VIBRATION SENSING AND CONTROL FOR A

CANTILEVER BEAM USING LABVIEW.

MEL 417

Dr. Navin

Kumar

Submitted by :

Vivek Dharnia

(P2009ME1089)

Ajeet

(P2009ME1090)

Lalit Aggrawal

(P2009ME1088)

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Acknowledgement

We express our sincere thanks to Dr. Navin Kumar to award us with a wonderful

opportunity to do a project on Experimental analysis of a cantilever beam and its

vibration control using Labview. Our project supervisors were instrumental in the

process of bringing this project to its present form. Without their key support,

knowledge and experience, procurement of set-up, our project and its analysis

would not have been possible.

Executive Summary

Whenever a cantilever beam gets any impulse or experiences any net external

force, it starts vibrating. In this project, the main objective is to control the

vibrations of a cantilever beam. A cantilever beam made of mild steel is mounted

at one end. It consists of a piezoelectric transducer and a piezoelectric actuator

placed at the root of the cantilever beam. The Vibrations can be caused by various

sources including human activity and harmonic exciter. The piezoelectric sensors

are used to detect the vibrations. Simultaneously, feedback controller sends

correction signal to the actuator to minimize the vibrations. A Proportional

derivative (PD) controller is used to control the vibrations. The controller as well

as the whole system is designed in Labview.

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Table of contents

List of figures

Introduction

Experimental Set up

Procedure

Experimental Results

Discussion

Conclusions and Recommendation

Reference

List of figures

Following are the figures of our setup of a cantilever beam and the

PZT crystals attached to it.

Figure-1 : Cantilever beam with PZT crystals mounted at top and

bottom surface

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Figure-2 : Data acquisition system.

Figure-3 : Soldered PZT crystals.

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Introduction

Active vibration control is defined as a technique in which the vibration of a

structure is reduced or controlled by applying counter force to the structure that is

approximately out of phase but equal in amplitude to the original vibration. As a

result two opposite forces cancel each other and dampen the vibration. Techniques

like the use of spring, dampers and pads are known as passive vibrations

controlled. These techniques were previously used but now a days, these have

become obsolete as they are incompatible with modern machines. These are very

heavy, large and thus not suitable for controlling vibrations in new modern, small

and sophisticated machines. Moreover, these techniques could work for a very

small range of vibrations.

Active vibrations controller has more life expectancy. They use sensors, actuators,

controllers, feedbacks for controlling the vibrations. Piezoelectric sensors operate

using the direct effect, i.e., electric charge is generated when a piezoelectric

material is stressed causing deformation. These sensors are extremely sensitive and

have superior signal to noise ratio. In this case, the sensor is bonded to the bottom

surface of the beam by means of soldering.

Typical piezoelectric actuators operate using the converse effect of piezoelectric

materials. Whenever a voltage is applied across its electrodes, a strain is induced in

the material. PZT is commonly used for actuation. PZT is ideal because of its

respectable maximum actuation strain, reasonable cost, and high accessibility.

They are bonded at the surface of the beam by soldering it.

Experimental Set up

To identify the dynamics of the beam, the beam needs to be stimulated via the

actuator. We give input signal (excitations) at the free end of the beam manually or

using a harmonic exciter. The impulse excites the beam and thus produces

vibrations in the beam. These vibration signals are sensed by the sensor and

generated, along with some noise, in Labview through the input port (ai0) of a

Data Acquisition system (DAQ). These signals are then passed on to a Proportional

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Derivative (PD) controller designed in Labview. The output of the controller is

then passed through the output port (ao0) of the Data Acquisition system (DAQ).

The output signals are fed to the actuator which transforms the electrical signals

into mechanical vibrations to the beam and corresponding out of phase vibrations

with equal magnitude will be produced to nullify the impact of the vibrations

which was produced due to the excitations. The following figure shows the basic

block diagram implemented in Labview.

Figure -4 : Block Diagram in Labview.

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Theory and Controller design

In the experiment, a beam (mild steel) was made and mounted it in a fixed place

with one end hanging. A piezoelectric transducer was placed at the fixed end. The

beam is then connected with the Labview system. The impulse is given at the free

end of the beam to produce vibrations. These vibrations are imparted into the

computer having Labview with the help of piezoelectric transducer. These

vibrations are analysed in the Labview and controlled with the help of PID

controller by producing out of phase vibrations of equal magnitude.

A proportional–integral–derivative controller (PID controller) is a control loop

feedback mechanism (controller) extensively used in control systems. It calculates

an "error" value as the difference between a measured process variable and a

desired set point which is given as input initially. It attempts to minimize the error

by adjusting the process control inputs.

The PID controller calculation involves three separate constant parameters: the

proportional, the integral and derivative values, denoted by P, I, and D.

Heuristically, these values can be interpreted in terms of time: P depends on the

present error, I on the accumulation of past errors, and D is a prediction of future

errors, based on current rate of change. The weighted sum of these three actions is

used to adjust the process via a control element such as the position of a control

valve, or the power supplied to a heating element.

In the absence of knowledge of the underlying process, a PID controller has

historically been considered to be the best controller. By tuning the three

parameters in the PID controller algorithm, the controller can provide control

action designed for specific process requirements. The response of the controller

can be described in terms of the responsiveness of the controller to an error, the

degree to which the controller overshoots the set point and the degree of system

oscillation. Note that the use of the PID algorithm for control does not guarantee

optimal control of the system or system stability.

In our experiment PD was used because we don’t need the accumulation of the

past error which is represented by I.

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Experimental Results

Using the procedure described above, the controller was implemented on the

system. The vibrations on the cantilever beam were successfully controlled with

the help of piezoelectric actuator and PD controller designed in the Labview.

Though we were unable to actuate the cantilever beam because the output signals

produced by the controller were too weak to produce mechanical vibrations and

hence cannot be implemented without an amplifier, nevertheless we observed the

output signals on Labview. Following figures show the input signal as well as the

output signal out of the controller.

Figure -5 : Input Signal

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Figure 6 : Input signal (Black wave) as well as output signal from controller

(red wave)

Discussion

Through this project, we carried out vibration sensing of a cantilever beam and

designed a controller to dampen the vibrations in Labview. Following observations

can be made during the analysis:

The cantilever beam is an under damped system with a natural frequency of

approximately 9 Hz.

During controller design, the proportional gain was set to 1. Increasing the

Proportional gain to more than 1 increase the amplitude of the output signal.

During controller design, the derivative time Td was set to a value of 0.001.

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Conclusions and Recommendation

A smart beam is constructed using mild steel, PZT sensor and a PZT actuator. A

controller is designed in Labview and is used to control the vibrations of the beam.

It can be concluded that a Proportional Derivative (PD) controller can be used to

control the vibrations and it further depends on the Proportional gain and

derivative time of the controller. An out of phase vibrations are produced to nullify

the impact of the actual vibrations and depends on the gain, differential time of the

PD controller. It is recommended that an amplifier is used with the actuator to

amplify the output signals from the controller and is able to actuate the beam.

Reference

1. K. B. Waghulde et al. /International Journal of Engineering and Technology

Vol.2(4), 2010, 259-262.

2. Journal of Vibration and Control March 2012 vol. 18 no. 3 366-372.

3. http://www.kyu.edu.tw/93/epaperv6/93-033.pdf

4. Wikipedia – The free encyclopaedia..

5. National Instruments (NI) manual.

6. Tutorials on Controller design by National Instruments (NI).