IRDE

LOS STABILISATION
DIT UNIVERSITY Page 1
A Report
On
Line of Sight Stabilization
Submitted by:
Harshit Shandilya
B.Tech.(III Year)
Department of Electrical Engineering, DIT University
Dehradun (Uttarakhand)
Under the able guidance of:
Mrs. Seema Sharma
Scientist ‘C’
Fire Control System Division
DRDO-Instruments Research and Development Establishment
Dehradun
Ministry of Defence
Government of India

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ACKNOWLEDGEMENT
I would like to express my sincere gratitude to Sh. L. Benjamin,
Director, I.R.D.E. Dehradun who provided me the opportunity to
undergo training at the organization.
I take this golden opportunity to express my heartiest gratitude to
Mr. Avnish Kumar Garg, Scientist ‘G’, Head of the department, Fire
Control systems Division (FCS), IRDE for his kind co-operation.
I am also very grateful to the guide-in-charge of my project
Mrs. Seema Sharma, Scientist ‘C’ who has helped me in imparting the
proper knowledge regarding the design and successful completion of
project.
I would also like to thank the Director, DIT University, Dehradun for his
kind permission to join the summer training program in this esteemed
Institute.
Thanks are also due to everyone who supported me and encouraged
me during the course of this study.

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TABLE OF CONTENTS
1. About IRDE,Dehradun
2. Fire Control System And History Of Line Of Sight Stabilisation
3. Line Of Sight (LOS) Stabilisation
4. Block Diagram Of Line Of Sight Stabilization Control System
5. Elements of LOS Stabilisation Control System
 Gyroscope
 Fibre Optic gyroscope
 MEMS
 Dynamically Tuned Gyroscope
 DC motor
6. Control System Stability Analysis
7. Control System Design
 Compensators
8. Control System DesignTerminologies
9. Introduction to MATLAB
10. MATLAB Control System Toolbox
11. ProjectDetails
 Problem Statement
 DescriptionOf Project
 MethodologyAdopted

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12. MATLAB code for the display of bode plot of
Uncompensated OpenLoop System
13. Implementationof the Compensatordesign
14. MATLAB code for display of bode plot of the Compensator
15. MATLAB code for display of comparison of bode plot of the
Compensatedand Uncompensated system.
16.MATLAB code for display of bode plot of Compensated Closed
Loop System
17.Conclusions
18. References

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About IRDE
VISION
Instruments Research and Development Establishment,
Dehradun, is a premier institution for research and development
activities in the field of electronics and electro-optics in India.
Formally known as Establishment of Inspectorate of Scientific
Stores, it originated in 1939. Later it underwent changes taking the
shape of Technical Development Establishment (Instruments and
Electronics) TDE, during subsequent years was converted to
IRDE, which came in its present form in February 1960.
IRDE is one of the establishments of Defence Research and
Development Organization (DRDO). Ever since its existence from
1st
December 1961, it has played a vital role in serving India in the
field of science, especially in electronics and optics.
ORGANISATIONAL SETUP
The establishment has been organized into different technical
divisions and independent groups directly responsible to the
director apart from administrative, financial and security aspects.
They can be listed as follows:
 Seeker and Fuse Instrumentation
 Optical design
 Optical Systems
 Servo systems
 Thermal Imaging Systems
 Naval Systems
 Optical Thin Films
 Optics Technology

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 Photonics
 Laser Division
 Design Workshop
 Library
MAJOR AREAS OF ACTIVITY
IRDE’s primary role is to indigenously design, develop and fabricate
modern and sophisticated instruments. This Establishment is at
present devoted to Design and Development of instruments in the
following areas:
1. Thermal imaging systems.
2. Conventional optical and fire control instruments.
3. Night vision instruments.
4. Gyro based instruments.
5. Microprocessor techniques for solving ballistic requirements.
6. Integrated fire control systems.
7. Fiber optics.
8. Holography
9. Technologies transfer control.
A large number of instruments have been designed and
developed in this Establishment during the past and most of these
are in the regular production with Ordinance Factory and trade
firms. IRDE has also made significant contribution in the field of
basic research in different areas of applied and allied optic
science. Apart from normal R&D work, the Establishment has also
undertaken major modification of the existing instruments with a
view to extend the role of equipment pertaining to their fields.

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INFRASTUCTURE
The Establishment has well equipped laboratories with most
sophisticated and modern test equipment for effective R&D work
in the specified field. It has also a well-equipped Repro graphic
division looking after preparation and printing of technical
documents and drawings.
LIBRARY
It has also a well-stocked technical library containing books and
publications including journals of international standard.
ABOUT FIRE CONTROL SYSTEMS DIVISION
It is one of the main technical divisions of I.R.D.E. This section is
associated with research and development of hardware for the
control of major devices. The department specializes in control
system engineering both by analog and digital means. In digital
controls, the dept. has specialized software and hardware for
signal processing. Also microprocessor- based controls are
checked and implemented.
As such this department takes part in all the major projects coming
to I.R.D.E. Thus, it is the department doing research in topics
related to electronics and electrical engineering.
All other departments need to refer this department at some point
or the other. This department has so far completed various projects
with perfection. Along with the new projects, the section is always
busy doing research on improvisation of projects already completed
by it so that India may also remain at par with other developed
countries in respect of technology.

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Fire Control System and History of Line of
Sight (LOS) Stabilization
A Fire-Control System is a number of components working together,
usually a gun data computer, a director, and radar, which is designed to
assist a weapon system in hitting its target. It performs the same task as
a human gunner firing a weapon, but attempts to do so faster and more
accurately.
A modern fire control system (FCS) consists of imaging devices (high
resolution TVs, IR sensors, direct viewing optics etc.) and LASER
designators/range finders. The modern day battle scenario requires our
defence forces to have all the weather fighting capability to engage
targets under dynamic conditions means that the sighting system should
allow surveillance and engagement of the enemy targets when either the
host vehicle or the enemy target or both are stationary or dynamic. This
is achieved by means of the line of sight stabilization technology. The
stabilization sub-system minimizes the jitter on the line of sight (LOS),
thereby enhancing the image quality for an E.O. sighting system.
The residual jitter is required to be reduced to sufficiently low level to
increase the resolution. This is achieved by suspending the EO sighting
system in a set of gimbals, sensing the disturbance by inertial
rate/position sensors (gyroscopes) and controlling the EO system by
means of a control system.
The stabilization requirement has been increasing steadily, due to ever
increasing requirement of the Defense forces to defeat the enemy at
longer and longer distances.
The first concern of a fire control system is to provide an effective way of
aiming. This is the function of the gun sights. Prior to 1800, there was no
need for elaborate gun sighting systems, because the guns themselves
were inaccurate except at close range. Guns were simply pointed at the
target by eye.

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Gun sights introduced early in the nineteenth century consisted of fixed
front and rear sights mounted so that the line of sight across their tips
was parallel to the bore of the gun.
Towards the end of the nineteenth century, a sight telescope was
developed by a Navy Lieutenant. It consisted of a simple telescope
containing a pair of crosshairs, and was mounted in such a way that the
line of sight could be moved with respect to the axis of the gun to correct
for some of the factors which affect the solution of the fire control
problem.
Present-day gun sights take many forms, but they still perform the basic
function of all gun sights-to provide a horizontal and vertical offset
between the line of sight and the axis of the gun bore in order that the
target may be kept in sight while the gun is aimed so that the fired
projectile will hit the target.
Line Of Sight (LOS) Stabilization
The line of sight is the vector between the sensor and a target. Passive
or active track sensors mounted on a mobile platform usually require
some form of control to stabilize the pointing vector along the line of
sight.
The Line-of-Sight (LOS) Stabilization System, presently in full scale
production, is a key element of the full solution Fire Control System
(FCS) presently being used on Main Battle Tanks and other fighting
vehicles.
The control problem can be divided into two parts ,tracking and
Disturbance rejection. The track servo loop uses the track sensor to
minimize kinematic-induced pointing error relative to a target. An inner
inertial referenced servo loop provides platform disturbance
suppression, stabilizing the LOS. Control methods that address the
stabilization control problem are often referred to as LOS stabilization.
The disturbance phenomenology and compensation techniques
impacting LOS stabilization performance covera wide range of subjects.

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The LOS subsystem is capable of operating in the following three
modes:
 Closed loop
 Open loop
The closed loop mode of operation represents the normal mission
situation. In this mode of operation, the gyro platform is stabilized in the
elevation axis relative to inertial space by the means of the primary
control loop.
The mechanization of this servo loop provides a stabilized reflected
image off the primary sight mirror. This unit interfaces with a laser range
finder, ballistic
computer, and gunners thermal imaging night sight to provide a
complete tank fire control system.
Block Diagram of LOS Stabilisation Control
System

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Elements used in los stabilisation control system:
GYROSCOPE
A gyroscope is a device for measuring or maintaining orientation, based
on the principles of angular momentum.
Mechanical gyroscopes typically comprise a spinning wheel or disc in
which the axle is free to assume any orientation. Although this
orientation does not remain fixed, it changes in response to an external
torque much less and in a different direction than it would with the large
angular momentum associated with the disc's high rate of spin and
moment of inertia. The device's orientation remains nearly fixed,
regardless of the mounting platform's motion, because mounting the
device in a gimbal minimizes external torque.
Applications of gyroscopes include inertial navigation systems where
magnetic compasses would not work or for the stabilization of flying
vehicles like radio-controlled helicopters or unmanned aerial vehicles.
Due to their precision, gyroscopes are also used in gyro theodolites to
maintain direction in tunnel mining.
Within mechanical systems or devices, a conventional gyroscope is a
mechanism comprising a rotor journeyed to spin about one axis, the
journals of the rotor being mounted in an inner gimbal or ring; the inner
gimbal is journeyed for oscillation in an outer gimbal for a total of two
gimbals.
The outer gimbal or ring, which is the gyroscope frame, is mounted so
as to pivot about an axis in its own plane determined by the support.
This outer gimbal possesses one degree of rotational freedom and its
axis possesses none. The next inner gimbal is mounted in the
gyroscope frame (outer gimbal) so as to pivot about an axis in its own
plane that is always perpendicular to the pivotal axis of the gyroscope
frame (outer gimbal). This inner gimbal has two degrees of rotational
freedom.
The axle of the spinning wheel defines the spin axis. The rotor is
journeyed to spin about an axis, which is always perpendicular to the

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axis of the inner gimbal. So the rotor possesses three degrees of
rotational freedom and its axis possesses two. The wheel responds to a
force applied about the input axis by a reaction force about the output
axis.
 Fibre optic gyroscope (FOG)
A fibre optic gyroscope (FOG) senses changes in orientation, thus
performing the function of a mechanical gyroscope. However its
principle of operation is instead based on the interference of light
which has passed through a coil of optical fibre which can be as long
as 5 km
Two beams from a laser are injected into the same fiber but in
opposite directions. Due to the Sagnac effect, the beam travelling
against the rotation experiences a slightly shorter path delay than the
other beam. The resulting differential phase shift is measured through
interferometry, thus translating one component of the angular velocity
into a shift of the interference pattern which is measured photometric
ally.
 Micro Electro-Mechanical System (MEMS)
A MEMS gyroscope takes the idea of the Foucault pendulum and uses a
vibrating element, known as MEMS. The underlying physical principle is
that a vibrating object tends to continue vibrating in the same plane as
its support rotates. In the engineering literature, this type of device is

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also known as a Carioles vibratory gyro because as the plane of
oscillation is rotated, the response detected by the transducer results
from the Carioles term in its equations of motion ("Carioles
force").Vibrating structure gyroscopes are simpler and cheaper than
conventional rotating gyroscopes of similar accuracy. Miniature devices
using this principle are a relatively inexpensive type of attitude indicator.
 Dynamically Tuned Gyroscope(DTG)
A DTG is a rotor suspended by a universal joint with flexure pivots. The
flexure spring stiffness is independent of spin rate. However, the
dynamic inertia (from the gyroscopic reaction effect) from the gimbal
provides negative spring stiffness proportional to the square of the spin
speed. Therefore, at a particular speed, called the tuning speed, the two
moments cancel each other, freeing the rotor from torque, a necessary
condition for an ideal gyroscope.
DC MOTOR
A DC motor relies on the fact that like magnet poles repels and unlike
magnetic poles attracts each other. A coil of wire with a current running
through it generates an electromagnetic field aligned with the centre of
the coil. By switching the current on or off in a coil its magnetic field can
be switched on or off or by switching the direction of the current in the
coil the direction of the generated magnetic field can be switched 180°.
A simple DC motor typically has a stationary set of magnets in the stator
and an armature with a series of two or more windings of wire wrapped
in insulated stack slots around iron pole pieces (called stack teeth) with
the ends of the wires terminating on a commutator. The armature
includes the mounting bearings that keep it in the centre of the motor
and the power shaft of the motor and the commutator connections. The
winding in the armature continues to loop all the way around the
armature and uses either single or parallel conductors (wires), and can
circle several times around the stack teeth. The total amount of current
sent to the coil, the coil's size and what it's wrapped around dictate the
strength of the electromagnetic field created. The sequence of turning a

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particular coil on or off dictates what direction the effective
electromagnetic fields are pointed. By turning on and off coils in
sequence a rotating magnetic field can be created. These rotating
magnetic fields interact with the magnetic fields of the magnets
(permanent or electromagnets) in the stationary part of the motor (stator)
to create a force on the armature which causes it to rotate. In some DC
motor designs the stator fields use electromagnets to create their
magnetic fields which allow greater control over the motor. At high power
levels, DC motors are almost always cooled using forced air.
The commutator allows each armature coil to be activated in turn. The
current in the coil is typically supplied via two brushes that make moving
contact with the commutator. Now, some brushless DC motors have
electronics that switch the DC current to each coil on and off and have
no brushes to wear out or create sparks. A servomotor is a rotary
actuator that allows for precise control of angular position, velocity and
acceleration. It consists of a suitable motor coupled to a sensor for
position feedback. It also requires a relatively sophisticated controller,
often a dedicated module designed specificallyfor use with servomotors.
Servomotors are not a specific class of motor although the term
servomotor is often used to refer to a motor suitable for use in a closed-
loop control system. Servomotors are used in applications such as
robotics, CNC machinery or automated manufacturing. As the name
suggests, a servomotor is a servomechanism. More specifically, it is a
closed-loop servomechanism that uses position feedback to control its
motion and final position. The input to its control is some signal, either
analogue or digital, representing the position commanded for the output
shaft.
The motor is paired with some type of encoder to provide position and
speed feedback. In the simplest case, only the position is measured.
The measured position of the output is compared to the command
position, the external input to the controller. If the output position differs
from that required, an error signal is generated which then causes the
motor to rotate in either direction, as needed to bring the output shaft to

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the appropriate position. As the positions approach, the error signal
reduces to zero and the motor stops.
Control System Stability Analysis
The stability of a control system is often extremely important and is
generally a safety issue in the engineering of a system. An example to
illustrate the importance of stability is the control of a nuclear
reactor. Instability of this system could result in an unimaginable
catastrophe. The stability of a system relates to its response to inputs or
disturbances. A system which remains in a constant state unless
affected by an external action and which returns to a constant state
when the external action is removed can be considered to be stable.
System’s stability can be defined in terms of its response to external
impulse inputs. A system is stable if its impulse response approaches
zero as time approaches infinity.. The system stability can also be
defined in terms of bounded (limited) inputs..A system is stable if every
bounded input produces abounded output.
There are two primary issues regarding the stability of a control system
1. Absolute Stability
2. Relative Stability
Absolute Stability tells whether a system is stable or not. Methods to
calculate absolute stability are:
1. Routh Stability Criterion
2. Hurwitz Criterion
3. By calculating the roots of the Characteristic Equation
Relative Stability tells the degree of stability and enables the designer to
design the control system in keeping the view that the stability margins
are met.
Methods to calculate Relative stability are:
1. Root Locus Technique

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2. Nyquist Stability Criterion
3. Phase plot
4. Bode Plot
Control System Design
The Control System Design is a process of analysing and calculating the
parameters of the given unstable system and to formulate a
compensatory method in order to nullify the causes of instability and to
achieve the desired performance specifications in the most cost-effective
manner.
Compensation is the process of modifying a closed-loop control system
(usually by adding a compensator or controller) in such a way that the
compensated system satisfies a given set of design specification. Two
compensators are used in classical design; the first is called a phase-
lag compensator, and the second is called a phase-lead
compensator. The general characteristics of phase-lag-compensated
systems are as follows:
1. The low-frequency behaviour of a system is improved. This
improvement appears as reduced errors at low frequencies, improved
rejection of low-frequency disturbances, and reduced sensitivity to plant
parameters in the low-frequencyregion.
2. The system bandwidth is reduced, resulting in a slower system time
response and better rejection of high-frequency noise in the sensor
output signal.

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The general characteristics of phase-lead-compensated systems are as
follows:
1. The high-frequency behaviour of a system is improved. This
improvement appears as faster responses to inputs, improved rejection
of high-frequency disturbances, and reduced sensitivity to changes in
the plant parameters.
2. The system bandwidth is increased, which can increase the response
to high-frequencynoise in the sensoroutput signal.
Fig: Life cycle of frequency domain design incorporating lead network compensation

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Control System Design Terminologies
 Bode diagram: A graph of the gain magnitude and frequency
response of a linear circuit or system, generally plotted on log-log
coordinates. A major advantage of Bode diagrams is that the gain
magnitude plot will look like straight lines or be asymptotic to
straight lines.
 Gain Crossover frequency: The frequency where the magnitude
of the open-loop gain is 1.
 Phase Crossover frequency: The frequency where the phase
angle of the open-loop gain is -180 deg.
 Phase Margin: Phase Margin is that amount of additional phase
lag at the gain crossover frequency required to bring the system o
the verge of instability.
 Gain Margin: Gain Margin is the reciprocal of the magnitude of
open loop gain at the phase cross over frequency.
 Compensator: A network inserted into a system that has a
transfer function or frequency response designed to compensate
for undesired amplitude, phase, and frequency characteristics of
the initial system. Filter and equalizer are generally synonymous
terms.
 Specification:A statement of the design or development
requirements to be satisfied by a system or product.
 Systems engineering:An approach to the overall life cycle
evolution of a product or system.Generally, the systems
engineering processcomprises anumber of phases.There are
three essential phases in any systems engineering life cycle:
formulation of requirements and specifications,designand
developmentof the system or product, and deploymentof the
system. Each of these three basic phases may be further
expanded into a larger number. For example, deployment
generally comprisesoperational test and evaluation, maintenance
over an extended operational life of the system, and modification
and retrofit (or replacement) to meet new and evolving user needs.

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Problem Statement
To design Compensator for the given unstable open loop control system
in order to achieve the desired performancespecifications
Description of the Project
The Project holds a very crucial role in defence applications especially in
the field of Fire Control System. When a target is spotted in a war zone,
it is very difficult to maintain that Line Of Sight manually as both the
target and the platform on which weapon is mounted are not stationary.
So, there has to be some mechanism by which that Line Of Sight can be
stabilised even in the presence ofjitters.
This project includes controlling of Line Of Sight with the help of control
system including Gyroscope as Angular Rate Sensor and a DC
servomotor coupled with motor driving circuit as an actuator to maintain
the Line Of Sight.
Methodology
The project was initialised by taking the frequency response readings of
the open loop system in the form of gain, phase and frequencies and the
data was stored in the form of text files.
With the use of MATLAB, the Bode Plot was drawn on the basis of given
data and its performance specifications were studied.
Then, according to the desired performance specifications, the
parameters of the compensator were calculated and were cascaded with
the system transfer function. The Bode Plot of the compensator was
then drawn with the help of MATLAB and was added with the given
Bode plot and verified whether the final Bode Plot has met with the
desired phase and gain margins or not.
If not, the values of the parameters of the compensators were gradually
changed until the desired performance specifications were achieved.

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Introduction to MATLAB
The MATLAB, a high-performance language for technical computing
integrates computation, visualization, and programming in an easy-to-
use environment where problems and solutions are expressed in familiar
mathematical notation.
Typical uses include
 Math and computation
 Algorithm development
 Data acquisition
 Modelling, simulation, and prototyping
 Data analysis, exploration, and visualization
 Scientific and engineering graphics
 Application development, including graphical user interface
building
MATLAB is an interactive system whose basic data element is an array
that does not require dimensioning. It allows you to solve many technical
computing problems, especially those with matrix and vector
formulations, in a fraction of the time it would take to write a program in a
scalar non-interactive language such as C or Fortran.
The name MATLAB stands for matrix laboratory. MATLAB was originally
written to provide easy access to matrix software developed by the
LINPACK and EISPACK projects. Today, MATLAB engines incorporate
the LAPACK and BLAS libraries, embedding the state of the art in
software for matrix computation.
MATLAB has evolved over a period of years with input from many users.
In university environments, it is the standard instructional tool for
introductory and advanced courses in mathematics, engineering, and
science. In industry, MATLAB is the tool of choice for high-productivity
research, development,and analysis.
MATLAB features a family of add-on application-specific solutions called
toolboxes. Very important to most users of MATLAB, toolboxes allow
you to learn and apply specialized technology. Toolboxes are
comprehensive collections of MATLAB functions (M-files) that extend the
MATLAB environment to solve particular classes of problems. You can

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add on toolboxes for signal processing, control systems, neural
networks, fuzzy logic, wavelets, simulation, and many other areas.
MATLAB – Control System Toolbox
MATLAB technical computing software has a rich collection of functions
immediately useful to the control engineer or system theorist. Complex
arithmetic, eigenvalues, root-finding, matrix inversion, and fast Fourier
transforms are just a few examples of important numerical tools found in
MATLAB. More generally, the MATLAB linear algebra, matrix
computation, and numerical analysis capabilities provide a reliable
foundation for control system engineering as well as many other
disciplines.
The Control System Toolbox product builds on the foundations of the
MATLAB software to provide functions designed for control engineering.
This product is a collection of algorithms, written mostly as M-files, that
implements common control system design, analysis, and modelling
techniques. Convenient graphical user interfaces (GUIs) simplify typical
control engineering tasks.
Control systems can be modelled as transfer functions, in zero-pole-gain
or state-space form, allowing you to use both classical and modern
control techniques. You can manipulate both continuous-time and
discrete-time systems. Conversions between various model
representations are provided. Time responses, frequency responses,
and root loci can be computed and graphed. Other functions allow pole
placement, optimal control, and estimation. Finally, this product is open
and extensible. You can create custom M-files to suit your particular
application.

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MATLAB Code for display Of Uncompensated
open Loop system
close all
clear all
................%DC Torquer
n1=1;
Kt =[1.7264];
d1 =[8.8e-3 13];
tf1=tf(Kt,d1);
................%Plant
n2 =[1];
d2=[0.3 0.94];
tf2= tf(n2, d2);
.................%Gyro parameters
fg = 100;
wg = 2*pi*fg;
zeta = 0.7;
n3=[wg^2];
d3=[1 2*zeta*wg wg^2];
tf3= tf(n3,d3);
..................%open loop system
[numf1,denf1] = series(n1,d1,n2,d2);
[numf2,denf2] = series(numf1,denf1,n3,d3);
tf4= tf(numf2,denf2);
f = logspace(-1,3,100);
w = 2*pi*f;
title('open loop plot');
[mag,ph]=bode(numf2,denf2,w);
dbmagol = 20*log10(mag);
figure(1),subplot(2,1,1),semilogx(f,dbmagol)
title('Uncompensated Curve Open loop plot of
plant'),grid on
ylabel('mag (in dB)')
subplot(2,1,2),semilogx(f,ph)
ylabel('phase (in deg)')
xlabel('freq (in Hz)'),grid on

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Fig: Uncompensated Open Loop System
From the above given Bode plot of the uncompensated system, the
descriptionof various stability margins is given as follows:-
 Gain Margin = 67.6 rad/s
 Phase Margin =infinity
From the above calculated data, it is clear that the given open loop
system is highly unstable and is obviously not suitable for a stable
control system required with the desired performancespecifications.
Hence, there is a need of implementing a compensator design which
when cascaded with the given uncompensated system will result in a
stable compensatedsystem with the desired performance specifications
Implementation of the Compensator Design
The first step in carrying out a compensatordesign work is to carefully
study the given frequencyresponse data and the stability margins to be
achieved.
Following are the details of the desired performance specifications of the
control system:

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 Phase Margin = 30-70 degrees
 Gain Margin >= 6dB
 Band width > 15Hz
From the above given data, following interpretations are made:
At w=1 rad/s , the desired Gain is about 40 dB, so adding a lag
compensator with a suitable gain which will act as a low pass filter can
achieve the desired gain at w=1 rad/s and moreover it will lower the gain
at high frequencies in order to decrease the gain cross over frequency.
But at the same time at high frequencies it will increase the lag in the
system which is already lagging at high frequencies which is not
required.
Adding a lead compensator can be a good option as it will add lead
angle to the system at higher frequencies which is highly desired in
order to achieve the phase margin requirement. But at the same time it
will act as a high pass filter and will add more gain at the higher
frequencies which is undesired as it is making the system highly
unstable. So, our requirement as depicted from the given Bode Plot is
that we require a compensator system which gives us the gain of about
40 dB at w=1rad/s and the gain should become constant over the
frequency range up to 10 rad/s and it should decrease rapidly in the
frequency range 10-100 rad/s, so that the graph cuts the 0 dB point at a
frequency where the phase angle is not so large and hence the desired
phase margin value is achieved. So, this calls for the installation of lag-
lead compensator whose parameters can be decided by carefully
observing the effects of adding a pole and a zero every time and at
every point.
From the careful analysis and study, the following are the details of the
location and number of poles and zeros of the compensator which are
making the overall system suitable for the desired performance
specifications.
Following is the table of poles and zeroes added:

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Sl. No. Zero/Pole
added
Nature of
zero/pole
Frequency Compensator
Gain
1. Zero Real 3.42
K=9010
2. Pole Real 0.62
3. Zero Real 3.97
4. Pole Real 0.51
MATLAB Code for Compensator Design
....................%Compensator
gain= 9010;
nc1=[1/(2*pi*3.42) 1];
dc1=[1/(2*pi*0.62) 1];
nc2=[1/(2*pi*3.97) 1];
dc2=[1/(2*pi*0.51) 1];
[nc,dc]=series(gain*numf2,denf2,nc1,dc1);
[ncf,dcf]=series(nc,dc,nc2,dc2);
[mc,pc]=bode(ncf,dcf,w);
tf_total=tf(ncf,dcf);
mdb=20*log10(mc);
figure(2),subplot(2,1,1),semilogx(f,mdb),grid
title('Compensated bode plot-stab loop')
xlabel('Frquency in Hz'),ylabel('mag in db')
subplot(2,1,2),semilogx(f,pc),grid
xlabel('Frquency in Hz'),ylabel('phase in deg.')
figure(3), margin(tf_total)
numc=[0.00188 0.087 1]
denc=[0.0806 0.57 1]
tfcomp= tf(numc,denc

LOS STABILISATION
Fig: Compensated System
MATLAB Code for Difference between
Uncompensated and Compensated Open Loop
System Design
...................%Uncompensated and Compensated
open loop
figure(4),subplot(2,1,1),semilogx(f,dbmagol,'-
b',f,mdb,'-r'),grid,
title('compensated & uncompensated open loop curve')
ylabel('mag in dB')
text(1,-10,'uncompensated')
text(1,60,'compensated')
subplot(2,1,2),semilogx(f,ph, '-b',f,pc,'-r'),grid,
title('Compensated open loop phase curve')
xlabel('frequency in Hz'),ylabel('phase in deg')
text(10,-20,'uncompensated')
text(1,-220,'compensated')

LOS STABILISATION
Fig: Uncompensated and Compensated Open Loop System
MATLAB Code for Compensated Closed Loop
System Design
tf_fb3=feedback(tf_total,1,-1);
[numfb,denfb]=tfdata(tf_fb3,'v');
[magfb,phfb]=bode(numfb,denfb,w);
magfbdb=20*log10(magfb);
figure(6),subplot(2,1,1),semilogx(f,magfbdb),grid,
title('compensated close loop mag curve')
ylabel('mag in dB')
subplot(2,1,2),semilogx(f,phfb),grid,
title('Compensated close loop phase curve')
xlabel('frequency in Hz'),ylabel('phase in deg')
[magfbdb,phfb,f']

LOS STABILISATION
Fig: Compensated Closed Loop System
Conclusions
From the above Bode Plots of the compensated open loop system,
following interpretations are made:
Gain CrossoverFrequency(fg) = 61.3 dB
Phase angle at fg = (-130) degree
Phase Margin = 47.9 degree
Phase CrossoverFrequency(fp) = 474 rad/s
Gain Margin = 20.5 dB
The above data depicts that both, phase and gain margins are positive
and the desired values which show that the compensated system is now
stable. This compensated system can be now physically realized.

LOS STABILISATION
References
1. Modern Control Engineering by K.OGATA
2. Control Systems Engineering by I.J. Nagrath & M.Gopal
3. Control System by B.S.Manke
4. www.Mathworks.in
5. www.google.com
6. www.wikipedia.com

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