review ppt modified kljlk

8/13/2019 Review Ppt Modified kljlk

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LOGO

ByMandipalli Naresh

12MC10F

Multi Input Multi Output

Active Vibration Control ofSmart Structures using PZT

GuideDr. K V Gangadharan


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Introduction

Vibration control

Passive Semi active Active

m

k c

m

k c

m

k c

Fd Fd Fd Fc


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Summary of literature review

Majority of literatures are on single input andsignal output systems but in reality many systems

are multi input and multi output (MIMO).

Majority of literatures are based on simulation

studies which require to be validatedexperimentally.

Basic controllers can result even the system to be

unstable, with large changes in system parameters.

This problem can be avoided using robust control

and adaptive control design techniques like

LQR/LQG controller.


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Summary of literature review (cont..)

Pole placement technique is the basic state feedbackcontroller.

Controller performance had been tested for

impulse i.e., for free vibration which is required to

be improved for forced vibration.


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Problem Statement

To analyze the nature of vibration in structures and

suppress the vibration effectively using pole

placement state feedback technique for MIMO

system


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Objectives

Comparative study of conventional controllers andstate feedback controller (Pole placement controller)

for active vibration control.

Vibration control for few dominant modes ofvibration and impulse vibration.


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Modeling and Simulation

System Configuration


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Modeling and Simulation (Cont)

Beam is modelled as two node element which has2DOF at each nodes ( Transversal displacement

and slope )

Assuming cubic polynomial equation for transverse

vibration of beam

2 3

0 1 2 3( )u x a a x a x a x

1u 2u

2

1


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The interpolation can be written in shape functionform after applying boundary conditions,

1 1 2 1 3 2 4 2( ) (x)u ( ) ( )u ( )u x w w x w x w x

2 3

2 3

2 31

22

2 33

2 3

4

2 3

2

3 21

2

3 2

x x

l l

w x xx

w l l

w x x

w l l

x x

l l


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Comparing finite element equation with mechanicaltranslational motion equation,

2 2

2 2

156 22 54 13

22 4 13 3[M]

54 13 156 22420

13 3 22 4

l l

l l l l Al

l l

l l l l

2 2

3

2 2

12 6 12 6

6 4 6 2

[ ] 12 6 12 6

6 2 6 4

l l

l l l l EI

K l ll

l l l l

[ ] [M] [K] ; 0.01, 0.001C


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Piezoelectric as sensor and actuator Direct and converse piezoelectric equations

Voltage produced by sensor

Equivalent force is given by piezoelectric

31

t

fd E s

31z fD d e E

c 31 c 310

(t) G e zb ' G e zb[0 1 0 1] '

pl

T

sV B d dx d

31 [ 1 0 1 0]V (t)

c p aF E d bz


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Model order reduction

System model equation is

Reduced model order equation can be found by

considering required modes

d cM d C d K d F F

d T q


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System matrices

Experimental FEM ANSYS

1stmodeFrequency(Hz)

29.604 32.33 32.782

2ndmodeFrequency(Hz)

169.5 172.76 183.71

3 0.103327733887813 -0.0000000000000134[m] 10-0.0000000000000134 0.0151176776852316

4.264094632032168 -0.0000000000814512[k]

-0.0000000000814014 18.639762290157726

0.000426512790937 -0.000000000000008[c]

-0.000000000000008 0.001863991346693


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State space model

0 0 1 0

0 0 0 1A

-4.1268e+04 8.7175e-07 -4.1278 8.7175e-11

-5.0048e-06 -1.2330e+06 -5.0048e-10 -123.2988

0 0 0

0 0 0

0.0112 0.0242 0.0356

0.1522 0.2523 0.2404

B

0 0 1.9515 05 3.2191 05

0 0 1.6118 05 8.5565 06

e eC

e e

0 0 0

0 0 0D

x Ax Bu

y Cx Du


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Particle system response

Voltage

Time


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Mode shapes in ANSYS


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Experimental Setup

ChargeAmplifier

Voltage

Amplifier

Beam with Sensor and

Actuator

PXI RTSystem


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Pole placement technique

Consider a system

State feedback control law is:

K is feedback gain vector

x Ax Bu

y Cx Du

1

2

1 2 3

( )

( )

.. . .

.

.

( )n

x t

x t

K K K

x t

( )u Kx t


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Pole placement technique (Cont..)

Closed-loop control system with u=Kx


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Substituting u in open loop system

Eigenvalues of A BK gives the closed loop poles of

the system

Thus the controller gain K will be determined by

placing closed loop poles at fixed desired position

Necessary and sufficient condition for arbitrary

pole placement is that the system be completely

state controllable and observable.

x( ) ( ) x(t)t A BK


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Condition for controllability

Condition for observability

Where n = number of states

m = number of outputs

1. . . nrank B AB A B n

2 1. . .

nrank CB CAB CA B CA B D m


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State feedback with controller


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Proportional controller result

Percentage reduction : 93.95

Time

Voltag

e


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Conclusion

The detail system dynamics is analysed successfully;

Mathematical model of the system is developed using

FEM technique for controller design and simulation;

It has been attempted to implement a classical controller

namely proportional controller for first mode of

vibration;

The Percentage strain (in voltage) reduction is observed

to be 93.95% with additional harmonic frequency;

The conventional controller implemented is not still

effective for the 2nd mode of vibration, thus it requiresfurther study.


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Future work

In the future it is planned to design state feedbackcontroller for MIMO active vibration system based on

pole placement technique.

Controller

Full state observer Experimentally validating the effectiveness of the

designed controller

Comparing the state feedback controller with classical

controller.


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review ppt modified kljlk

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