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CHAPTER - 6

EXPERIMENTATION FORACTIVE VIBRATION CONTROL

6.1 INTRODUCTION

The important issues in vibration control applications are

modeling the smart structure with in-built sensing and actuation

capabilities and the implementation of active control schemes in real

time experiments. The piezoelectric materials are strain rate sensors

and produce output charges proportional to displacements at

locations where they are surface bonded. In this chapter, experiments

are conducted to study the effectiveness of Linear Quadratic Gaussian

(LQG) control in suppressing the vibration of shell system with MFC

actuators. A CFRP shell structure shown in the Fig. 6.1 with

collocated piezoelectric actuators and sensors is considered to assess

the control performance.

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Fig. 6.1 MFC actuators location on the CFRP shell

The vibration control model is developed in chapter 5 for the

laminated composite cylindrical shell with LQG control system. To

verify the efficiency of the control system, active control experiments

are conducted using optimal gains obtained from numerical solution.

Further the simulated active control scheme is implemented in

an experiment using digital control system to achieve vibration

reduction of cylindrical shell. The laminated composite cylindrical

shell is shown in Fig. 6.2.

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Fig. 6.2 CFRP composite cylindrical shell

6.2 CONTROL SYSTEM ELECTRONICS

The active vibration control experiments are carried out with the

help of a digital controller (LQG) in the present study. This control

system consists of Piezo Sensing System (PSS), DSP card with ADC

(Analog to Digital Converter) and DAC (Digital to Analog Converter),

Signal generator, power amplifier and shaker, High voltage amplifier

for piezo actuators (PAS) and PC with MATLAB software.

The Piezo Sensing System (PSS) consists of charge amplifier

circuit, i.e. charge conditioner to collect signals from the distributed

PZT sensors. The charge amplifier converts the charge to a

Compositeshell

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proportional output voltage to make the signal independent of cable

capacitance and length. Since the present Active Vibration Control

(AVC) study has employed with MFC actuators, three channel high

voltage amplifiers are used to supply the amplified control signals (-

500 V to 1500 V, 300mA). In a dynamic environment, these amplifiers

are able to give output voltage of 750 V. An eight channel Digital

Signal Processor (made by dSPACE) is interconnected with the LQG

controller. This DSP board has 8 ADC’s and 8 DAC’s. Each ADC is

used to receive sensor signal and DAC is to supply actuator signal.

6.3 EXPERIMENTAL SETUP

The composite cylindrical shell is fabricated using Carbon Fiber

Reinforced Plastic (CFRP). Subsequently it is instrumented with three

MFC actuators on the top. The MFC actuators M4010 P1 and M8528

F1 are procured from Smart Materials® corporation, Germany. The

instrumentation employed in experimental setup is shown in Fig. 6.3.

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Fig. 6.3 Experimental setup for Active vibration control

Sensingelectronics

High voltageamplifiers Signal

generator

DS 1104

Control desk

Shell

RTI/RTW

138

The experimental setup for active vibration control of laminated

composite cylindrical shell along with MFC actuators and PZT sensors

are shown in Fig. 6.4 and 6.5.

Fig. 6.5 shell with PZT Sensor’s at the bottom

Fig. 6.4 cylindrical shell equipped with MFC actuators

Accelerometer

MFC actuators

PZT sensors

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An accelerometer is shown in Fig. 6.6 at the tip of the shell for

measuring the vibrations.

A line schematic diagram shown in Fig. 6.7 is used for the

control of active vibrations.

Fig. 6.6 Shell with Accelerometer

Accelerometer

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The control signal is generated with the help of a Piezo

Actuation System (PAS), taking the filtered output signal as input and

is applied to the piezoelectric actuator patch.

In displacement feedback control, the vibration suppression is

achieved by generating the actuation signal 180° out of phase with

respect to the disturbance signal. Hence, the PAS has got the

provision to change the phase of the signal from 0° to 180° degrees

and fine-tune the actuation voltage. The disturbance signal is

generated through a digital function generator and is subsequently

Fig. 6.7 Active vibration control system

141

amplified using a power amplifier, before it is supplied to the

electromagnetic shaker. The disturbance level is measured with the

help of a force transducer. In addition, an oscilloscope is employed to

monitor the structural response and input force/output level in real

time.

The feedback controller design needs system or plant

characteristics as input, i.e state space matrices. Since a modern

control concept employing the state-space matrices has been adopted.

The structural system is parameterized using stiffness, mass and

damping matrices. However, an active structure must be

characterized additionally with distributed actuator and sensor

matrices. The developed finite element (chapter 3) and control (chapter

5) procedures are coded in MATLAB. Therefore, it is possible to carry

out both structural and control analyses in the same platform. The

CFRP shell is analyzed using the developed 4-node facet shell element.

Structural and piezoelectric coupled matrices are used in the control

analysis.

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6.4 CONTROL LAW IMPLEMENTATION

The control system designed to estimate the optimal feedback

control gain (off-line) for different weighting factors (Q, R). The sensor

gain and the filter gain are taken as one unit while estimating the

control gain of LQR. Feedback voltage is then calculated ( a) by

multiplying the sensor signals ( s) and is applied to the actuator,

which is fixed at the same location (collocated). The feedback voltage

obtained using the optimal gain (LQG) is experimentally tuned in HVA

system; besides HVA has got provision to introduce electrical biasing.

This facilitates the MFC actuators to be used in dynamic environment,

as these active elements do not have the same amount of extension

and contraction. The proposed LQG controller has included both

displacement and velocity as states; therefore the control signal

contains displacement and velocity information. Thus both active

stiffening (induced strain) as well as active damping effects are

expected to be introduced by the MFC actuators.

A periodic excitation is applied as disturbance through shaker

and the amplitude response control is achieved by controlling the

displacement and velocity of the vibrating system. A virtual

instrumentation panel is created in control desk® (dSPACE product)

to monitor the disturbance force, sensors’ output and actuators’

input. It facilitates to fine tune the control gains of the actuators in

real time. Indeed the on/off control will be more efficient once the

control gains are scheduled for different disturbances. The processed

signals (control inputs) are then taken through the DAC’s of DS1104

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and supplied to the high voltage amplifiers of Smart Materials ®.

These amplifiers have got an inbuilt gain of 200. Therefore while

tuning the designed LQG gain, this value has been taken in to

account. MFC actuators are used with -500 to 1500 VDC in quasi-

static applications. However in dynamic case they can be used in the

range of 500 VAC without DC biasing or 750 VAC with DC biasing.

In the present application, MFC’s within 500 VAC without DC

biasing are used. Care is taken for proper insulation, isolation of the

actuators and wiring is done so as to avoid any electric leakage.

6.5 CLOSED LOOP EXPERIMENTS

A thorough modal survey is performed on the shell to establish

the frequencies, damping of the first four modes. Active vibration

control experiments are then conducted using independent modal

controller, i.e. IMSC as well as selective modal control (SMSC)

approaches. A typical modal controller (Simulink model) that has been

implemented is shown in Fig. 6.8.

Fig. 6.8 Simulink model of LQGcontroller

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The Linear Quadratic Gaussian (LQG) controller is designed such that

each mode is significantly controlled through independent modal

space control (IMSC) scheme. The effectiveness of modal control

concept for multiple modes is examined through a combination

resonance or selective modal space control (SMSC) technique. For this

purpose, two modal sets are selected, namely modes 1, 3 and 2, 4.

The state-space matrices of selective modes are combined to form a

single system with multiple target modes. LQG control is designed for

these combination resonances. Modal coupling is a normal

phenomenon in thin walled composite structures. With the presence

of aerodynamics, noise etc., the coupled problems such as

aeroelasticity, vibro-acoustic may pose serious challenges for the

designers. Therefore, in such situations, the selective modal control

may certainly improve the structural performances and reduce the

control spillover. In order to examine the usefulness of the developed

SMSC technique, active control experiments are conducted on the

cylindrical CFRP shell. The instrumentation scheme used in the

feedback control architecture is shown in Fig. 6.3. The applied

voltages to actuators for various modes control are listed in Table 6.1.

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Table 6.1: Voltages applied to actuators for control of various modes

The AVC experiments are conducted by implementing the

designed LQG (IMSC and SMSC) controllers in DS1104, a R&D DSP

board of dSPACE®. The DSP has got multi-channel ADC’s and DAC’s,

which are used for sensor and actuator loops, respectively. The

actuators A1 and A2 are made to work for the first and second modes’

control. The chord wise placed actuator A3 has targeted the third and

fourth modes. The outcome of the experiment is presented as time

responses and power spectral densities. Accelerometer (Sensitivity

100 mV/g) is employed as the observation sensor, which is located at

the tip of the shell. The disturbance force is monitored through a force

transducer.

The structure considered for experiment is a deep shell category

and therefore its elastic couplings appear to be very significant. Hence

the first four modes are targeted to demonstrate the ability of in-plane

actuation of MFC’s in controlling out-of-plane elastic couplings. The

Mode(s) Actuator voltage in (volts)A1 A2 A3

IMSC1 44 44 --2 96 88 --3 -- -- 484 -- -- 96

SMSC1&3 35 35 602&4 60 60 60

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PZT fibers are oriented in actuators A1, and A2 along the length (span

wise) of the shell; thus they are expected to induce actuation strains

to counteract first two modes, which are predominantly span wise

dominated.

6.6 EXPERIMENTAL RESULTS AND DISCUSSION

The vibration control experiments are carried out on a

composite cylindrical shell structure using IMSC and SMSC

techniques. The control data collected from experiments using IMSC

technique is processed in “digisigpro” (digital signal processor)

software to obtain power spectral density plots for the first four modes

as shown in Fig. 6.9 to 6.12. The amplitude values measured from

power spectral density plots are tabulated in Table 6.2. From the table

it is noticed that the percentage of vibration control achieved for the

first four modes are 88.95, 96.93, 73.33 and 76.22 respectively.

The control data collected from experiments using SMSC

technique is processed in “digisigpro” (digital signal processor)

software to obtain power spectral density plots for the modes 1, 3 and

2, 4 are shown in Fig. 6.17 and 6.18. The amplitude values measured

from power spectral density plots are tabulated in Table 6.3. From the

table it is observed that the the percentage of vibration control

achieved in selective mode technique for the modes 1, 3 and 2, 4 are

85.67, 96.67, 88.57 and 70.73 respectively.

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Also using the digisigpro software the time response plots before

and after control for the duration of 10 seconds using IMSC technique

are shown in Fig. 6.13 through 6.16. In figures the first 4 seconds

show the vibrations without control and the next 6 seconds with

control for shell structure. From the figures it is observed that the

percentage vibration reduction achieved in first four modes are

respectively 88% (50.86 Hz), 96% (103.44 Hz), 73% (165.99 Hz) and

76% (185.88 Hz).

Similarly, the time response plots before and after control

for the duration of 10 seconds using SMSC technique is shown in Fig.

6.19 and 6.20. From the figures it is seen that the percentage

vibration reduction achieved for the modes 1, 3 and 2, 4 are 85%

(50.86 Hz), 96% (165.99 Hz), 88% (103.44 Hz) and 70% (185.88 Hz)

respectively.

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Table 6.2: Vibration control performance by IMSC scheme

Mode

Natural

frequencies

(Hz)

Amplitude (g2/Hz)%

controlOpen loop

response

Closed loop

response

1 50.86 1.9e-4 2.1e-5 88.95

2 103.44 1.5e-4 4.6e-6 96.93

3 165.99 1.2e-4 3.2e-5 73.33

4 185.88 3.7e-5 8.8e-6 76.22

where percentage control is = (open loop response-closed loop

response)/open loop response. Table 6.3 Vibration control

performance by SMSC scheme.

Table 6.3: Vibration control performance by SMSC scheme

Mode(s)

Natural

frequencies

(Hz)

Amplitude (g2/Hz)%

controlOpen loop

response

Closed loop

response

Mode 1

Mode 3

50.86

165.99

6e-5

3.3e-5

8.6e-6

1.1e-6

85.67

96.67

Mode 2

Mode 4

103.44

185.88

4.2e-5

4.1e-5

4.8e-6

1.2e-5

88.57

70.73

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0 20 40 60 80 100 1200

1

x 10-4

Frequency(Hz)

Amplitude(g

2/Hz)

open loopclosed loop

50 60 70 80 90 100 110 120 130 140 1500

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6x 10

-4

Frequency(Hz)

Amplitude(g2/Hz)

open loopclosed loop

Fig. 6.9: First mode power spectral density plot in LQG control

Fig. 6.10: Second mode power spectral density plot in LQG control

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130 140 150 160 170 180 190 200 210 2200

0.2

0.4

0.6

0.8

1

1.2x 10

-4

Frequency(Hz)

Amplitude(g2/Hz)

open loopclosed loop

140 150 160 170 180 190 200 210 220 2300

0.5

1

1.5

2

2.5

3

3.5

4x 10

-5

Frequency(Hz)

Amplitude(g

2/Hz)

open loopclosed loop

Fig. 6.12: Fourth mode power spectral density plot in LQG control

Fig. 6.11: Third mode power spectral density plot in LQG control

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0 1 2 3 4 5 6 7 8 9 10-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time(sec)

Amplitude(V)

0 1 2 3 4 5 6 7 8 9 10-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time(sec)

Amplitude(V)

Control on

Control on

Fig. 6.13 First mode time response before and after control

Fig. 6.14 Second mode time response before and after control

Control ON

Control ON

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Fig. 6.15 Third mode time response before and after control

0 1 2 3 4 5 6 7 8 9-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Time(sec)

Amplitude(V)

0 1 2 3 4 5 6 7 8 9 10-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time(sec)

Amplitude(V)

Fig. 6.16 Fourth mode time response before and after control

Control on

Control on

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20 40 60 80 100 120 140 160 180 2000

1

2

3

4

5

6x 10

-5

Frequency(Hz)

Amplitude(g2/Hz)

open loopclosed loop

80 100 120 140 160 180 2000

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

-5

Frequency(Hz)

Amplitude(g2/Hz)

open loopclosed loop

Fig. 6.17 PSD plot of selective modes 1and 3 before and after control

Fig. 6.18 PSD plot of selective modes 2 and 4 before and after control

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Fig. 6.20 Time response of selective modes 2 and 4 before and after control

0 1 2 3 4 5 6 7 8 9-0.015

-0.01

-0.005

0

0.005

0.01

0.015Time Plot

Time(sec)

Amplitude(V)

Control ON

Fig. 6.19 Time response of selective modes 1 and 3 before and after control

0 1 2 3 4 5 6 7 8 9 10-0.03

-0.02

-0.01

0

0.01

0.02

0.03Time Plot

Time(sec)

Amplitude(V)

Control ON