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Sang-Myeong Kim
UNESP @ Ilha Solteira
2013
Vibration Modeling, Measurement and Control
ACTIVE VIBRATION CONTROL 3/3
III. Practical Considerations in Vibration
Control
ContentsContentsA FACT: “Although not many around the world have yet experienced it, control of sound & vibration is no more a theory but a reality.”
1. Actuators: piezoelectric, electromagnetic
2. Sensors: strain, acceleration
3. Controllers: analog, digital
4. Some tips:
A fundamental question in all control systems: “(+) or (-), that is the question.”
PrerequisitesPrerequisites
- Understanding the physics of the plant : Vibration
- System identification tools: Digital Signal Processing
- Implementation: Circuit theory, Control
At least, one should know about Vibration and Control.
I. Actuators I. Actuators -- PZT PZT
• PZT Strain Type
• Mechanism : similar to bimetal.
I. Z1T25×60R-S (C-83H) : 10 pieces
(TERMINAL: NEGATIVE) －
(TERMINAL: POSITIVE) +
PIEZO CERAMIC PLATE FOR NDT.
-DIMENSIONS : 60(L)×25(W)×1(T) mm 10PCS @W87,000
-ELECTRODE : FIRED SILVER,
-MATERIAL. : C-83H
I. Actuators I. Actuators -- PZTPZT
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csks
Cp
pe CjZ 1
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I. Actuators I. Actuators -- PZTPZT
• PZT Strain Type Actuation
I. Actuators I. Actuators -- PZTPZT
• PZT Inertial Type Actuation
I. Actuators I. Actuators -- EMEM
• Electromagnetic Type; Grounded Installation
LjRZe
Bl
jkcmjZ sssS
E
i
F v
i
E F vms
cs
ks
R, L,
i
v
Z
Z
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F
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F
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ms
csks
C
p
I. Actuators I. Actuators -- EMEM
• Electromagnetic Type; Mounted Installation
m
xmf
x
I. Actuator Comparison – Duality
Coupling
Coefficient
Electrical
Impedance
Mechanical Impedance
Dynamic Equation
PEEM
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v
Z
Z
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F
e
S
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1)( pe CjZ LjRZe
Bl
I. Actuators – Equivalent Circuits
F
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FA Cp
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F
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:1
FA
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ZF
A
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FA10
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ZF
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II. Sensors II. Sensors –– mounting type and grounding typemounting type and grounding type
• Accelerometer
piezo type for high temp.
ICP type
• Strain gauge
• PVDF (should be used with care)
• Encoder
• Proximate Sensor, camera
III. Digital Controller III. Digital Controller –– Introduction to the Introduction to the xPCxPC Target Target
xPC Target: a new standard for real time processing; a DSP prototyping machine;
running in Matlab Simulink environment;
ideal for realizing a real time filtering processing (i.e. a controller)
Construction: Host PC + Target PC (DAQ Board) + DAQ Frontend
III. Introduction to the III. Introduction to the xPCxPC Target Target
III. Introduction to the III. Introduction to the xPCxPC Target Target
1. Cabling as shown in the figure
2. type ‘xpcexplr’ on Matlab command window; set IP address of the target PC; make
a boot diskette. A C compiler (e.g., Visual Studio) must have been installed.
3. Boot the target PC with the boot diskette
4. copy & paste blocks in Simulink; Build block; Connect; Run
5. Measure the controller response
III. Test Run 1 with Fs = 9000 Hz III. Test Run 1 with Fs = 9000 Hz
III. Test Run 1 III. Test Run 1 --Results Results
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (s)Le
vel (
V)
inputoutputTime domain analysis
Frequency domain analysis for a random noise input
200 400 600 800 1000 1200 1400 1600 1800 2000-10
-8
-6
-4
-2
0
2
4
6
8
10
Frequency (Hz)
Am
plit
ud
e (d
B)
Frequency Response Function
200 400 600 800 1000 1200 1400 1600 1800 2000
-150
-100
-50
0
50
100
150
Frequency (Hz)
Ph
ase
(D
eg
ree
s)Frequency Response Function
ExperimentApproximation Delay=1.6*dt
• Ideally, 0 dB & 0
• For NI PCI-6024E with Fs= 9kHz:
Amp slightly decreasing with frequency
Anti-aliasing filter delay = 1.6 dt
III. Test Run 2 with NI PCI 6251 and Fs = 40 kHzIII. Test Run 2 with NI PCI 6251 and Fs = 40 kHz
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-10
-8
-6
-4
-2
0
2
4
6
8
10
Frequency (Hz)
Am
plit
ude
(dB
)
Frequency Response Function
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
-150
-100
-50
0
50
100
150
Frequency (Hz)
Ph
ase
(D
eg
ree
s)
Frequency Response Function
ExperimentApproximation Delay=1.6*dt
1. Proportional Gain
2. Bandpass Filter
100
101
102
103
104
-60
-50
-40
-30
-20
-10
0
Frequency (Hz)
Am
plit
ud
e (
dB
)
Frequency Response Function
exp.analog filter
100
101
102
103
104
-150
-100
-50
0
50
100
150
Frequency (Hz)
Ph
ase
(D
eg
ree
s)
Frequency Response Function
Experimentanalog filterwith Approximation Delay=1.6*dt
III. Comparison of some NI boardsIII. Comparison of some NI boards
930$ 1630$ 217$ 3100$ 1400$
Perform OK
III. III. SimulinkSimulink Block Block ConstrutionConstrution = Causal machines= Causal machines
• How to implement a digital filter for an analogue EDA filter
III. Analog EDA filters III. Analog EDA filters
III. Discrete equivalences of EDA filters III. Discrete equivalences of EDA filters
• Impulse invariant method
IV. Safety concerns and OthersIV. Safety concerns and Others
• (+) or (-), that is the question.
• Volume control for PZT
• Fuses for EM (high current type, high temp. type)
• Others: Coupling between electric and electronic devices
Summary
• xPC target is a cheap and convenient tool for real time DSP prototyping
• Impulse invariant method is accurate for digitally realizing EDAs.
References
[Impulse Invariant Method]
• A theoretical overview - "Ch. 7 Filter Design Techniques, Discrete Time Signal Processing by
Oppenheim and Schafer, 1989."
• A practical shortcut - "Table 13.1 A Table of Z transforms, p629, Modern Control Engineering by Ogata,
1970."
• Digital realization of an Electrical Dynamic Absorber (EDA) -" Appendix A.
S M Kim, J E Oh, A modal filter approach to non-collocated vibration control of structures, Journal of
Sound and Vibration 332 pp. 2207-2221(2013).“
[Dynamics of Piezoelectric Material]
• 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)
[Dynamics of Transducers]
• L E Kinsler et al., Chapter 14 Transduction, Fundamentals of Acoustics, 4th ed. (2000)
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