View
3
Download
0
Category
Preview:
Citation preview
-
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)
Those recommendable to read in blue.
Recommended