This thesis introduces simple fuzzy logic controller designed for the
vibration control using active vibration technique. Chapter 1 includes
introduction to the vibrations, different types of vibration control
techniques.

Chapter 2 gives fundamental fuzzy concepts and fuzzy inference system and
its types. It also covers various steps involved in designing an inference
system.

Chapter 3 includes simulating fuzzy controller using ï¿½FUZZY LOGIC
TOOLBOXï¿½. It also gives the detail description of the various functions
used in designing this project.

Chapter 4 includes the block diagram of the active vibration control
experiment and results obtained with various waveforms.

**
INTRODUCTION TO VIBRATIONS**

** Vibration**

Vibrations are omnipresent in all mechanical systems. A
vibration is a continuing change in the position of a body that follows
slightly a regular pattern. It is the main characteristic that defines the
motion in structures and machine components of any bulk structure. Force
and stress in the vibrating bodies comprise the bulk of the vibrations.
Vibrations are detrimental to system performance in many ways.

The study of source of vibration and their effects is necessary in the
view of designer to develop structures that are free from vibration.
Vibrations are to be isolated in systems because they lead to increased
fatigue and degeneration of the system and the final result being the
failure of the system. System performance becomes unpredictable in the
wake of such of a plight.

** Vibration in aerospace structures**

Modern supersonic aircraft under different operating conditions are
subjected to vibrations caused by the engine, aerodynamics turbulence,
gust etc. this may excite some of the resonant modes of the structure to
cause failure of the structure or to violated the efficiency and hence the
system performance.

When an aircraft stationary on ground, there will be no vibrations
experienced by it. Once the aircraft takes of vibrations are developed. As
it takes of it experiences forces due to aerodynamic forces on its wings,
fines, cockpit etc, which leads to undesirable effects. Some times these
vibrations are so large that they lead to catastrophic failure that is,
sudden failure of wings and fines of the aircraft. Thus it is imperative
to control and reduce the vibration to the maxima possible extent

**
Effects of vibration and its control **

The study of effect and control of vibration is necessary to develop
structure that do not succumb to vibrations and fail under operating
condition. The study also impresses the need to provide isolation of
vibration for the safety of the personal and the equipment.

In order to study the behavior and effect of the structure the system
under dynamic condition, curtain essential parameter are to be made note
of. This could be done basically by two approaches namely,

ï¿½
analytical methods

ï¿½
vibration tests

Vibration tests are carried out to

ï¿½
Find response of the aircraft structure under various load
condition and obtaining the characteristics of the structure in terms of
frequency, damping and mode shapes.

ï¿½
Define the vibration environment.

ï¿½
Monitor and control a system.

Vibration
could be eliminated to certain extent using the following methods.

ï¿½
Removal of the external excitations.

ï¿½
Use of shock absorbers.

ï¿½
Use of dynamic absorbers.

ï¿½
Providing proper vibration isolation.

Vibration
method could be classified as.

ï¿½
Passive vibration control

ï¿½
Active vibration control

**
Passive vibration control**

The physical parameters after structure such as itï¿½s mass, damping
coefficient and stiffness of the structure determined the response of the
system to vibrations. Changing this parameters can be considered as a
redesigning process for an already existing structure to produce more
desirable response this is passive vibration control method.

The frequency of such a system is derived from the equation 1,

Frequency=1/2∏ï¿½√(k/m)cpsï¿½ï¿½ï¿½ï¿½ï¿½(1)

Where
m-mass

K-stiffness

Disadvantages of passive vibration control:

The constraints mass (m), damping coefficient(c) and the
stiffness (k) are such that only two of them can be varied because damping
co efficient for given structure is constant.

The response of the structure will be altered far from desired
response because of many reasons; one of them being only a 10 % vibration
is possible in the desired value of the mass.

When the frequency of vibration is equal to natural frequency
of the passive system, resonance occurs. This leads to failure of the
flexible structures such as satellite truss or a peace of vibrating
machinery.

They can be bulky and heavy when used at low frequencies
(bellow 500 Hz) since; size and mass of passive method usually depend on
acoustic wavelength.

**
Active vibration
control**

Active vibration control aims at minimizing the response of
vibration rather than to control the source of vibration. It is a related
technique that resembles active noise control. They use actuators, which
are electrochemical devices that control the response of the elastic
medium. Actuators are the secondary vibration source (shakers,
piezoceramic patches etc), which can modify the vibration. Actuators used
in active vibration control can be broadly classified as,

1)
Fully
active

2)
Semi
active

1) Fully active actuators supply mechanical power to the
system. They can be used to generate a secondary vibrational response in
the linear mechanical system. This reduces the overall response by
destructive interference with the original response of the system, caused
by the primary source of vibration.

2) Semi active actuators behave essentially as passive
systems. Their use in ac0Vï¿½)V0Vï¿½)VPï¿½ï¿½)VPï¿½)Vï¿½Vï¿½)VPVï¿½)V8PVï¿½)Vd by the application of
a control signal and in such systems, one of the special types active
control is adaptive control system.

Active vibration control
is brought about using the ï¿½Smart Structure Technologyï¿½. Generally the
methodology involved in vibration reduction is achieved by introducing
additional vibrations in anti-phase to the structure through a
controller-actuator combination.

Active vibration Control is a process of reducing existing
levels of vibration by means of one or more secondary control sources.

*
Summary*

In this chapter we studied vibration as a continuing change in
the position of the body that follows slightly regular pattern. Causes
for the vibrations in aerospace structures and different applications
where control of vibration is of prime importance. Also this chapter
covered the effects of vibrations and various controlling techniques.

In this project we are implementing ï¿½active vibration controlï¿½
(AVC) concept using fuzzy logic. So its very important to know the basic
concepts of fuzzy logic. All these are covered in detail in the next
chapter.

** ACTIVE CONTROL EXPERIMENT**

In the present study, it is the off-line vibration control
which is implemented in MATLAB environment using fuzzy toolbox. The block
diagram is shown below in figure 29:

Figure : Block diagram
of vibration control using fuzzy logic.** **

The vibrations are read for various frequencies and compared
with the reference value to generate error signal. Now these two vibration
and error signals both are normalized then for each of the input 5 fuzzy
rules are written and are executed using FIS file. 25 rules are written in
rule editor and for output also 5 membership functions are defined. Now
these output values are renormalized to get the crisp values which are
combined with vibration amplitudes which suppress them to reference value.

.

**FLOWCHART**

**
**

**
RESULTS**

The frequency domain signals captured from vibration sensor and are stored
in excel file form. Further the acquired data is processed to suppress the
vibration amplitudes to the reference values.

As the present work is based on amplitude (displacement)
control concept, the efficiency of the fuzzy controller is assessed with
respect to achieved reduction in amplitude. The vibration amplitude is
reduced to reference level very significantly and the input and out plots
are shown below.

Figure Input
vibrations, error and output suppressed vibrations.

**
CONCLUSION **

The present study has helped to understand the active control
concept that can be employed for the vibration control. The vibrations of
the systems are much effectively suppressed using fuzzy logic controller
algorithm in MATLAB. The experimental results are shown in figure 31.

Since fuzzy does not make use of the mathematical model it is
much easier in controlling non-linear systems. For variety of applications
like aircraft/aerospace and robotics etc. now a days it is required
economical and practical solution of vibration control. Keeping this in
mind our project is built using fuzzy logic in MATLAB environment which
makes cost effective.

As the fuzzy controller is easy to implement in real time, fuzzy rules can
be used to design a controller and implemented as a control for structural
vibration suppression purposes.

Like everything** **in this world, this product also has scope of
improvements. It is used for off line control and only two parameters are
taken into consideration i.e. amplitude and frequency. But it is possible
to develop for real time application. Also we can consider more parameters
such as phase. The future work can be attempted to develop an Active
Vibration Control (AVC) scheme for real time applications like flexible
robotic arm.

Also it can be attempted develop AVC with Multi Input Multi Output (MIMO)
concept for aircraft structural vibration control application.