Frequency (Hz)

Ve

loci

ty (

dB

)

OriginaldamperDVA

ca

F

v ka

ma

ca

F

v

Equivalent Model

aaa

aaa j

jcjH

2

2)(

22

Electrical Dynamic Absorber

Comparison between ED and EDAComparison between ED and EDA

)( jH

u

FsF

Tools Electrical Damper Electrical Dynamic Absorber

Performance Broadband Device Narrowband Device

Mechanism Narrowband Skyhook Damper

Advantage

• ?

“EDA is ALWAYS better than ED.”

10-1

100

101-40

-20

0

20

40

Frequency (Hz)

Lo

op

Ga

in (

dB

)

damperDVA

Loop Gain

• RobustnessEffectively in the control bandwidth &

Ineffectively otherwise.

Uncertainty

Unmodeled Dynamics

Low Sen-sitivity

Unmodeled Dynamics

AdvantageAdvantagess of of Electrical Dynamic Absorber (EDA)Electrical Dynamic Absorber (EDA)

Most eminent advantages come from the fact that it is a narrowband controller.

If it is tuned to a mode, it simply becomes a modal controller controllong only a single target mode.

1. multi-modal control is feasible. 2. Non-collocated control is feasible for multiple modes of mixed phases 3. Time delay system control is feasible

by compensating each of multiple modes of different phases.

Summary

Active Tools Electrical Damper Electrical Dynamic Absorber

Passive Tools Mechanical Damper Mechanical Dynamic Absorber

Kim et al (2005)

)( jH

VOID

By Karnopp (1974)

By Hartog (1947)

Three General Tools for Noise & Vibration ControlThree General Tools for Noise & Vibration Control

Installation

Performance

Cost

Advantages:1.Effective2.Convenient to design 3.Very stable

Design Rules Design Rules –– using Den using Den HartogHartog’’ss FixedFixed--Point TheoryPoint TheoryObtain maximally flat response.

PP2 dB

Normalized Frequency

Q

Velocity (d

B)

(mass ratio) 2a

sa Frequency tuning

Damping Tuning

Plant Controller Methods

Position 2nd order HP filter

PAF (position acceleration feedback)

Velocity 2nd order BP filter

VVF (velocity velocity feedback)

Acceleration 2nd order LP filter

APF (acceleration position feedback)

Three Ways to realize the same EDAThree Ways to realize the same EDA

ca

F

v ka

ma

1.A

ctive Vibration Isolation

2.T

ransducer Dam

ping

3.M

ulti-Modal C

ontrol

4.P

PF

v.s. NP

F

5.B

roadband Vibration C

ontrol

6.N

on-Collocated C

ontrol

7.T

ime D

elay Control

8.V

ibration Control of a F

lexible Manipulator

II. Ap

plicatio

ns

1. Active Vib. Isolation (IEEE 2008) 2. Electrical Transducer Damping (JSV 2011)

3. Modal Control using strain sensors (SMS 2011) 4. Multi-modal Control using Acc. (SMS 2011)

5. Broadband Control (SMS 2011) 6. Non-collocated Control (JSV 2013)

7. Time Delay Control (SMS 2013) 8. Flexible Manipulator (SMS 2013)

v2

v1

1. Active Vibration Isolation : Background (1/3)1. Active Vibration Isolation : Background (1/3)

Commercial product by multiprobe

Fv

-H

FC

4-mount experimental rigKinetic energy

Frequency

Test rig Construction Performance

1. Active Vibration Isolation : Goal (2/3)1. Active Vibration Isolation : Goal (2/3)

• Task: Improve Stability and Performance

• Solution: EDA

• Method: Comparison between ED and EDA

Isolator

Primary shaker

Equipment and secondary shaker

Digital EDA filter using an x-PC Target

aaa

aaa j

jcjH

2

2)(

22

1. Active Vibration Isolation : Performance (3/3)1. Active Vibration Isolation : Performance (3/3)

ED

Loop Gain

EDA is more robust to undesirable effectsoutside the control bandwidth

EDA works as well as ED.

EDA

2. Transducer Damping : Background (1/3) 2. Transducer Damping : Background (1/3)

Inertial Actuator

Accelerometer

2. Transducer Damping : Construction (2/3)2. Transducer Damping : Construction (2/3)

Passive shunt circuit EDA

2. Transducer Damping : Performance (3/3) 2. Transducer Damping : Performance (3/3)

1. Exact mechanical analogy

2. Optimal absorber damping

Contributions

(mass ratio) 2a sa

Velocity Acceleration

3. Multi-Modal Control : Experimental Setup (1/3)

Plant description

Task : Suppress t

he first t

hree

modes

Digital EDA filter

3. Multi3. Multi--Modal Control : Single Mode Control Performance (2/3)Modal Control : Single Mode Control Performance (2/3)

100

101

102

103

−10

0

10

20

30

40

50

Frequency (Hz)

Acc

eler

atio

n (d

B)

100

101

102

103

−10

0

10

20

30

40

50

Frequency (Hz)

Acc

eler

atio

n (d

B)

100

101

102

103

−10

0

10

20

30

40

50

Frequency (Hz)

Acc

eler

atio

n (d

B)

1st Mode 2nd Mode 3rd Mode

Plant Response

Non-m

inimum

Phase

3. Multi3. Multi--Modal Control : Performance (3/3)Modal Control : Performance (3/3)

• Optimal and robust control methodology:• Optimal because the controller maximally flattens the mobility• Robust because it does not allow the control spillover any more than 2 dB

Contributions

4. Comparison between PPF and NPF : Plant (1/2)4. Comparison between PPF and NPF : Plant (1/2)

H(j) fp

PVDF Sensor

a pair of PZT actuators

Monitoring Sensor

PZT

PVDF Accelerometer

Hammer

Beam

Using PZT + PVDF

Plant Response

Digital EDA filter using an x-PC Target

4. Comparison between PPF and NPF : Performance (2/2)4. Comparison between PPF and NPF : Performance (2/2)

Contributions

1. NPF = eDVA

2. NPF is useful for multi-modal control

2

2 2

( )( )

2a

NPFa a a

k jH j

j

2

2 2( )

2a a

PPFa a a

kH j

j

Highpass Filter

Lowpass Filter

5. Robust Broadband Vibration Control : Setup (1/4)

Analog EDA filter

Plant : The same as for 3. the Modal Control using an Accelerometer

Task : Suppress all the vibrations in the frequency bandwidth of two decades from 10 Hz to 1 kHz

5. Robust Broadband Vibration Control : Analog Control Filter (2/4)

Analog EDA filter

Original plant

5. Robust Broadband Vibration Control : Performance (3/4)

Perturbed plant

Original plant Perturbed plant

Conclusions

It is possible to control broadband vibrations using a single EDA.This has been possible because it have been implemented electrically.

5. Robust Broadband Vibration Control : Robustness (4/4)

6. Non-Collocated Control : Setup (1/3)

Task : Suppress both in- and out-of-phase modes

Concept: negatively FB for in-phase modes and positively FB for out-of-phase modes

Plant mobility Controller Loop Gain

6. Non-Collocated Control : Concept (2/3)

Original plant Perturbed plant

6. Non-Collocated Control : Results (3/3)

7. Time Delay Control : Setup (1/3)

Task : Suppress the first two modes that are time delayed

7. Time Delay Control : Plant (2/3)

7. Time Delay Control : Results (3/3)

8. Vibration Control of a Flexible Manipulator (1/3)

8. Vibration Control of a Flexible Manipulator (2/3)

8. Vibration Control of a Flexible Manipulator (3/3)

1.

Vib

ratio

ns

2.

Dynam

ics

3.

Acoustic

s II. Po

tential

Ap

plicatio

ns

Sensors & Actuators

Smart panels for vehicles

Sound absorbers for vehiclesNoise barriers

Applications

Robot arms

Flexible manipulators

Hard disk drivesActive Noise ControlActive Noise Control

Occlusion ControlOcclusion Control

Summary

• EDA is an electrical realization of mechanical dynamic vibrationabsorber.

• It is stable and robust as it realizes a physically existing mechanism.

• It is rather a general method that has many applications: ex. multi-modal control, non-collocated control, time delay control.

• Prospect: It may survive for a long time as we can not think of any simpler and more effective method to control a mode than using the dynamic absortion mechanism.

• Hot Challenges: Adaptive EDA, Non-resonance control

References

• J L Fanson and T K Caughey, Positive position feedback control for large space structures, AIAA

Journal, 28, pp. 717-724, 1990

• S M Kim, S Pietrzko and M J Brennan, Active vibration isolation using an electrical damper or an electr

ical dynamic absorber, IEEE Transactions on Control Systems Technology, 16(2), pp. 245-254 (2008)

• S M Kim, S Wang and M J Brennan, Dynamic analysis and optimal design of a passive and an active

piezo-electrical dynamic vibration absorber, Journal of Sound and Vibration, 330, pp. 603-614 (2011)

• S M Kim, S Wang, and M J Brennan, Comparison of negative and positive position feedback control of

a flexible structure, Smart Materials and Structures, vol. 20, 015011 (10pp) (2011)

• S M Kim, S Wang, and M J Brennan, Optimal and robust modal control of a flexible structure using an

active dynamic vibration absorber, Smart Materials and Structures vol. 20, 045003 (11pp) (2011)

• S M Kim, S Wang, and M J Brennan, Broadband vibration control of a flexible structure using an electri

cal dynamic absorber, Smart Materials and Structures vol. 20, 075002 (9pp) (2011)

• S M Kim, J E Oh, A modal filter approach to non-collocated vibration control of structures, Journal of S

ound and Vibration 332 pp. 2207-2221 (2013)

• S M Kim, M J Brennan, Active vibration control using delayed resonant feedback, Smart Materials and

Structures 22, 095013 (7pp) (2013)

• S M Kim, H S Kim, K S Boo, M J Brennan, Demonstration of non-collocated vibration control of a flexib

le manipulator using electrical dynamic absorbers, Smart Materials and Structures 22, 127001 (4pp) (

2013)

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