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UNIVERSITY OF ENGINEERING AND TECHNOLOGY
TAXILA
2K11 MECHANICAL ENGINEERING
CONTROL SYSTEM ENGINEERING
Submitted By: Submitted To :
QAMAR UZ ZAMAN (11-ME-10) SIR. SAJJAD SABIR
WALEED AZHAR (11-ME-91)
M. USMAN GHANI (11-ME-121)
MUHAMMAD ANSAR (11-ME-127)
ABDUL BASIT JAMA (11-ME-205)
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Antenna Positioning Control System
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ABSTRACT
We have described the design and construction of a
human-controlled Antenna
Positioning Control System. We analyzed the open loop
characteristics of the system and
found the transfer function for this system. We have also
determined the step loop
response for this system in MATLAB.
Our suggested design to this system is to implement a
Potentiometer with a 10 volts
power supply through a step-down AC transformer, followed by a
Bridge Rectifier ahead
of the Power Amplifier but after the Preamplifier. This
potentiometer will control the
rotational speed of this antenna system. The exact velocity is
achieved by using gearing
mechanism with the motor and driven shaft. The potentiometer
will allow us to rotate the
antenna at desired speed to get the desired angle of the
antenna.
We have not studied the close loop response for this system, but
it can also be
implemented by adding a feedback potentiometer with the antenna.
This is done to
minimize the error and to enhance the stability of the system.
For our system we have
skipped the feedback potentiometer as the system would become
sophisticated and more
complex. We have used visual inspection to observe if the
antenna has turned to the
desired angle or not, without using any feedback.
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TABLE OF CONTENTS
1. INTRODUCTION........... 1
2. MATHEMATICAL
MODEL.....................................................................................
2
2.1 Analysis..2
2.2
Subsystems....................................................................................................
4
2.2.1 Subsystem 1............ 6
2.2.2 Subsystem 2.... 6
2.2.3 Subsystem 3 ........... 6
2.2.4 Subsystem 4........ 7
2.3 Open loop System Transfer Function.7
2.3.1 Input potentiometer......8
2.3.2 Pre amplifier.....8
2.3.3 Power
Amplifier..............................................................................
8
2.3.4 Motor &
Load..................................................................................
8
2.4 Step Response of Open Loop
System.............................................................
9
2.4.1 MATLAB
Coding...........................................................................10
2.4.2 Simulation
Results.........................................................................
10
2.5 Damping Ratio & Natural Frequency
Calculations...................................... 11
3.
RESULTS...................................................................................................................
12
4. IMPLEMENTATION..13
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1. INTRODUCTION
An antenna positioning control system converts a position
command via a potentiometer
to a position output on the antenna mounted on the driven gear
shaft. Position control
systems find widespread applications in antennas, robot arms,
and computer disk drives.
The radio telescope antenna is one example of a system that uses
position control
systems. In this section, we will look in detail at an antenna
position control system that
could be used to position an antenna.
We will see how the system works and how the rotational speed of
antenna can be
controlled. The discussion here will be on a qualitative level,
with the objective of
getting an sensitive feeling for the system with which we will
be dealing. A more
detailed layout and schematic is shown in the attached figure
below and some figures
also show a functional block diagram of the system. The transfer
functions are shown
above the blocks, and the required hardware is indicated inside
the blocks.
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2. MATHEMATICAL MODEL
2.1 Analysis
The project was split into four distinct sections and analyzed
by section. Matlab was the
primary tool used for the analysis and all of the modeling.
Below is the analysis of the
control system; separated by section.
There are 4 subsystems of the overall system, each with its
associated transfer function.
These are described both in the schematic and the given block
diagram (Figure 1).
Figure 1 Provided Block Diagram
Figure 2 Schemetic Diagram
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There are many variables used in the following sections to
represent significant inputs,
outputs, signals etc. A quick reference is included below to
define all used variables.
Schematic Parameters
Parameter Definition
V Voltage across Potentiometer [Volts]
N Turns of potentiometer
K Preamplifier gain
K1 Power Amplifier Gain
a Power Amplifier pole
Ra Motor Resistance [ohms]
Ja Motor Inertial constant [kg-m2]
Da Motor Dampening constant [N-m
s/rad]
Kb Back EMF constant [V-s/rad]
Kt Motor Torque constant [N-m/A]
N1 Gear teeth
N2 Gear teeth
JL Load inertial constant [kg-m2]
DL Load inertial constant [N-m s/rad]
Block Diagram Parameters
Parameter Definition
K Preamplifier gain
K1 Power Amplifier gain
a Power Amplifier pole
Km Motor and load gain
am Motor and load pole
Kg Gear ratio
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2.2 SUB-SYSTEMS
There are 4 subsystems of the overall system, each with its
associated transfer function.
These are described both in the schematic and the given block
diagram (Figure 3).
Figure 3 Block diagram
SUBSYTEM INPUT OUTPUT
Input Potentiometer
Angular rotation from the
user
i (t)
Voltage to pre amplifier
Vi (t)
Pre Amplifier Voltage from potentiometer
Ve (t)= Vi (t)
Voltage to power amplifier
Vp (t)
Power Amplifier Voltage from pre amplifier
Vp (t)
Voltage to motor
Ve (t)
Motor Voltage from power amplifier Angular rotation to load
o (t)
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BLOCK DIAGRAM PARAMETERS
PARAMETERS VALUES
K 1
K1 2
a 2
Km 0.8
am 1.32
Kg 0.383
SCHEMATIC PARAMETERS
PARAMETERS VALUES
V 10
n 10
K 1
K1 2
a 2
Ra 7.5
Ja 0.02
Da 0.01
Kb 0.5
Kt 0.5
N1 23
N2 60
JL 1
DL 1
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2.2.1 Subsystem 1
The input and feedback potentiometer each have an associated
transfer function, in the
form of a gain. The potentiometer changes the input angle i (s)
, to a voltage, Vi(s).
This ratio is described by the value Kpot-i. This value is
computed by Equation 1. The
value of this gain is determined by the voltage applied to the
potentiometer and the
number of turns the potentiometer is built for, both of these
values are given in Table
Equation 1
2.2.2 Subsystem 2
The purpose of the preamplifier is to take the input signal
voltage and output a voltage
that the power amplifier can use. The Preamplifier is also
modeled by a gain that can be
specified by the design engineer to achieve a desired output.
The Preamplifier is a system
in which the input voltage is amplified by some gain K and
output as a voltage. The
resulting equation therefore is quite simple, as shown in
Equation 2.
Equation 2
2.2.3 Subsystem 3
The third subsystem is a Power Amplifier which takes the output
voltage from the
Preamplifier and converts it to a Voltage that is useable by the
motor. This requires the
Power Amplifier to output a significant amount of power,
something that the
Preamplifier is not capable of. The power amplifier type is
given in the design schematic
and the given block diagram. Also the value of K1 and a in the
transfer function are
given in the configuration data.
Equation 3
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2.2.4 Subsystem 4.
After the Power Amplifier is the motor, attached to the gears
and load, which in this case
is an antenna. All of these items must be considered when
computing the transfer
function of the resulting mechanical system. Motor used is a DC
motor, having the
following transfer function.
Equation 4
Where Km is the motor load gain and am is the motor load
pole.
2.3 Open Loop System Transfer Function:
Pre-amplifier &
Power-Amplifier
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2.3.1 Input potentiometer:
Voltage from step-down transformer is 10 volts.
Turns on potentiometer are 5, so total angle of rotation is 5*2
= 10
2.3.2 Pre-amplifier:
2.3.3 Power-amplifier:
2.3.4 Motor & load:
Now putting the values in Km and am
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By putting in Equation 4:
2.4 Step Response of the Open Loop System
By block diagram reduction
The forward transfer function for angular velocity is,
Pre-amplifier &
Power Amplifier
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2.4.1 MATLAB Coding
'Antenna positioning control system'
num=0.613;
den=poly([-2 -1.32]);
G=tf(num,den)
step(G)
2.4.2 Simulation Results
ans = Antenna positioning control system
0.613
G = -------------------
s^2 + 3.32 s + 2.64
Continuous-time transfer function.
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2.5 n & Calculations:
By taking the Laplace Inverse
By simplifying the transfer function
2 n = 3.32
= 1.022
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3. RESULTS
Theoretically, the system shows a smooth step response in MATLAB
simulation. The
system is found to be stable under this transfer function. From
the value of damping ratio
that the system is Critically-damped since the value of damping
ratio is approximately
equal to one.
In real-time, we can turn the antenna at desired angle using the
potentiometer even if the
antenna setup is placed far away from the potentiometer
controller. The rotational speed
can also be altered by this potentiometer and there is a toggle
switch to reverse the motor
polarity to allow motor to rotate in clockwise as well as
anti-clockwise direction.
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4. IMPLEMENTATION
Position control system could be implemented to position various
systems. Input desire
angle can be given to any system and the system can align itself
according to the input.
This alignment can be in the form of rotational degrees as well
as linear position. Linear
position can be controlled with the help of Rack and Pinion
mechanism of gears. Linear
position control examples can be found in material handling
techniques and in
automotive power steering system.
This position control can be applied in many fields of
engineering such as in Robotic arm
control , Radar system , Dish antennas , Revolving CCTV cameras
and to control the
position of wicket gates in hydral power plants etc.