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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.