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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