light tracking servomotor

8/19/2019 light tracking servomotor

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BIRLA INSTITUTE OF TECHNOLOGY, MESRA

RANCHI, JHARKHAND, INDIA

MINOR PROJECT ON

LIGHT TRACKING SERVO SYSTEM

BY-

AISHWARYA MISHRA (BE/10360/2012)

PIYUSH RANJAN (BE/10345/2012)

AKASH KUMAR (BE/10027/2012)

ELECTRICAL AND ELECTRONICS ENGINEERING

7th SEMESTER

GUIDED BY-

DR. (MRS.) S. CHAKRABORTY

ASSOCIATE PROFESSORPROJECT GUIDE

DEPT. OF EEE

BIT MESRA


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CERTIFICATE

This is to certify that the contents of this project report titled “Light Tracking

Servo System” is a bona fide work carried out by Akash Kumar (BE/10027/2012),

Piyush Ranjan (BE/10345/2012) and Aishwarya Mishra (BE/10360/2012); under

my guidance and supervision in partial fulfilment of the requirement for the

degree of Bachelor of Engineering in Electrical and Electronics Engineering.

The contents of this report have not been submitted earlier in any other formand I hereby commend them for their work.

DR. (MRS.) S CHAKRABORTY

ASSOCIATE PROFESSOR

PROJECT GUIDE

DEPT. OF EEE

BIT MESRA


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CERTIFICATE OF APPROVAL

The project titled ”light tracking servo system” carried out by

Mesers PIYUSH RANJAN, AKASH KUMAR and AISHWARYA

MISHRA, is hereby approved as creditable study of

engineering in Electrical and Electronics and is represented in

a satisfactory manner.It warrants its acceptance as a pre-requisite in partial

fulfilment in engineering for the award of BACHELOR OF

ENGINEERING in ELECTRICAL AND ELECTRONICS

ENGINEERING at Birla Institute of Technology, Mesra, Ranchi,

India.

Internal Examiner External Examiner

Dr.(Prof) R.C. Jha,

Professor and Head,

Department of EEE,

BIT Mesra, Ranchi


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ACKNOWLEDGEMENT

We express our deep sense of gratitude to our project supervisor

Dr.(Mrs). S Chakraborty, Professor, Department of EEE, under whose

guidance we were able to learn and applythe concepts presented in

this project. Their consistent supervision, constant inspiration and

invaluable guidance have been of immense help in carrying out this

project work with success.

A sense of indebtedness extends from core of our heart to Dr. R C Jha,

Professor and Head, Department of EEE for extending his facilities, and

giving valuable suggestions at all times for pursuing this course.

We are also thankful to staff and other faculties of our department for

their help and suggestions on our project.


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ATTENDANCE

NAME ROLL NO. TOTAL NO.

OF CLASSES

NO. OF

CLASSES

ATTENDED

PERCENTAGE

AKASH

KUMAR

PIYUSH

RANJAN

AISHWARYA

MISHRA

DR. (MRS.) S CHAKRABORTY

PROFESSOR

PROJECT GUIDE

DEPT. OF EEE

BIT MESRA


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PROGRAM EDUCATIONAL OBJECTIVES (PEO)-

1.To understand the fundamentals of Science in general and Electrical and

Electronics in particular to be able to analyse the problems with a futuristic

approach. 2. To be confident in solving real-life engineering problems.

3.To develop an attitude for identifying and undertaking developmental

work both in industry and the academic environment with emphasis on learning

so as to excel in competitions at the global level.

4.To nurture communication and interpersonal skills to be able to work well in

a team with a sense of ethics and moral responsibility for achieving goals.

PROGRAM OUTCOMES (PO)-A student shall:

a) Be competent in applying basic knowledge of science and

engineering to obtain solution to a multi-disciplinary problem. b) Gain knowledge of analyzing complex engineering problems.

c)

Be able to design system components and processes meeting allrules and regulations.

d) Be capable of undertaking suitable experiments or research methods

while solving a problem and would arrive at a conclusion after

interpreting the data and experimental results. e) Be confident in applying recent engineering practices and soft tools

along with other techniques and resources.


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COURSE OBJECTIVES-

1. Familiarize oneself with working and applications of servo motors.

2. To develop a light tracking servo system.

3.

To develop mathematical model of the given system.

4. To analyze qualitatively the response of the system to various parameter

changes.

5. To understand and implement various control techniques to better the

performance of the system in an industrial environment.

6. To be able to simulate the model in a software environment.

7. To be able to implement it in hardware.

COURSE OUTCOME-A student will be confident in-

1. Explaining the working and applications of servo motors.

2.

Developing a functional light tracking servo system.3. Developing a mathematical model of the system.

4. Analyzing the response of the system to various parameter changes.

5. Understanding and implementing various control techniques to

better the performance of the system in an industrial environment.

6. Analysing the control system, step response and finding out best

configuration which is at par with stability, efficiency and faster

response.


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Mapping between course outcomes and program

outcomes-

Pos

Course Outcomes

A B c D E

1

2 3 4

5

Mapping between course objectives and course outcomes-

Course outcomes

Course

objectives

1 2 3 4 5

1

2

3

4

5

6

7


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ABSTRACT

The project discusses a light tracking servo model which has been built to

simulate the movement of a light follower robot. A mathematical model is

developed and a qualitative comparison of the mathematical model and the

actual physical model is done to demonstrate the dynamics of a light tracking

servo system. A hardware model has been designed using the sensors and

servomotors which have been interfaced using a light tracking algorithm. Themathematical model has been adopted on the principle of servomechanism

using a motor run by amplification of error signal. The software platform used

for programming is Arduino (for algorithm) and Matlab (for simulation). Aim of

this project is to understand the principles that govern a control system and

using a physical example to explain the working of the system under various

conditions producing various responses.


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CONTENTS

1. INTRODUCTION

2. APPLICATIONS OF LIGHT TRACKING SERVO SYSTEMS

3. LITERATURE REVIEW

4. SPECIFICATIONS OF THE PROJECT

a) SERVOMOTOR

b) LIGHT DEPENDENT RESISTORSc) MICROCONTROLLER

5. STAGES OF THE PROJECT

6. ALGORITHM

7.RESULTS

8. MATHEMATICAL MODELLING OF THE SYSTEM

9.a) SIMULATION

b) HARDWARE DESIGN

10. CONCUSION

11. REFERENCES


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1. INTRODUCTION

A servo motor is a dc, ac, or brushless dc motor combined with a position sensing

device (e.g. a digital decoder). They are self-contained electrical devices that

rotate or push parts of a machine with great precision. Servos are found in many

places: from toys to home electronics to cars and airplanes. In a model car or

aircraft, servos move levers back and forth to control steering or adjust wing

surfaces. By rotating a shaft connected to the engine throttle, a servo regulates

the speed of a fuel-powered car or aircraft. Servos also appear behind the scenes

in devices we use every day. Electronic devices such as DVD and Blu-ray Disc

players use servos to extend or retract the disc trays. In 21st-century

automobiles, servos manage the car’s speed: The gas pedal, similar to the

volume control on a radio, sends an electrical signal that tells the car’s computer

how far down it is pressed. The car’s computer calculates that information and

other data from other sensors and sends a signal to the servo attached to the

throttle to adjust the engine speed. Commercial aircraft use servos and a related

hydraulic technology to push and pull just about everything in the plane. And of

course, robots might not exist without servos.


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2. APPLICATIONS OF LIGHT TRACKING

SERVO SYSTEMS

For use in light follower robots, servo systems are indispensable. Some of the

most important applications of light-tracking servo motors are-

a) Street lights

b) Alarm devices

c) To measure light intensity for applications that require greater precision

d) Cameras may use this technology to determine proper exposure time.

e) Laptops may use it in a circuit that varies screen brightness according to

ambient light conditions.

f) As solar tracking systems in photovoltaic panels to increase their

efficiency.


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3. LITERATURE REVIEW

Paul Batcheller in July 1992 wrote the “Analysis of Light Tracking servo

system. The paper discusses a light tracking servo model which has been

built to simulate the movement of a PV array. A mathematical model is

developed and a qualitative comparison of the mathematical model and

the actual physical model is done to demonstrate the dynamics of a light

tracking servo system. An overall transfer function for a permanent

magnet direct current (dc) motor was also developed. The motor transfer

function is used in the development of an overall transfer function for the

light tracking servo system. Using the overall transfer function, a

computer simulation program within Matlab is used to simulate the

dynamics of the servo system. A qualitative analysis of the Matlab results

and the dynamics of the working physical model are compared to clearly

illustrate the important dynamics of the system.

A paper on “Solar Photovoltaic Servo Tracking Controlled System” was

presented by Murad Shibli Abu Dhabi Polytechnic, Institute of Applied

Technologies, UAE. The design of the system is based on the fuzzy

reasoning applied to crisp sets. In this case, it can be easily implemented

on general purpose microprocessor systems. Four light sensitive devices,

such as LDR, photodiodes or phototransistors are mounted on the solar

panel and placed in an enclosure. The four light detectors are screened

from each other by opaque surfaces. Each pair of the light sensors is used

to inform the controller on the orientation of the solar panel vertically and

horizontally respectively.

Daniel A. Pritchard had given the design, development, and evaluation of

a microcomputer-based solar tracking and control system (TACS) in 1983.


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It was capable of maintaining the peak power position of a photovoltaic

(PV) array by adjusting the load on the array for maximum efficiency and

changed the position of the array relative to the sun. At large PV array

system installations, inverters were used to convert the dc electrical

output to ac for power grid compatibility. Adjustment of the inverter or

load for maximum array output was one function performed by the

tracking and control system. Another important function of the system

was the tracking of the sun, often a necessity for concentrating arrays.

The TACS also minimized several other problems associated with

conventional shadow-band sun trackers such as their susceptibility to

dust and dirt that might cause drift in solar alignment. It also minimized

effects of structural war page or sag to which large arrays might be

subjected during the day. Array positioning was controlled by Q single-

board computer used with a specially designed input output board. An

orderly method of stepped movements and the finding of new peakpower points was implemented. This maximum power positioning

concept was tested using a small two-axis tracking concentrator array. A

real-time profile of the TACS activity was produced and the data analysis

showed a deviation in maximum power of less than 1% during the day

after accounting for other variations [Daniel A. Pritchard, 1983].

Ashok Kumar Saxena and V. Dutta had designed a versatile

microprocessor based controller for solar tracking in 1990 .Controller had

the capability of acquiring photovoltaic and metereological data from a

photovoltaic system and controlled the battery/load. These features were

useful in autonomous PV systems that were installed for system control

as well as monitoring in remote areas .Solar tracking was achieved in both

open loop as well as closed loop modes. The controller was totally


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automatic and did not require any operator interference unless needed

[Ashok Kumar Saxena and V.Dutta, 1990].

A. Konar and A.K. Mandal had given a microprocessor based automatic

position control scheme in 1991. They had designed for controlling the

azimuth angle of an optimally tilted photovoltaic flat type solar panel or a

cylindrical parabolic reflector to get the illuminating surface appropriately

positioned for the collection of maximum solar irradiance. The proposed

system resulted in saving of energy . The tracking system was not

constrained by the geographical location of installation of the solar panel

since it was designed for searching the MSI in the whole azimuth angle of

360” during the locking cycle. Temporal variations in environmental

parameters caused by fog, rain etc., at a distance from the location where

panel was mounted, did not affect proper direction finding [A. Konar and

A.K Mandal, 1991].

A. Zeroual et al. had designed an automatic sun-tracker system foroptimum solar energy collection in 1997. They used electro-optical

sensors for sun finding and a microprocessor controller unit for data

processing and for control of the mechanical drive system. This system

allowed solar energy collectors to follow the sun position for optimum

efficiency. The system had been applied to control a water heating

parabolic solar system for domestic uses. Many parameters had been

controlled for system security such as temperature, pressure and wind

velocity. The system had been tested for a long period in variable

illumination. The result showed that it operated satisfactorily with high

accuracy [A.Zeroual et al., 1997].

Z.G. Piao et al. proposed a 150W solar tracking system in 2003. In solar

tracking system, they used DC motors, special motors like stepper motors,


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servo motors, real time actuators, to operate moving parts. DC motors

were normally used to operate solar tracking system but it was highly

expensive to maintain and repair. The system was designed as the normal

line of the solar cell always moved parallel to the ray of the sun. [Z.G. Piao

et al., 2003].

Jing-Min Wang and Chia-Liang Lu presented a novel and a simple control

implementation of a Sun tracker that employed a single dual-axis AC

motor to follow the Sun and used a stand-alone PV inverter to power the

entire system. The proposed one-motor design was simple and self-

contained, and did not require programming and a computer interface. A

laboratory prototype has been successfully built and tested to verify the

effectiveness of the control implementation. Experiment results indicated

that the developed system increased the energy gain up to 28.31% for a

partly cloudy day. The proposed methodology is an innovation so far. It

achieves the following attractive features: (1) a simple and cost-effectivecontrol implementation, (2) a stand-alone PV inverter to power the entire

system, (3) ability to move the two axes simultaneously within their

respective ranges, (4) ability to adjust the tracking accuracy, and (5)

applicable to moving platforms with the Sun tracker. [Jing-Min

Wang and Chia-Liang Lu, 20


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4. PROJECT COMPONENT AND THEIR

SPECIFICATIONS

a) LIGHT DEPENDENT RESISTORS-

LDRs or Light Dependent Resistors are very useful especially in light/dark sensor

circuits. Normally the resistance of an LDR is very high, sometimes as high as

10000 ohms, but when they are illuminated with light resistance drops

dramatically.

A light dependent resistor is a small, round semiconductor. Light dependent

resistors are used to re-charge a light during different changes in the light, or

they are made to turn a light on during certain changes in lights. One of the most

common uses for light dependent resistors is in traffic lights. The light

dependent resistor controls a built in heater inside the traffic light, and causes

it to recharge over night so that the light never dies. Other common places to

find light dependent resistors are in: infrared detectors, clocks and security


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alarms. One major benefit of LDRs is that they consume less power. It is made

of cadmium sulphide compound which has the property of varying resistance

with intensity of light. LDR or light dependent resistor is the main sensing

element in the dual axis solar tracker we have worked upon. We plan to use 3

or 5 LDRs that are positioned at the 3 corners of the solar plate.

b) SERVOMOTOR-

This is nothing but a simple electrical motor, controlled with the help of

servomechanism. If the motor as controlled device, associated withservomechanism is DC motor, then it is commonly known DC Servo Motor. If the

controlled motor is operated by AC, it is called AC Servo Motor. A servo system

mainly consists of three basic components - a controlled device, a output sensor,

a feedback system. This is an automatic closed loop control system. Here instead

of controlling a device by applying variable input signal, the device is controlled

by a feedback signal generated by comparing output signal and reference input

signal. When reference input signal or command signal is applied to the system,

it is compared with output reference signal of the system produced by outputsensor, and a third signal produced by feedback system. This third signal acts as

input signal of controlled device. This input signal to the device presents as long

as there is a logical difference between reference input signal and output signal

of the system. After the device achieves its desired output, there will be no

longer logical difference between reference input signal and reference output

signal of the system. Then, third signal produced by comparing these above said

signals will not remain enough to operate the device further and to produce

further output of the system until the next reference input signal or commandsignal is applied to the system. Hence the primary task of a servomechanism is

to maintain the output of a system at the desired value in the presence of

disturbances. A servo motor is basically a DC motor(in some special cases it is AC

motor) along with some other special purpose components that make a DC

motor a servo. In a servo unit, you will find a small DC motor, a potentiometer,

gear arrangement and an intelligent circuitry. The intelligent circuitry along with

the potentiometer makes the servo to rotate according to our wishes.As we

know, a small DC motor will rotate with high speed but the torque generated byits rotation will not be enough to move even a light load. This is where the gear


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system inside a servomechanism comes into picture. The gear mechanism will

take high input speed of the motor (fast) and at the output; we will get a output

speed which is slower than original input speed but more practical and widely

applicable.

Say at initial position of servo motor shaft, the position of the potentiometer

knob is such that there is no electrical signal generated at the output port of the

potentiometer. This output port of the potentiometer is connected with one of

the input terminals of the error detector amplifier. Now an electrical signal is

given to another input terminal of the error detector amplifier. Now difference

between these two signals, one comes from potentiometer and another comes

from external source will be amplified in the error detector amplifier and feedsthe DC motor. This amplified error signal acts as the input power of the dc motor

and the motor starts rotating in desired direction. As the motor shaft progresses

the potentiometer knob also rotates as it is coupled with motor shaft with help

of gear arrangement. As the position of the potentiometer knob changes there

will be an electrical signal produced at the potentiometer port. As the angular

position of the potentiometer knob progresses the output or feedback signal

increases. After desired angular position of motor shaft the potentiometer knob

is reaches at such position the electrical signal generated in the potentiometerbecomes same as of external electrical signal given to amplifier. At this

condition, there will be no output signal from the amplifier to the motor input

as there is no difference between external applied signal and the signal

generated at potentiometer. As the input signal to the motor is nil at that

position, the motor stops rotating. This is how a simple conceptual servo motor

works.


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c) ARDUINO MICROCONTROLLER-

Arduino/Genuino Uno is a microcontroller board based on the ATmega328P. It

has 14 digital input/output pins (of which 6 can be used as PWM outputs), 6

analog inputs, a 16 MHz quartz crystal, a USB connection, a power jack, an ICSP

header and a reset button. It contains everything needed to support the

microcontroller; simply connect it to a computer with a USB cable or power it

with a AC-to-DC adapter or battery to get started.. You can tinker with your UNO

without worrying too much about doing something wrong, worst case scenario

you can replace the chip for a few dollars and start over again.

"Uno" means one in Italian and was chosen to mark the release of Arduino

Software (IDE) 1.0. The Uno board and version 1.0 of Arduino Software (IDE)

were the reference versions of Arduino now evolved to newer releases. The Uno

board is the first in a series of USB Arduino boards, and the reference model forthe Arduino platform; for an extensive list of current, past or outdated boards

see the Arduino index of boards. The Arduino/Genuino Uno can be programmed

with the Arduino Software (IDE). Select "Arduino/Genuino Uno" from the Tools

> Board menu (according to the microcontroller on your board). The ATmega328

on the Arduino/Genuino Uno comes preprogrammed with a boot loader that

allows you to upload new code to it without the use of an external hardware

programmer. It communicates using the original STK500 protocol.


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TECHNICAL SPECIFICATIONS

LDR: Range of 100 ohms -10k ohms

SERVOMOTOR:

Weight 55g

Dimensions40.7 x 19.7 x 42.9

mm

Stall Torque8.5 kg cm (4.8V),

10 kg cm (6V)

Operating

Speed

0.20 sec/60d

(4.8V), 0.16

sec/60d (6V)

Operating

Voltage4.8 - 7.2 V

Temperature

Range 0 - 55 C

ARDUINO MICROCONTROLLER:

Microcontroller ATmega328P

Operating Voltage 5V

Input Voltage(recommended)

7-12V

Input Voltage (limit) 6-20V

Digital I/O Pins14 (of which 6 provide PWM

output)


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PWM Digital I/O Pins 6

Analog Input Pins 6

DC Current per I/O Pin 20 mA

DC Current for 3.3V Pin 50 mA

Flash Memory

32 KB (ATmega328P)

of which 0.5 KB used by

bootloader

SRAM 2 KB (ATmega328P)

EEPROM 1 KB (ATmega328P)

Clock Speed 16 MHz

Length 68.6 mm

Width 53.4 mm

Weight 25


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5. OPERATIONS UNDERTAKEN IN THE PROJECT

1. Signal processing: This stage involves conversion of analog signal

obtained from the sensor to a digital value using analog to digital convertafter amplification and filtering of noises and then converting these digital

values into the values that can be used to determine the intensity. 2. Algorithm: We have developed algorithm to compare the intensity

values received from each of the 4 sensors, find the average values for

top, down, left and right faces of the surface which will rotate in the

direction of maximum intensity. Then we find out the difference between

average values for each axis and compare it with a threshold voltage level

(or digital value of the same) which is adjustable according to the

environment (dark or bright so that fine control can be obtained). If the

difference exceeds a threshold value in a given direction, the motor will

turn the surface in the same direction until average intensity is

normalised.

3. Mathematical modelling: Once the information about theposition is received from microcontroller the mathematical model

developed will convert the position instructed by the controller intoactual position required. Mathematical model is only a theoretical

representation supported by some calculations done on the basis of the

working of the light follower and it shows how the motor will respond

actually( by performing a movement) when the instruction about the

motion is given to it.

4. Simulation: Then we use the mathematical model to analyse whatwill happen if we take various case of the constants and gain values by

running them through a program and finding out the response of thesystem. The simulation will show what will be the most suitable

configuration parameters for designing the hardware.

5. Hardware Design: This involves using the values obtained fromsimulation to design a suitable hardware that can run to produce desired

result. The hardware design also involves making an efficient design such

that the performance of each of the sensors and actuators used in

modelling is efficient and according to the simulation.


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6. ALGORITHM

We have used algorithm to compare the intensity values received from each

of the 4 sensors, find the average values for top, down, left and right faces of

the surface which will rotate in the direction of maximum intensity. Then we

find out the difference between average values for each axis and compare it

with a threshold voltage level (or digital value of the same) which is adjustable

according to the environment (dark or bright so that fine control can be

obtained). If the difference exceeds a threshold value in a given direction, the

motor will turn the surface in the same direction until average intensity is

normalised. Following is the flow chart for algorithm.

No No

Yes Yes

No Yes Yes No

START

Read

top,left,down,righ

t sensors

Calculate avt,

avl,avd &avr

Dvrt= |avt-avd| Dhrz= |avl-avr|

Dvrt>thre

shold?

Dhrz>thr

eshold?

Avt>

Avl>

Pos=pos+1 Pos2=pos2

+1

Pos=pos-1 Pos2=pos2-

1


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PROGRAM FOR ALGORITHM

#include

int ldrlt = 0; //LDR top leftint ldrrt = 1; //LDR top rigt

int ldrld = 2; //LDR down left

int ldrrd = 3; //ldr down rigt

int pos2=0;

int pos=0;

Servo myservo;

Servo myservo2;

void setup()

{

Serial.begin(9600);

// servo connections

// name.attacht(pin);

// horizontal.attach(9);

//ertical.attach(10);

myservo.attach(9);

myservo2.attach(10);

}

void loop()

{

int lt = analogRead(ldrlt); // top left

int rt = analogRead(ldrrt); // top

right

int ld = analogRead(ldrld); // downleft

int rd = analogRead(ldrrd); // down

rigt

//int dtime = analogRead(4)/20; //

read potentiometers

int tol = analogRead(5);

int avt = (lt + rt) / 2; // average value

top

int avd = (ld + rd) / 2; // average

value down

int avl = (lt + ld) / 2; // average value

left

int avr = (rt + rd) / 2; // average

value right

lt=lt-200;

ld=ld-370;

int dvert = avt - avd; // check the

diffirence of up and down

int dhoriz = avl - avr;// check the

diffirence og left and rigt

/*Serial.println("top left:");

Serial.println(lt);

delay(1000);

Serial.println("top right:");

Serial.println(rt);

delay(1000);


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Serial.println("down left:");

Serial.println(ld);

delay(1000);

Serial.println("down right:");

Serial.println(rd);

delay(1000);*/

Serial.println("av top:");

Serial.println(avt);

delay(10);

Serial.println("av down:");

Serial.println(avd);

delay(10);

Serial.println("av left:");

Serial.println(avl);

delay(10);

Serial.println("av right:");

Serial.println(avr);

delay(10);

Serial.println("diffvert:");

Serial.println(dvert);

delay(10);

Serial.println("diffhoriz:");

Serial.println(dhoriz);

delay(10);

Serial.println("tolerance");

Serial.println(tol);

if (-1*tol > dvert || dvert > tol) //

check if the diffirence is in the

tolerance else change vertical angle

{

if (avt > avd)

{

pos=++pos;

myservo.write(pos);

if (pos > 180)

{

pos = 180;

}

}

else if (avt < avd)

{

pos= --pos;

myservo.write(pos);

if (pos < 0)

{

pos= 0;

}

}

Serial.println("position:");

Serial.println(pos);

}

delay(10);


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if (-1*tol > dhoriz || dhoriz > tol) //

check if the diffirence is in the

tolerance else change vertical angle

{

if (avl > avr)

{

pos2=++pos2;

myservo2.write(pos2);

if (pos2 > 180)

{

pos2 = 180;

}

}

else if (avl< avr)

{

pos2= --pos2;

myservo2.write(pos2);

if (pos2 < 0)

{

pos2= 0;

}

}

Serial.println("position2:");

Serial.println(pos2);

}


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7.RESULTS

The input of the sensor going to Arduino microcontroller was also given as an

input to the Matlab program for a given period of sample time and intensity

values and corresponding position values were recorded which have been

shown through following figures-

Fig 1:Intensity vs sample time for sensors and the average values

Fig2: Intensity values for up and down sensors and corresponding position values (scaled)


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Fig3: Position and intensity curve red line indcating’down’ and geen indicating’up’

Fig 4&5: The graph for left and right movement


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Fig 5:The sensor output values in digital value


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8. MATHEMATICAL MODEL OF THE SYSTEM

Once the information about the position is received from microcontroller the

mathematical model will convert the position instructed by the controller into

actual position required. Mathematical model is only a theoretical

representation supported by some calculations done on the basis of the working

of the light follower and it shows how the motor will respond actually( by

performing a movement) when the instruction about the motion is given to it.

An overall transfer function is developed for the light tracking system by using

block diagram algebra on the transfer functions of the photo detecting circuit,

amplifier, and motor. The overall gain of servomotor which amplifies the error

signal can be considered as a single variable K, where K is a proportionality

constant with units of volts per radian. K can be adjusted using the voltage

divider circuit that sends the signal to the microcontroller.

A frequency domain block diagram for a position loop servo system is easily

developed from the transfer functions of the motor and gain of the photo

detector circuit and amplifier. Following the signal from the input to the output,

a rotational error from the displacement of the photoresistors results in an error

voltage. This voltage is converted to a rotational velocity by the motor. The

rotational position output is related to the velocity of the motor by integratingthe velocity or, in the frequency domain, by dividing by s. The output position is,

in effect, subtracted from the input position, which is represented by a direct

line from the output to a summing junction with a negative sign into the

junction.

The parameters used in the mathematical model are-

E(s) = ΘL(s)-ΘA(s)

Va(s) = KE(s)

Wa(s) = Gm(s)KE(s)

ΘA(s) = Wa(s)/s= Go(s)E(s)

ΘA(s) = (Go(s)/(1+Go(s)))*ΘL(s)=Gc(s)*ΘL(s)

ΘL(s) is light position( position given by microcontroller) in radians; ΘA(s) is

position of panel in radians; K= proportional gain achieved by the gain of

amplification of the error signal(internal gain of analog servomotor); Va(s) is theamplified voltage applied to the motor used in the servomechanism; E(s) is the


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error signal; Gm(s) is the motor transfer function; Wa is the angular velocity;Go(s)

is open loop t.f.;Gc(s) is closed loop t.f.

Block diagram using the following parameter looks like-

The equivalent electrical circuit of a dc motor is shown below. It can be

represented by a voltage source (Va) across the coil of the armature. The

electrical equivalent of the armature coil can be described by an inductance

(La) in series with a resistance (Ra) in series with an induced voltage (Vc) which

opposes the voltage source. The induced voltage is generated by the rotation

of the electrical coil through the fixed flux lines of the permanent magnets.

This voltage is often referred to as the back emf (electromotive force).

Electrical Characteristics:

Va – VRa – VLa - Vc =0

VRa= ia Ra

VLa= La di/dt

Vc= KvWa

Mechanical Characteristics:

Performing an energy balance on the system, the sum of the torques of themotor must equal zero. Therefore,


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Te-Tw-Tw’-TL=0

where Te is the electromagnetic torque, Tw ' is the torque due to rotational

acceleration of the rotor, Tw is the torque produced from the velocity of the

rotor, and TL is the torque of the mechanical load. The electromagnetic torqueis proportional to the current through the armature winding and can be

written as

Te = kt ia

where kt is the torque constant and like the velocity constant is dependent on

the flux density of the fixed magnets, the reluctance of the iron core, and the

number of turns in the armature winding. Tw ' can be written as

Tw’= J dWa/dt

where J is the inertia of the rotor and the equivalent mechanical load. The

torque associated with the velocity is written as

Tw=BWa

where B is the damping coefficient associated with the mechanical rotational

system of the machine.

Va- ia Ra - La di/dt – KvWa = 0 :Eqn1

kt ia -Jdwa/dt- Bwa-TL=0 :Eqn2

Transfer Function:

sIa(s)- ia(0) = -Ra Ia(s) /La - KvΘa(s) /La- Va(s) /La

sΘa(s) – Wa(s)=kt Ia(s)/J - B Θa(s)/J – TL(s)/J

Therefore,

Θa(s)=(- kt Ia(s) – TL(s))/(Js+B)

Ia(s) =(- KvΘa(s)+ Va(s))/( Las+ Ra)

In the case of a sun tracking servo system, the only load torque to be

concerned with is the friction in the system, which is relatively constant while


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the motor is moving. Since the change in TL is zero, it does not need to appear

in the block diagram.

Fig :Block diagram of motor

Fig: Reduced block diagram of motor

Fig: Servomechanism with motor & reduced block diagram of servomotor


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9. a) SIMULATION

The simulation was done using a Matlab program where the final transfer

function (in the last figure) was taken and its parameters were used for

designing a system with a similar transfer function.

The value of Ra, La, Jeq & Beq were taken from data sheet of the

servomotor we bought ( V3003 Vega Robotics analog servo) and put in

the logic.

The values of K, Kp & Kt were not known so they were found out using

trial method where an initial gain of K , Kp & Kt was considered to be 1

and several adjustments were made while finding out the value.

Optimum value of K, Kp & Kt was selected and the step response and bode

plot was found out.

These values were taken and put into a Simulink model (model was made

only on the basis of mathematical equation and only the values were used

so the output is not accurate; code was not used to generate the model

nor it was designed using any electrical parameters to behave like an

electrical circuit; it was only a block diagram representation of the

transfer function we obtained).

The simulation was done only for one axis as movement of both the axis

is not linked through any mathematical equation. For this purpose it was

considered that there is no magnetic coupling between two motor

systems so that individuals results for single axis could be obtained

easily.

Results of simulation are shown below:-

Fig: User Interface of the program


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Kp=1,Kt=1, K=1(low gain),25(mid),50(high)

Fig Kp=.5, Kt=.5, K=1,25,50

Fig: Kp=.5, Kt=.1


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Fig: Kp=.1, Kt=.1

Fif: Kp=.01, Kt=.01

Fig: Input position values to Simulink for Kp=.1, Kt=.1, K=20-30

Fig: Output values

It is seen that for unity gain values of K,Kv&Kt, system is highly over

damped and response time & rise time is very large. This will make

servomechanism slow to the response for the instruction.


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Again for higher values of K, the response improves but it is still highly

over damped.

Again by changing the values of Kv& Kt to median values we see that

response is still over damped and slow.

At the values Kv=.1, Kt=.1 the system is over damped for low values of

gain, just underdamped for median values and underdamped severely for

high values. So the faster rise time is achieved in high values (around 70)

but response time falls behind the median value response time (around

25). Since the value of response time is important to us so median value

of gain can be used with given values of Kv& Kt for the design.

The Simulink response for the same values shows extra over damping due

to non- linearity of elements used in the block and it has only been used

to show how the motor will produce an output in response to change of

input. It is seen that at even these values of step response there will be

some oscillation.


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b) HARDWARE DESIGN

The entire circuitry rests on the rectangular panel of dimension

55*170*14 mm.

4 sensors for detecting light were placed on the four corners of the panel.

The sensor were placed in accordance with a resistance of high value to

form a potential divider circuit across which voltage could be taken(range

of voltage 0-5 V)

The wires from four sensors were brought to 4 analog pins of the

microcontroller which uses an internal ADC to convert the analog voltage

o/p of sensor to a digital value in the range of 0-1023 corresponding to 0-

5 V.

2 potentiometers were used – one pot for controlling the value of

threshold to which the logic would respond which could be adjusted

according to ambient light and the other for controlling the time delay

after which the intensity value would be taken again.

The supply for motors was given using 12V adapter circuit.

To prevent activation of all sensors from a distant source of light, 4

cardboard pillars were used surrounding the sensor in a semi-circle such

that when light fell on one sensors, the pillars would cast a shadow on the

other sensors causing them to deactivate. Same could be used for any of

the two sensors causing a shadow on the other two sensors.


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10. CONCLUSION

An algorithm for the project was developed. This algorithm was simulatedin Matlab environment and the intensity vs position values were obtained

for various positions of light source. A mathematical model was

developed for the servomotor used and various gain values were

experimented obtain optimum values of gain and constants which was

most suitable for the motor. The mathematical model was simulated in

Matlab environment to produce desired output. Then finally a hardware

was prepared based on the calculations and algorithm which was then

simulated by areal light source.The following project was found to be a prototype for dual axis solar

tracker circuits, ambient light follower circuit, light focusing circuit to read

data from blu-ray and cd drives etc. The following project also worked as

a platform to realise a real time working model of a closed loop system

with various angles included like physical property and mechanical

property of motor, sensors etc.


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11. REFERENCES 1. Design and Research of Dual-Axis Solar Tracking System in

Condition of Town Almaty.

1Shyngys Almakhanovich Sadyrbayev, 1Amangeldi Bekbaevich

Bekbayev,

1Seitzhan Orynbayev and 2Zhanibek Zhanatovich Kaliyev

1Kazakh National Technical University, Almaty, Republic of

Kazakhstan

2Kazakh Academy of Transport and Communications, Almaty,Republic of Kazakhstan

2. Designing a Dual Axis Solar Tracker For Optimum PoweR,First A.

AASHIR WALEED Second B. DR. K M HASSAN University of

Engineering and Technology, Lahore

3. Design and Implementation of a Sun Tracker with a Dual-Axis

Single Motor for an Optical Sensor-Based Photovoltaic System Jing-

Min Wang * and Chia-Liang Lu,Department of Electrical Engineering,

St. John’s University.

4. Research papers by Daniel A. Pritchard, 1983

5. Research papers by A.Zeroual et al., 1997

6. Research papers by Z.G. Piao et al., 2003

7. Research papers by A. Konar and A.K Mandal, 1991

light tracking servomotor

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