1
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.
134
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.
135
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
136
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.
137
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
139
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
140
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.
142
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
143
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
144
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.
145
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
146
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.
147
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.
148
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
149
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
150
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
151
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
152
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
153
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
154
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