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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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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

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I. Actuators I. Actuators -- EMEM

• Electromagnetic Type; Mounted Installation

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I. Actuator Comparison – Duality

Coupling

Coefficient

Electrical

Impedance

Mechanical Impedance

Dynamic Equation

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I. Actuators – Equivalent Circuits

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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

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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

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Frequency (Hz)

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plit

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Frequency Response Function

200 400 600 800 1000 1200 1400 1600 1800 2000

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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

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Frequency (Hz)

Am

plit

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(dB

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Frequency Response Function

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

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0

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100

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Frequency (Hz)

Ph

ase

(D

eg

ree

s)

Frequency Response Function

ExperimentApproximation Delay=1.6*dt

1. Proportional Gain

2. Bandpass Filter

100

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Frequency (Hz)

Am

plit

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dB

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Frequency Response Function

exp.analog filter

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Frequency (Hz)

Ph

ase

(D

eg

ree

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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)