16.part1.activevibrationcontrolpiezo

7/28/2019 16.Part1.ActiveVibrationControlPiezo

1/71

116. Active Vibration Control Using Piezoelectric Materials - Classical Control Methods

Instructor: Dr. SongDept. of Mechanical Engineering

Topic 16. Active Vibration ControlUsing Piezoelectric Materials

Part 1. Classical Control Methods

Dr. G. Song, Associate Professor

University of Houston


2/71



OutlineOutline1. Introduction

2. Experimental Set Up3. Modal Analysis and Open Loop Testing

4. Vibration Suppression Methods

(a) PPF

(b) SRF

(c) Lead Compensator5. Conclusions


3/71



1. INTRODUCTION FRP Shapes(Beams and columns) have shown to provide efficient

and economical applications for Bridges, Piers, Retaining walls,

Airport facilities, Storage structures exposed to salt and chemicals.

FRP are thin walled structured manufactured by pultrusion processand although economical have

* relatively high deflection low elastic modulus resins.* considerable shear deformation.

* critical global and local stability.

* potential material failure.

External vibrations aggravates these limitations.


4/71



Review of control of civil structures using smart materials Huston R D et al(1994) developed and tested numerous fiber-

optic and conventional sensor techniques and designs for the

implementation in smart civil structures .

Krumme R et al(1995) studied passive control of the dynamicresponse of civil structures utilizing shape-memory alloy (SMA)

damping techniques.

Aizawa S et al(1998) used piezoelectric stack actuators forresponse control of a four story structural frame.

Very little Use of Piezoelectric patch actuators for vibration control ofcivil structures has been reported.


5/71



Review of control using Piezo patches for SRF and PPF control Positive position feedback (PPF) method was applied by Goh and

Caughey (1985), Fanson and Caughey(1990), Agrawal and Bang(1994), Song et al(2000) for control of flexible beams.

Strain rate feedback (SRF) for bonded and embedded piezoceramicsensor and actuator was considered by Hanagud, Won and Obal(1988).

Hagood and Anderson of MIT studied the possibility of using a singlepiezo element for actuator and sensor.

Song, Schmidt and Agarwal studied the vibration suppression offlexible structure using modular control patch.

6


6/71



Piezoelectricity Piezo Effect.

Conversion between mechanical and electrical energy

- materials that respond to stress by producing a voltage

- materials that respond to a change in electric field by changing shapes.

Discovered in 1880 by Pierre and Jacques Curie.

Electrically neutral solid contains polar bonds and noncentrosymmetric

units - typically dipoles cancel out in a solid, but not necessarily when

the solid is distorted

7


7/71



Piezoelectric Action

Resulting Strain (S)

+

-

Electrodes

Resulting Strain (S)

-+

Polling Axis

8


8/71



Piezoelectric material as an actuator

-

+-+

No Voltage

Direction

of Polarity

Applied Voltage

opposite polarity

Applied Voltage

same as polarity

Direction

of PolarityDirection

of Polarity

9


9/71



Piezoelectric material as a sensor

-+ - +No voltage generated

Direction

of Polarity

Voltage generated

same as polarityVoltage generated

opposite polarity

Direction

of PolarityDirection

of Polarity

FF

1016 A i i i C i i i i C i C


10/71



2. Experimental Set Up

I-Beam CompositeSignal Generator, Oscilloscope and Power Amplifier

Fixture to Hold

the beam PC with Real

Time Controls

1116 A ti Vib ti C t l U i Pi l t i M t i l Cl i l C t l M th d


11/71



EXPERIMENTAL SET UP

BLOCK DIAGRAM

Power

Amplifier

Oscilloscope

dSPACE data Acq.

System

D/A

Converter

PC with

MATLAB

Piezoelectric

actuator

Composite

I-beamPZT

Sensor

A/D

Converter



12/71



EXPERIMENT CONNECTIONSCANTILEVER END

FIXTURE

SIGNAL

GENERATOR ANDOSCILLOSCOPE

POWER AMPLIFIERS

ADA

MATLAB &

dSPACE



13/71



ACTUATORS AND SENSORS CONNECTIONS

Actuators

Sensors

Strong

Weak


14/71

1516 Active Vibration Control Using Piezoelectric Materials Classical Control Methods


15/71



Simulink Model for the Modetest of the I-beam

For Multi-mode excitation

Free End



16/71



MODAL TESTING PROCEDURE

Ensure beam is tightly clamped on the fixture.

Manual excitation at the free end in strong, weak and twistingdirections.

Manual excitation at the center of the beam in all three directions to

generate multimode results captured by dSPACE and analyzed using

MATLAB

Natural Modes evaluated and energy levels are compared.

Strong

Weak

45 DegreesMultimode

3. Modal Analysis and Open Loop Testing



17/71



RESULTS OF MODE TEST

Amplitude Vs Time Response for Strong and Weak Sides

0 5 1 0 1 5 2 0 2 5 3 0-1

-0 .5

0

0 .5

1t im e r e s p o n s e

t im e (s e c s ) ; M a n u a l E x c i t a t io n i n S t ro n g d i re c t i o n

amplitude(Volts

)

s t r o n g

0 5 1 0 1 5 2 0 2 5 3 0-0 .1

-0 .05

0

0 . 0 5

0 .1

0 . 1 5

t im e ( s e c s ) ; M a n u a l E x c i ta t io n in W e a k d i re c t i o n

amplitu

de(Volts)

w e a k

1816 Active Vibration Control Using Piezoelectric Materials - Classical Control Methods


18/71



Power Spectral Density Plot for Strong direction




19/71



Power Spectral Density Plot for Weak direction

0 1 0 20 30 40 50 6 0 70 80 90 10 0-100

-9 0

-8 0

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0

F re q u e n c y

PowerSpectrumM

agnitude(dB)

P o w e r S p e c t ru m : W e a k




20/71

16. Active Vibration Control Using Piezoelectric Materials Classical Control Methods



Experimental Modal Frequencies

MODE STRONG DIRECTION (Hz) WEAK DIRECTION (Hz)

FIRST 7.62 4.5

SECOND 45.5 13.28

THIRD 80.86 28.47

FOURTH 45.5



21/71



Drop In Energy Levels Strong and Weak Directions

0 5 10 15 20 25 30 35 40 45 50-80

-70

-60

-50

-40

-30

-20Power spectral density Comparision plot for 1-2 and 8-10th second: Weak

Frequency (Hz)

Ener

gylevelinDecibels

0-2 second

8-10 second

0 10 20 30 40 50 60 70 80 90 100

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5Power spectral density Comparision plot for 0-2 and 10-12th second: Strong

Frequency (Hz)

0-2 second

10-12 second




22/71



Comparative Energy Drop in 20 seconds in Strong and

Weak directions

Serial

No

Frequency

(Hz)

Energy

Level

(dB)

Energy Drop in

20 Seconds

Strongdirection (dB)

Energy Drop in

20 Seconds

Weak direction(dB)

Remarks

1 4.5 -49.5 14.00 14Dominant in Weak

direction

2 7.62 -7.68 15.25 20.13Most dominantpeak in Strong

direction

3 13.28 -58.5 15.00 6.75Dominant at 45

Degrees

Torsional Mode

4 28.47 -63 23.50 8.00Dominant in Weak

direction

5 45.5 -34.62 34.50 12.40Dominant in both

directions

6 80.86 -46.20 26.40 6.25Dominant in strong

direction



23/71



4. VIBRATION SUPRESSIONMETHODS

PPF CONTROL SRF CONTROL

LEAD COMPENSATOR- ROOT LOCUS APPROACH

- BODE PLOTS APPROACH



24/71

g


Block Diagram of PPF Control

Compensator

+ 2

+2 = 0

+ 2cc2

+c2= 0

G2 c2

Structure+

+



25/71

g


PPF Phase Angle Plot

PhaseAngle

2

Active Flexibility

Active Damping

Active stiffness

c =



26/71

g


PPF CONTROL OBJECTIVE Simulation and Modeling

- Using Sinusoidal Input- Using Impulse Input

Free Vibration of the Beam-Reference Test Controlled Response

- Effect of the Damping Ratio 0.5 0.1

- Changes in the Targeted Frequencies 6 9 Hz

Result Analysis



27/71

g


Simulation and Modeling using sinusoidal

responsePlant

Compensator

Plant

Compensator



28/71

g


Simulated Time Response comparison

using PPF Control



29/71


Simulation and Modeling for an impulse

response: PPF Control



30/71


Bode Plot of the Closed Loop System for the

PPF Simulation



31/71


Root Locus Plot of the Open Loop System for

the PPF Simulation

New Pole Locations



32/71


PPF Real Time Control of Composite I-Beam



33/71


Summary of PPF control data and analysis (Experimental)

P PF C O N T R O L D A T A A N A L Y SIS D A T A R E M A R K S

Sl

N o .

T E S T

N O P P F G A INF R E Q

( H z )

Z E T A

( )

E N E R G Y

D R O P d B5 - 1 0 s e c

S t r o n g

E N E R G Y

D R O P d B1 0 - 1 5 s e c

S t r o n g

Z E T AU N -

C O N T R O L

Z E T A

C O N T

P e r c e n t a g e

I n c r e a se i nZ e t a fo r c o n t c a s e

1 2 6 - 0 . 5 6 0 . 5 2 4 . 4 0 . 0 0 3 4 0 . 0 0 4 8 4 1 . 1 8

2 2 7 - 1 6 0 . 5 3 . 9 6 9 . 5 0 . 0 0 3 4 0 . 0 0 6 4 8 8 . 2 4

3 2 8 - 1 . 5 6 0 . 5 5 . 9 1 5 . 0 8 0 . 0 0 3 4 0 . 0 0 8 4 1 4 7 . 0 6

4 2 9 - 2 6 0 . 5 7 . 6 3 2 0 . 2 6 6 0 . 0 0 3 4 0 . 0 1 0 1 1 9 7 . 0 6

5 3 0 - 2 . 5 6 0 . 5 9 . 1 7 2 5 . 4 5 0 .0 0 3 4 0 . 0 1 2 0 2 5 2 . 9 4

6 3 1 - 3 6 0 . 5 1 0 . 4 4 3 0 . 2 1 0 . 0 0 3 4 0 . 0 1 3 4 2 9 4 . 1 2

7 3 2 - 3 . 5 6 0 . 5 1 1 . 4 6 3 4 . 6 0 . 0 0 3 4 0 . 0 1 3 6 3 0 0 . 0 08 3 3 - 5 6 0 . 5 1 3 . 5 5 3 9 . 9 1 0 . 0 0 3 4 0 . 0 1 4 4 3 2 3 . 5 3

U n s t a b l e a tP P F g a in = - 5 . 5

9 3 4 0 6 0 . 5 0 . 0 0 3 4 R e f t e s t f o r t e s t s 2 6 - 3 3

1 0 3 5 0 6 .2 0 . 5 0 . 0 0 3 4 R e f t e s t f o r t e s t s 3 6 - 3 9

1 1 3 6 - 1 6 .2 0 . 5 4 . 2 9 1 0 . 6 8 0 .0 0 3 4 0 . 0 0 6 9 1 0 2 . 9 4

1 2 3 7 - 2 6 .2 0 . 5 8 . 3 1 2 2 . 8 7 0 .0 0 3 4 0 . 0 1 1 4 2 3 5 . 2 9

1 3 3 8 - 3 6 .2 0 . 5 1 1 . 3 7 3 4 . 4 3 0 . 0 0 3 4 0 . 0 1 4 2 3 1 7 . 6 5

1 4 3 9 - 4 6 .2 0 . 5 1 3 . 1 5 4 1 . 3 7 0 . 0 0 3 4 0 . 0 1 4 5 3 2 6 . 4 7

U n s t a b l e a tP P F ga in = - 5


1 6 4 1 - 1 6 .4 0 . 5 4 . 5 6 1 1 . 4 5 0 .0 0 3 4 0 . 0 0 7 2 1 1 1 . 7 6

1 7 4 2 - 2 6 .4 0 . 5 9 . 1 8 2 6 . 3 2 0 .0 0 3 4 0 . 0 1 2 2 2 5 8 . 8 2

1 8 4 3 - 3 6 .4 0 . 5 1 2 . 2 7 3 7 . 3 8 0 . 0 0 3 4 0 . 0 1 4 4 3 2 3 . 5 3

1 9 4 4 - 4 6 .4 0 . 5 1 3 . 9 4 4 . 4 6 0 .0 0 3 4 0 . 0 1 6 4 3 8 2 . 3 5

2 0 4 5 - 4 . 5 6 .4 0 . 5 1 4 . 8 2 5 0 . 9 6 0 . 0 0 3 4 0 . 0 1 3 8 3 0 5 . 8 8

U n s t a b l e a t

P P F g a in = - 5


2 2 4 7 - 1 6 .6 0 . 5 5 . 1 3 1 3 . 1 9 0 .0 0 3 4 0 . 0 0 7 7 1 2 6 . 4 7

2 3 4 8 - 2 6 .6 0 . 5 1 0 . 1 8 3 0 . 7 0 . 0 0 3 4 0 . 0 1 3 1 2 8 5 . 2 9

2 4 4 9 - 3 6 .6 0 . 5 1 3 . 0 1 4 2 . 3 8 0 . 0 0 3 4 0 . 0 1 4 8 3 3 5 . 2 9

2 5 5 0 - 4 6 .6 0 . 5 1 4 . 7 1 4 9 . 9 0 . 0 0 3 4 0 . 0 1 6 5 3 8 5 . 2 9

U n s t a b l e a t

P P F g a in = -

4 .5


2 7 5 2 - 1 6 .8 0 . 5 6 . 0 8 1 5 . 8 8 0 .0 0 3 2 0 . 0 0 8 3 1 5 9 . 3 8

2 8 5 3 - 2 6 .8 0 . 5 1 1 . 2 8 3 5 . 2 0 . 0 0 3 2 0 . 0 1 4 3 3 4 6 . 8 8

2 9 5 4 - 3 6 .8 0 . 5 1 4 . 0 5 4 6 . 2 3 0 . 0 0 3 2 0 . 0 1 7 0 4 3 1 . 2 5

3 0 5 5 - 3 . 5 6 .8 0 . 5 1 4 . 9 2 5 2 . 2 6 0 . 0 0 3 2 0 . 0 1 9 8 5 1 8 . 7 5

U n s t a b l e a t

P P F ga in = - 4

Contd



34/71



Contd

P P F CO N T RO L D A T A ANALYSIS DAT A

Sl

N o.

TEST

N O PP F

GAIN

FREQ

Z ET

A

ENERGY

DROP dB

5-10 secStrong

ENERGY

DROP dB

10-15 secStrong

Z E T A

U N -

CO N T RO L

Z E T A

CO N T

Pe rc e n ta geIncrease in

Zeta for

control

case

RE MA RK S

31 56 0 7 0.5 0.0032Ref test for tests 57-

60

32 57 -1 7 0.5 6.66 17.57 0.0032 0.0090 181.25

33 58 -2 7 0.5 12.04 39.87 0.0032 0.0148 362.50

34 59 -3 7 0.5 14.64 57.28 0.0032 0.0149 365.63

35 60 -3.5 7 0.5 15.69 54.89 0.0032 0.0150 368.75Unstable at PPF

gain= -4

36 61 0 7.2 0.5 0.0032

Ref test for tests 62-

64

37 62 -1 7.2 0.5 7.02 18.56 0.0032 0.0091 184.38

38 63 -2 7.2 0.5 12.87 43.92 0.0032 0.0157 390.63

39 64 -3 7.2 0.5 15.24 55.69 0.0032 0.0262 718.75Unstable at PPF

gain= -3.5

40 65 0 7.4 0.5 0.0032Ref test for tests 65-

69

41 66 -1 7.4 0.5 7.79 21.27 0.0032 0.0099 209.38

42 67 -2 7.4 0.5 13.41 45.51 0.0032 0.0184 475.00

43 68 -2.5 7.4 0.5 14.72 52.96 0.0032 0.0246 668.75

44 69 -3 7.4 0.5 15.78 57.06 0.0032 0.0309 865.63

Unstable at PPF

gain= -3.545 3 0 7.62 0.5 0.0030 Ref test for tests 4-8

46 4 -0.5 7.62 0.5 4.09 9.85 0.0030 0.0062 106.67

47 5 -1 7.62 0.5 8.88 24.64 0.0030 0.0112 273.33

48 6 -1.5 7.62 0.5 12.36 41.23 0.0030 0.0197 556.67

49 7 -2 7.62 0.5 14.37 45.22 0.0030 0.0207 590.00

50 8 -2.5 7.62 0.5 15.41 51.07 0.0030 0.0383 1176.67Unstable at PPF

gain= -3


13

52 10 -0.5 7.62 0.4 5.03 12.76 0.0032 0.0073 128.13

53 11 -1 7.62 0.4 10.65 32.87 0.0032 0.0160 400.00

54 12 -1.5 7.62 0.4 13.8 47.06 0.0032 0.0250 681.25

55 13 -2 7.62 0.4 15.16 54.91 0.0032 0.0315 884.38Unstable at PPF

gain= -2.5


17

57 15 -0.5 7.62 0.3 7.22 18.89 0.0028 0.0088 214.29

58 16 -1 7.62 0.3 13.07 45.21 0.0028 0.0142 407.14

59 17 -1.5 7.62 0.3 15.2 57.3 0.0028 0.0298 964.29Unstable at PPF

gain= -2

60 18 0 7.62 0.2 0.0027


20



35/71



PPF CONTROL DATA ANALYSIS DATA

Sl No

.

TESTNO

PP FGAIN

FR -EQ

Hz ZETA

ENERGYDROP dB

5-10 sec

Strong

ENERGYDROP dB

10-15 sec

Strong

ZETAUNCONT

ZETACON-

TROL

Percentage

IncreaseControl

case

REMARKS

61 19 -0.5 7.62 0.2 11.5 36.62 0.0027 0.0147 444.44

62 20 -1 7.62 0.2 15.31 55.31 0.0027 0.0322 1092.59

Unstable at

PPF gain= -1.5

6 3 2 1 0 7 .6 2 0 .1 0 .0 02 2


25

64 22 -0.5 7.62 0.1 9.71 32.08 0.0022 0.0159 622.73

65 23 -0.3 7.62 0.1 12.78 57.29 0.0022 0.0251 1040.91

66 24 -0.2 7.62 0.1 8.73 23.68 0.0022 0.0099 350.00

67 25 -0.5 7.62 0.1 16.11 38.67 0.0022 0.0163 640.91 With filter added

68 70 0 7.8 0.5 0.0035

Ref test for tests 71-74

69 71 -1 7.8 0.5 8.66 24.9 0.0035 0.0114 225.71

70 72 -1.5 7.8 0.5 12.12 42.54 0.0035 0.0186 431.43

71 73 -2 7.8 0.5 13.88 57.26 0.0035 0.0256 631.43

72 74 -2.5 7 .8 0.5 14.88 57.06 0.0035 0.0386 1002.86

Unstable atPPF gain= -3

73 75 0 8 0.5 0.0032


78

74 76 -1 8 0.5 9.14 26.57 0.0032 0.0117 265.63

75 77 -1.5 8 0.5 12.79 50.49 0.0032 0.0177 453.13

76 78 -2 8 0.5 14.32 54.26 0.0032 0.0239 646.88

Unstable atPPF gain= -2.5

77 79 0 8.2 0.5 0.0032


82

78 80 -1 8.2 0.5 9.18 28.67 0.0032 0.0135 321.88

79 81 -1.5 8.2 0.5 12.71 44.52 0.0032 0.0211 559.38

80 82 -2 8.2 0.5 14.41 44.52 0.0032 0.0268 737.50

Unstable at

PPF gain= -2.5

81 83 0 8.4 0.5 0.0032

Ref test for tests 84-86

82 84 -1 8.4 0.5 9.14 31.21 0.0032 0.0123 284.38

83 85 -1.5 8.4 0.5 12.36 54.93 0.0032 0.0211 559.38

84 86 -2 8.4 0.5 14.11 55.33 0.0032 0.0279 771.88

Unstable at

PPF gain= -2.5

85 87 0 8.6 0.5 0.0032


91

86 88 -0.5 8.6 0.5 4.29 11.26 0.0032 0.0067 109.38

87 89 -1 8.6 0.5 8.8 32.93 0.0032 0.0142 343.75

88 90 -1.5 8.6 0.5 11.66 52.03 0.0032 0.0215 571.88

89 91 -2 8.6 0.5 13.2 57.41 0.0032 0.0348 987.50

Unstable atPPF gain= -2.5

90 92 0 8.8 0.5 0.0032


95

91 93 -0.5 8.8 0.5 4.2 11.53 0.003 2 0.0067 109.38

92 94 -1 8.8 0.5 8.31 34.92 0.0032 0.0150 368.75

93 95 -1.5 8.8 0.5 10.87 59.09 0.0032 0.0319 896.88

Unstable at

PPF gain= -2



36/71


Effect of Gain Change, PPF Damping Ratio = 0.5

PPF CONTROL DATA ANALYSIS DATA

Sl No. TEST N

PPF GAIN

FREQ

ZETA

ENERGY

DROP dB5-10 sec

Strong

ENERG

DROP dB10-15 sec

Strong

ZETA

UN-CONT

ZETA

CONT

Increase

inZeta for

control

case %

REM-ARKS

45 3 0 7.62 0.5 0.0030 Ref testfor tests

4-8

46 4 -0.5 7.62 0.5 4.09 9.85 0.0030 0.0062 106.67

47 5 -1 7.62 0.5 8.88 24.64 0.0030 0.0112 273.33

48 6 -1.5 7.62 0.5 12.36 41.23 0.0030 0.0197 556.6749 7 -2 7.62 0.5 14.37 45.22 0.0030 0.0207 590.00

50 8 -2.5 7.62 0.5 15.41 51.07 0.0030 0.0383 1176.67Unstable

at PPF

gain= -3



37/71



PPF CONTROL DATA ANALYSIS DATA REMARKS

TEST N PPF GAI

FREQ

ZETA

ENERGDROP d

5-10 secStrong

ENERGYDROP dB

10-15 secStrong

ZETAUNCON

ZETACONT

PercentageIncrease in

Zeta forCONT

51 9 0 7.62 0.4 0.0032

Ref test for tests 10

13

52 10 -0.5 7.62 0.4 5.03 12.76 0.0032 0.0073 128.1353 11 -1 7.62 0.4 10.65 32.87 0.0032 0.0160 400.00

54 12 -1.5 7.62 0.4 13.8 47.06 0.0032 0.0250 681.25

55 13 -2 7.62 0.4 15.16 54.91 0.0032 0.0315 884.38

Unstable at PPFgain= -2.5



38/71



PPF CONTROL DATA ANALYSIS DATA REMARKSSl No. TEST NO PPF GAINFREQ ZET ENERGY

DROP dB

5-10 secStrong

ENERGY

DROP dB

10-15 secStrong

ZETA

UNCON

T

ZETA

CONT

Percentage

Increase in

Zeta forCONT case

63 21 0 7.62 0.1 0.0022Ref test fortests 22-25

64 22 -0.5 7.62 0.1 9.71 32.08 0.0022 0.0159 622.73

65 23 -0.3 7.62 0.1 12.78 57.29 0.0022 0.0251 1040.91

66 24 -0.2 7.62 0.1 8.73 23.68 0.0022 0.0099 350.00

67 25 -0.5 7.62 0.1 16.11 38.67 0.0022 0.0163 640.91With filter

added



39/71


Effect of Gain Change , frequency varied from 6.2 to 6.8 HzPPF CONTROL DAT A ANALYSIS DAT A REMA RKS

Sl No. TEST NO PPF GAIN

FREQ

ZETA

ENERGY

DROP dB

5-10 sec

Strong

ENERGY

DROP dB

10-15 sec

Strong

ZETA

U N CO N T

ZETA

CONT

Percentage

Increase in

Zeta for

CONT case

10 35 0 6.2 0.5 0.0034

Ref test for

tests 36-39

11 36 -1 6.2 0.5 4.29 10.68 0.0034 0.0069 102.94

12 37 -2 6.2 0.5 8.31 22.87 0.0034 0.0114 235.29

13 38 -3 6.2 0.5 11.37 34.43 0.0034 0.0142 317.65

14 39 -4 6.2 0.5 13.15 41.37 0.0034 0.0145 326.47Unstable at

PP F gain= -5

15 40 0 6.4 0.5 0.0034Ref test fortests41-45

16 41 -1 6.4 0.5 4.56 11.45 0.0034 0.0072 111.76

17 42 -2 6.4 0.5 9.18 26.32 0.0034 0.0122 258.82

18 43 -3 6.4 0.5 12.27 37.38 0.0034 0.0144 323.53

19 44 -4 6.4 0.5 13.9 44.46 0.0034 0.0164 382.35

20 45 -4.5 6.4 0.5 1 4.82 50.96 0.0034 0.0138 305.88

Unstable at

PP F gain= -5

21 46 0 6.6 0.5 0.0034

Ref test for

tests 47-50

22 47 -1 6.6 0.5 5.13 13.19 0.0034 0.0077 126.47

23 48 -2 6.6 0.5 10.18 30.7 0.0034 0.0131 285.29

24 49 -3 6.6 0.5 13.01 42.38 0.0034 0.0148 335.29

25 50 -4 6.6 0.5 14.71 49.9 0.0034 0.0165 385.29

Unstable at

PPFgain= -4.5

26 51 0 6.8 0.5 0.0032

Ref test for

tests 52-55

27 52 -1 6.8 0.5 6.08 15.88 0.0032 0.0083 159.38

28 53 -2 6.8 0.5 11.28 35.2 0.0032 0.0143 346.88

29 54 -3 6.8 0.5 14.05 46.23 0.0032 0.0170 431.25

30 55 -3.5 6.8 0.5 1 4.92 52.26 0.0032 0.0198 518.75Unstable at

PP F gain= -4



40/71


Time Response for PPF gain = 2.5 & damping

ratio=0.5



41/71


Drop in Energy Level

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0- 1 0 0

-8 0

-6 0

-4 0

-2 0

0

2 0

4 0P o w e r s p e c t r a l d e n s i ty C o m p a r is i o n p l o t (1 0 - 1 5 s e c ) f o r w i t h a n d w / o c o n t r o l: S t ro n g

F r e q u en c y (H z )

EnergylevelinDecibels

w i t h c o n t r o l

w i t h o u t c o n t ro l

Drop of 51

dB



42/71


Inferences With lower values of damping ratio, the system becomes unstable at lower

gains. Higher values of damping ratio (0.5) yields a better control of damping ratio

of 1176.67 percentage.

At higher values of damping ratio we get a broader range for control

operation. Lower frequencies than the modal frequency produced lower percentage

increase in damping ratio for controlled case as compared to the higherfrequencies.

The highest increase in percentage of controlled damping ratio is effective for

the modal frequency (1176.67).

At lower frequencies the drop in energy level is lower as compared to highervalues and varies from 2 dB to 62.35 dB.



43/71


SRF CONTROL OBJECTIVE Simulation and Modeling

- Using Sinusoidal Input- Using Impulse Input

Free Vibration of the Beam-Reference Test

Controlled Response

- Effect of the Damping Ratio

- Changes in the Targeted Frequencies

- Effect of SRF Gain Value

Result Analysis



44/71


BLOCK DIAGRAM OF SRF CONTROL

+

0)()(2)( 2 =++ ttt

tc

0)()(2)(

2

=++ ttt ccc

2G

Structure

Compensator

-



45/71


SRF Phase Angle Plot

= c

2/

Active Negative DampingActive Damping

PhaseAngle

-/2

+/2

Active Stiffness

0



46/71


Simulation and Modeling using sinusoidal

response : SRFPlant

Compensator

Compensator

Plant



47/71


Simulated Time Response comparison

using SRF Control



48/71


Simulation and Modeling for an impulse

response: SRF Control



49/71


Bode Plot of the Closed Loop System for

the SRF Simulation



50/71


Root Locus Plot of the Open Loop System

for the SRF Simulation

New pole Locations



51/71


Real Time Control Using SRF



52/71


Target Frequencies 8, 9 ,10 &11 Hz andControlled damping ratio evaluated (Experiment)SR F C O N T R O L D A T A A N A LYSIS D A T A

S

N o.

TEST

N OSR F G A I N F R E Q Z E T A

E N E R G Y

D R O P ' D B '5-10 sec

E N E RG Y

D R O P ' D B '10-15 sec

Z E T A

U N C O N T

Z E T A

C O N T

Percentage

Increase in

Zeta for cont case

R E M A R K S

1 30 0 8 0 .5 2 4 .4 0 .0031 Ref tes t for tes ts 31-35

2 31 -0 .01 8 0 .5 3 .96 9 .5 0 .0031 0 .0101 165 .79

3 32 -0 .02 8 0 .5 5 .9 15 .08 0 .0031 0 .0110 189 .47

4 33 -0 .03 8 0 .5 7 .63 20 .266 0 .0031 0 .0116 205 .26

5 34 -0 .04 8 0 .5 9 .17 25 .45 0 .0031 0 .0119 213 .16

6 35 -0 .05 8 0 .5 10 .44 30 .21 0 .0031 0 .0121 218 .42

7 36 0 9 0 .5 11.46 24.6 0 .0031 Ref tes t for tes ts 37-41

8 37 -0 .01 9 0 .5 11 .55 25 .76 0 .0031 0 .0142 330 .30

9 38 -0 .02 9 0 .5 15 .10 29 .50 0 .0031 0 .0149 351 .52

10 39 -0 .03 9 0 .5 17 .50 30 .30 0 .0031 0 .0153 363 .64

11 40 -0 .04 9 0 .5 20 .26 30 .16 0 .0031 0 .0157 375 .76

12 41 -0 .05 9 0 .5 21 .56 29 .93 0 .0031 0 .0158 378 .79

13 42 0 10 0.5 11.37 34.43 0.0031 Ref tes t for tes ts 43-45

14 43 -0 .01 10 0 .5 11 .16 27 .84 0 .0031 0 .0144 362 .16

15 44 -0 .02 10 0 .5 15 .00 34 .50 0 .0031 0 .0174 461 .29

16 45 -0 .03 10 0 .5 17 .38 33 .26 0 .0031 0 .0213 587 .10

17 46 0 11 0.5 9 .18 26.32 0.0031 Ref tes t for tes ts 47-48

18 47 -0 .01 11 0 .5 12 .27 37 .38 0 .0031 0 .0215 465 .79

19 48 -0 .02 11 0 .5 13 .9 44 .46 0 .0031 0 .0204 436 .84



53/71


Time Response Curve for SRF Control: Strong( Experimental )



54/71


Drop in Energy Levels SRF: Strong( Experimental )

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0-8 0

-6 0

-4 0

-2 0

0

2 0

4 0P o w e r s p e c t ra l d e n s i t y C o m p a r i s i o n p lo t (1 0 - 1 5 s e c ) fo r w it h a n d w / o c o n t ro l : S t r o n g

F r e qu e n c y (H z )

EnergylevelinDecibels


w i t h o u t c o n t r o l



55/71


PHASE LEAD COMPENSATOR

Gc(S) GP(S)C(S)(S)



56/71


Lead Compensator for the I-beam

(Root Locus Approach)

Lead compensator designed for first dominant mode :7.62 Hz.

Transfer function =

Block Diagram of Lead Compensator

22562831.0

2382 ++ ss

)(

)(

ps

zsK

c ++

PlantLow Pass

Filter

Com ensator

Continued..



57/71


Lead Compensator for the I-beam

(Root Locus Approach)

- 4 . 4 + 5 4 . 8 2 i

- 9 5 . 6 1 - 3 1 . 6 9 0 , 0

- 4 . 4 + 5 4 . 8 2 i

- 9 5 . 6 1 - 3 1 . 6 9 0 , 0

location of pole and zero for lead compensatorPole Zero

Compensator = 6.33

+

+

61.95

69.31

s

s

Transfer function =005157.2228389.95

004778.4150823 esss

es

++++



58/71


Root Locus Plot of lead compensator

(Simulation)Root Locus

Real Axis

ImagAxis

-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10

-400

-300

-200

-100

0

100

200

300

400

400

350

300

250

200

150

100

50

350

300

250

200

150

100

50

0.6

0.36

0.230.17 0.115 0.08 0.05 0.025

0.6

0.36

0.230.17 0.115 0.08 0.05 0.025 Broken: Uncompensated

Solid: Compensated

Dominant new Poles



59/71


Bode Plot comparison between Plant and System(Root Locus Approach- simulation )



60/71


Impulse response of the Lead Compensator(Simulation)



61/71


Block Diagram of lead compensator

based on Root Locus Approach



62/71


PSD Plot Comparison: Strong

(Root Locus Approach-Experimental)

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0-8 0

-7 0

-6 0

-5 0

-4 0

-3 0

-2 0

-1 0

0

1 0

2 0P o w e r s p e c t ra l d e n s i t y C o m p a r is i o n p l o t (1 0 - 1 5 s e c ) fo r w i th a n d w / o c o n t ro l : S t ro n g

F r e q u e n c y ( H z )

Energyleve

linDecibels


w i t h o u t c o n t ro l



63/71


Time Response Curve for Strong direction

(Root Locus Approach-Experimental)



64/71


Lead Compensator Gain Comparison(Root Locus Approach)

ANALYSIS DATA

Test

No

Lead

Compen-

sator

Gain

Energy

drop'dB'

5-10 sec

Strong

Energy

Drop'dB'

10-15 sec

Strong

dB' drop

10-15 sec

overall

Zeta

uncont

zeta cont

intial

response

Zeta

cont

%

increase

initial

%

Increase

Zeta for

controlled

1 0 2.00 4.40 0.0030 Reference Tes t

2 4 3.96 9.50 18.95 0.0030 0.0073 0.0068 143.3333 126.67

3 6 5.90 15.08 23.45 0.0030 0.0079 0.0073 163.3333 143.33

4 8 7.63 20.27 25.55 0.0030 0.0081 0.0076 170.0000 153.33

5 10 9.17 25.45 26.70 0.0030 0.0082 0.0078 173.3333 160.00

6 12 10.44 30.21 27.80 0.0030 0.0083 0.0081 176.6667 170.00

7 14 11.46 24.60 28.21 0.0030 0.0082 0.0081 173.3333 170.00

8 16 13.55 39.91 27.68 0.0030 0.0081 0.0082 170.0000 173.33



65/71


Lead Compensator for the I-Beam(Bode Plot Approach)



66/71


Bode Plot comparison between Plant and System(Bode Plot Approach-simulated)


Ti R C i St


67/71


Time Response Comparisons: Strong

(Experimental)



68/71


PSD Plot Comparisons: Strong

0 10 20 30 40 50 60 70 80 90 100-120

-100

-80

-60

-40

-20

0

20Power spectral density Comparision plot (10-15sec) for with and w/o control: Strong

Frequency (Hz)

Energylevel

inDecibels

with control

without control



69/71


Movie



70/71


Frequency Response Comparison of the four Compensators

100

101

102

103

-120

-100

-80

-60

-40

-20

0

20

40

Magnitude(dB)

Without Control

With Lead Control

With Pole Placement Control

With PPF Control

With SRF Control

Bode Diagram

Frequency (rad/sec)



71/71

5. CONCLUSION

Experimental results have shown greatpotential for active control.

PPF, SRF and Lead Compensatormethods were very successful

1176% increase in damping in PPF

control

16.part1.activevibrationcontrolpiezo

Documents