This document describes a project to control vibrations of a cantilever beam using LabVIEW. A cantilever beam with piezoelectric sensors and actuators is used to sense and control vibrations. A proportional-derivative controller in LabVIEW analyzes input signals from the sensor and outputs signals to the actuator to produce out-of-phase vibrations that counteract the original vibrations. The controller was able to dampen vibrations when simulated in LabVIEW, but an amplifier is needed to actuate the physical beam. The project demonstrates vibration control of a beam using piezoelectrics and proportional-derivative feedback control.

1. MEL 417
Dr. Navin
Kumar
VIBRATION SENSING Submitted by :
 Vivek Dharnia
AND CONTROL FOR A (P2009ME1089)
 Ajeet
CANTILEVER BEAM (P2009ME1090)
 Lalit Aggrawal
USING LABVIEW. (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).