Thai Nguyen University of Technology, Thai Nguyen, Viet Nam

International Training Cooperation

Senior Design I

Design on Controllerfor Photo-Voltaic Tracking System

Supervisor: Dr. Nguyen Minh Y

Student: Pham Duy Tung

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Table of content

Section PageAcknowledgments…………………………………………………………….. 3Abstract……………………………………………………………………...... 4

I.Introduction………………………………………………………………… 5

II. Background………………………………………………………………. 6

2.1 Solar Energy………………………………………………………………. 6

2.2 The earth’s orbit………....……………………………………………………………………..

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2.3 Altitude angle of the sun at solar noon………....………………………………………

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2.4 Solar position at any time of day……………………………………..........................

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2.5 Solar time and civil time…………………………………………………………………..

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2.6 Sunrise and sunset…………………………………………………………………………..

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2.7 Clear sky direct-beam radiation……………………………………………………….

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III. Solar Tracker……………………………………………………………. 16

3.1 Single-axis tracker…………………………………………………………

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3.2 Dual-axis trackers………………………………………………………… 17

3.3 Advantage of solar trackers……………………………………………….

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IV. System Modeling………………………………………………………… 18

4.1 Light sensor selection and circuit…………………………………………..

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4.2 Actuator and drive selection………………………………………………..

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V. Mathematical Formulation and Modeling……………………………...V. Mathematical Formulation and

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Modeling……………………………...

5.1 PMDC motor equation…………………………………………………….. 205.12 Tranfer functions………………………………………………………….

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5.23 Block Diagram……………………………………………………………..

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VI. Controller Design……………………………………………………….. 21

VII. Simulation and Result…………………………………………………. 22

VIII. Conclusion……………………………………………………………... 2325

IX. Reference………………………..……………………………………………

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Acknowledgments

I would like to express my very great appreciation to my Senior Project Advisor,Dr. Nguyen Minh Y for his valuable and constructive suggestions during the planning and writing the report.

I would also like to thank ITC’s lecturers and AP46’s student for their help to complete this research.

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Abstract

The last two decades has observed the quick development of the population, economics and industry. As a consequence, every nation faces the increasing needs of energy, food and environmental pollution. For example, the fossil fuel shortage and the global warming are major concerns nowadays. These are the key reasons for many technologies to be developed; one of them is alternative energy sources such as solar energy, wind energy, etc. which took many scientific attentions over the years. Vietnam is located in Southeast Asia having high sunlight intensity in average and advantages to use solar energy.

In this report, mathematical analysis, control system, and simulink model have been developed, designed and tested using the MATLAB/Simulink for photovoltaic module tracking , if the angle of incidence is equal to zero during the sunshine, the designed tracking system can be obtained the highest efficiency.

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I. Introduction

Solar energy is the most essential and prerequisite resource of sustainable energy because of its ubiquity, abundance, and sustainability. Regardless of the intermittency of sunlight, solar energy is widely available and completely free of cost. Recently, photovoltaic (PV) system is well recognized and widely utilized to convert the solar energy for electric power applications. It can generate direct current (DC) electricity without environmental impact and emission by way of solar radiation. The DC power is converted to AC power with an inverter, to power local loads or fed back to the utility. Being a semiconductor device, the PV systems are suitable for most operation at lower maintenance costs.

Electrical energy from photovoltaic panels is derived by converting energy from the sunlight into electrical current in the solar cells. A majority of solar panels in use today are stationary and therefore do not consistently output the maximum amount of power that they can actuall produce. A solar tracker will track the sun throughout the day and adjust the angle of the solar panel to make the sun normal to the solar panels at all times. The orientation of the solar panels may increase the efficiency of the conversion system from 20% up to 50%.

In solar PV tracking systems, PVsolar panels are mounted on a structure which moves to track the movement of the sun throughout the day. There are three methods of tracking: active, passive and chronological tracking. These methods can then be configured either as single-axis or dual-axis solar trackers. In active tracking, the position of the sun in the sky during the day is continuously determined by sensors. The sensors will trigger the motor or actuator to move the mounting system so that the solar panels will always face the sun throughout the day.

Electrical energy from photovoltaic panels is derived by converting energy from the sunlight into electrical current in the solar cells. A majority of solar panels in use today are stationary and therefore do not consistently output the maximum amount of power that they can actuall produce. A solar tracker will track the sun throughout the day and adjust the angle of the solar panel to make the sun normal to the solar panels at all times. The orientation of the solar panels may increase the efficiency of the conversion system from 20% up to 50%.

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II. Background

2.1 Solar Energy

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields. The temperature inside the sun reach over 20 million degrees kelvin. The sun generates its energy by nuclear fusion of hydrogen nuclei into helium.The total power emitted by the sun is calculated by multiplying the emitted power density by the surface area of the sun which gives 9.5 x 1025 W.

Solar energy can be harnessed by a variety of natural and synthetic processes photosynthesis by plants captures the energy of sunlight and converts it to chemical form (oxygen and reduced carbon compounds), while direct heating or electrical conversion bysolar cells are used by solar power equipment to generate electricity or to do other useful work, sometimes employing concentrating solar power (that it is measured in suns). The energy stored in petroleum and other fossil fuels was originally converted from sunlight byphotosynthesis in the distant past.

Fig.1 The Solar Energy Global Map indicate that Vietnam’area can receive the radiation from 1700 to 2600 Kwh/year (from midle to the south of vietnam) and 1350 to 177 KWh/year in the north of vietnam.

The source of insolation is, of course, the sun that gigantic, 1.4 million kilo-meter diameter, thermonuclear furnace fusing hydrogen atoms into helium. Theresulting loss of mass is converted into about 3.8 × 1020 MW of electromagnetic energy that radiates outward from the surface into space. Every object emits radiant energy in an amount that is a function of its temperature. The usual way to describe how much radiation an object emits is to compare it to a theoretical abstraction called a blackbody. A

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blackbody is defined to be a perfect emitter as well as a perfect absorber. As a perfect emitter, it radiates more energy per unit of surface area than any real object at the same temperature. As a perfect absorber, it absorbs all radiation that impinges upon it; that is, noneis reflected and none is transmitted through it. The wavelengths emitted by a blackbody depend on its temperature as described by Planck’s law:

E λ=3.78 ×108

λ5[exp( 14,400λT )−1]

where E λ is the emissive power per unit area of a blackbody (W/m2 µm), T is the absolute temperature of the body (K), and λ is the wavelength (µm). Modeling the earth itself as a 288 K (15◦ C) blackbody results in the emission spectrum plotted in Fig.2 .

Fig.2 : The spectral emissive power of a 288 K blackbody.

The area under Planck’s curve between any two wavelengths is the power emit-ted between those wavelengths, so the total area under the curve is the total radiant power emitted. That total is conveniently expressed by the Stefan–Boltzmann law of radiation:

E = AσT 4

where E is the total blackbody emission rate (W), σ is the Stefan–Boltzmann constant = 5.67 × 10−8 W/m2-K4, T is the absolute temperature of the black-body (K), and A is the surface area of the blackbody (m2). Another convenient feature of the blackbody radiation curve is given by Wien’sdisplacement rule, which tells us the wavelength at which the spectrum reachesits maximum point:

λmax ( µm )= 2898

T (K)

Where the wavelength is in microns (µm) and the temperature is in kelvins.

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2.2 The Earth’s orbit

The earth revolves around the sun in an elliptical orbit, making one revolutionevery 365.25 days. The eccentricity of the ellipse is small and the orbit is, infact, quite nearly circular. The point at which the earth is nearest the sun, theperihelion, occurs on January 2, at which point it is a little over 147 millionkilometers away. At the other extreme, the aphelion, which occurs on July 3, theearth is about 152 million kilometers from the sun. This variation in distance isdescribed by the following relationship:

d=1.5× 10 {1+0.017 sin [ 360(n−93)365 ]}(km)

wherenis the day number, with January 1 as day 1 and December 31 being daynumber 365. Table 1 provides a convenient list of day numbers for the first dayof each month.

January n = 1 July n =182

February n =32 August n =213

March n =60 September n =244

April n =91 October n =274

May n =121 November n =305

June n =152 December n =335

Table 1 Day Numbers for the First Day of Each Month

Each day, as the earth rotates about its own axis, it also moves along the ellipse. If the earth were to spin only 360◦in a day, then after 6 months time our clocks would be off by 12 hours; that is, at noon on day 1 it would be the middle of the day, but 6 months later noon would occur in the middle of the night. To keep synchronized, the earth needs to rotate one extra turn each year, which means that in a 24-hour day the earth actually rotates 360.99◦,whichisalittle surprising to most of us.

As shown in Fig.2, the plane swept out by the earth in its orbit is called the ecliptic plane. The earth’s spin axis is currently tilted 23.45◦ with respect to the ecliptic plane and that tilt is, of course, what causes our seasons. On March 21 and September 21, a line from the center of the sun to the center of the earth passes through the equator and everywhere on earth we have 12 hours of daytime and 12 hours of night, hence the termequinox (equal day and night). On December 21, the wintersolsticein the Northern Hemisphere, the inclination of the North Pole reaches its highest angle away from the sun (23.45◦), while on June 21 the opposite occurs. By the way, for convenience we are

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using thetwenty-first day of the month for the solstices and equinoxes even though the actual days vary slightly from year to year.

Fig. 2: The tilt of the earth’s spin axis with respect to the ecliptic plane is what causes our seasons. “Winter” and “summer” are designations for the solstices in the Northern

Hemisphere.

For solar energy applications, the characteristics of the earth’s orbit are considered to be unchanging, but over longer periods of time, measured in thousands of years, orbital variations are extremely important as they significantly affect climate. The shape of the orbit oscillates from elliptical to more nearly circular with a period of 100,000 years (eccentricity). The earth’s tilt angle with respectto the ecliptic plane fluctuates from 21.5° to 24.5° with a period of 41,000 years (obliquity).

2.3 Altitude angle of the sun at solar noon

We all know that the sun rises in the east and sets in the west and reaches its highest point sometime in the middle of the day. In many situations, it is quiteuseful to be able to predict exactly where in the sky the sun will be at any time, at any location on any day of the year. Knowing that information we can use knowledge of solar angles to help pick the best tilt angle for our modules to expose them to the greatest insolation for photovoltaics.

As shown in Fig. 3, the angle formed between the plane of the equator and a line drawn from the center of the sun to the center of the earth is called the solar declination, δ. It varies between the extremes of ±23.45◦, and a simple sinusoidal relationship that assumes a 365-day year and which puts the spring equinox on dayn=81 provides a very good approximation. Exact values of declination, which vary slightly from year to year, can be found in the annual publication The American Ephemeris and Nautical Almanac.

δ=23.45 sin [ 360365

(n−81)]10

Figure 3 An alternative view with a fixed earth and a sun that moves up and down. The angle between the sun and the equator is called the solar declination δ.

The declination is zero at the equinoxes (March 22 and September 22), positive during the northern hemisphere summer and negative during the northern hemisphere winter. The declination reaches a maximum of 23.45° on June 22 (summer solstice in the northern hemisphere) and a minimum of -23.45° on December 22 (winter solstice in the northern hemisphere).

Computed values of solar declination on the twenty-first day of each month are given in Table 2:

Month

Jan Feb Mar

Apr May Jun July

Aug

Sept

Oct Nov Dec

δ -20.1 -11.2 0.0 11.6 20.1 23.4

20.4 11.8 0.0 -11.8 -20.4 -23.4

Table 2. Solar Declination δ for the 21st Day of Each Month (degrees)

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Figure 3 A south-facing collector tipped up to an angle equal to its latitude is perpendicular to the sun’s rays at solar noon during the equinoxes.

The altitude angle βN of the sun at solar noon. The altitude angle is the angle between the sun and the local horizon directly beneath the sun. From Fig.3 we can write down the following relationship by inspection:

βN = 90◦− L + δ

Where L is the latitude of the site. Notice in the figure the term zenith is introduced, which refers to an axis drawn directly overhead at a site.

Figure 4 The altitude angle of the sun at solar noon.

Figure 5 illustrates the variation of the altitude angle and solar declination in different days in a year in Thai Nguyen, Vietnam

An example,Find the optimum tilt angle for a south-facing photovoltaic module in Thai Nguyen, Vietnam (latitude 21.56°) at solar noon on March 1.

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Solution. From Table 1, March 1 is the sixtieth day of the year so the solar declination is:

δ=23.45 sin [ 360365

(n−81)]=23.45 °sin ⌊ 360365

(60−80)° ⌋=−8.3 °

which, makes the altitude angle of the sun equal to

βN= 90°−L+δ = 90−21.56−8.3 = 60.14°

The tilt angle that would make the sun’s rays perpendicular to the module at noon would therefore be:

Tilt = 90 − βN= 90 –60.14 = 29.86

Figure 6. a tilt angle for a south-facing photovoltaic module in Thai Nguyen city.

2.4 Solar position at any time of day

The location of the sun at any time of day can be described in terms of its altitude angleβ and its azimuth angle φ s as shown in Fig. 7.10. The subscript s in the azimuth angle helps us remember that this is the azimuth angle of the sun. Later, we will introduce another azimuth angle for the solar collector and a different subscriptcwill be used.

Figure 7 The sun’s position can be described by its altitude angleβand its azimuth angle φ S. By convention, the azimuth angle is considered to be positive before solar noon.

The azimuth and altitude angles of the sun depend on the latitude, day number, and, most importantly, the time of day. The following two equations allow us to compute the altitude and azimuth angles of the sun. For a derivation see, for example, T. H. Kuen et al. (1998):

sinβ=cosLcosδcosH+sinLsinδ

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sin φ s=cosδsi nH

cosβ

Notice that time in these equations is expressed by a quantity called the hour angle, H. The hour angle is the number of degrees that the earth must rotate before the sun will be directly over your local meridian (line of longitude). As shown in Fig. 7.11, at any instant, the sun is directly over a particular line of longitude, called the sun’s meridian. The difference between the local meridian and the sun’s meridian is the hour angle, with positive values occurring in the morning before the sun crosses the local meridian.

Considering the earth to rotate 360◦ in 24 h, or 15◦/h, the hour angle can be described as follows:

Hour angleH = [ 15°h our ] . (hours before solar noon)

Figure 8 The hour angle is the number of degrees the earth must turn before the sun is directly over the local meridian. It is the difference between the sun’s meridian and the local meridian.

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Figure 9 the changing of solar Azimuth and Solar Elevation in Thai Nguyen, Vietnam

2.5 Solar time and civil time

The adjustment between solar time and local clock time is the resultof the earth’s elliptical orbit, which causes the length of asolar day (solar noonto solar noon) to vary throughout the year. As the earth moves through its orbit, the difference between a 24-hour day and a solar day changes following anexpression known as theEquation of Time, E:

E = 9.87sin2B−7.53 cosB−1.5sinB (minutes)

Where B = 360365

[ n−81 ] . (degrees)

Figure 10 The Equation of Time adjusts for the earth’s tilt angle and noncircular orbit.

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2.6 Sunrise and sunset

To calculate the sunrise and sunset time the altitude angle β is zero, so we can write:

Sinβ = cosLcosδcosH + sinLsinδ = 0

cosH=sinLsinδcosLcosδ

=−tanLtanδ

Solving for the hour angle at sunrise, H SR, gives:

H SR = cos−1(−tanLtanδ) (+for sunrise)

Since the earth rotates 15°/h, the hour angle can be converted to time of sunrise or sunset using:

Sunrise (geometric) = 12:00 − H SR

15° /h

Table 3 A sample of the calculated data for Thai nguyen City on Dec 12t h, 2013

Day time Sunrise Sunset Local Solar noon

10 hours and 50minutes

6 hours and 25 minutes

17 hours and 15minutes

11 hours and 50minutes

2.7 Clear sky direct-beam radiation

Solar collectors that focus sunlight usually operate on just the beam portion of the incoming radiation since those rays are the only ones that arrive from a consistent direction. Most photovoltaic systems, however, don’t use focusing devices, so all three components—beam, diffuse, and reflected—can contribute to energy collected. The goal of this section is to be able to estimate the rate at which just the beam portion of solar radiation passes through the atmosphere

Figure 11 Solar radiation striking a collector,I C, is a combination of direct beam, I BC,diffuse,I DC, and reflected, I RC

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Ignoring sunspots, one expression that is used to describe the day-to-day variation in extraterrestrial solar insolation is the following:

I 0=SC·[1+0.034 cos ( 360 n365 )](W/m2)

Where SC is called thesolar constantandnis the day number. The solar constantis an estimate of the average annual extraterrestrial insolation. Based on early NASA measurements, the solar constant was often taken to be 1.353 kW/m2, but1.37 kW/m2is now the more commonly accepted value.

Air mass ratio m = 1

sinβ

Where β is the altitude angle of the sun.

III. Solar Tracker Systems

In the process of converting solar energy to electricity we use photovoltaic panels which consist of silicon made solar cells. Photovoltaic effect is the concept used in the panels where light energy due to the sun’s radiation is converted into electric power. The conversion of solar energy into electric power also depends on the angle at which the panel is fixed or made to rotate. There are two types of panel usage: 1) In fixed form and 2) In solar trackers. When a panel is fixed they are tilted in ground or on a roof at an angle appropriate for sun’s radiation. In solar trackers the panel is made to rotate in the directions with respect to sun.

Solar trackers are racks for photovoltaic modules that move to point at or near the sun throughout the day. There are two kinds of solar trackers:Single-axis trackers follow the sun accurately enough that their output can be very close to full tracking. Trackers need not point directly at the sun to be effective.Dual-axis trackers (“full tracking”) move on two axes to point directly at the sun, taking maximum advantage of the sun’s energy.

3.1 Single-axis tracker

A Single axis tracking system is a method where the solar panel tracks the sun from east to west using a single pivot point to rotate. Under this system there are three types: Horizontal single axis tracking system, Vertical single axis tracking system and Tilted single axis trackingsystem. In the Horizontal system the axis of rotation is horizontal with respect to the ground, and the face of the module is oriented parallel to the axis of rotation. In the Vertical system the axis of rotation is vertical with respect to the ground and the face of the module is oriented at an angle with respect to the axis of rotation. In the Tilted tracking system the axes of rotation is between horizontal and vertical axes and this also has the face of the module oriented parallel to the axis of rotation, similar to the Horizontal tracking system. The single axis tracking system consist of two LDR’s placed on either side of the panel. Depending on the intensityof the sun rays one of the two Light Depend Resistor (LDR) will be shadowed and the other will be illuminated.The LDR with the maximum intensity of

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the sun’s radiation sends stronger signal to the controller which inturn sends signal to the motor to rotate the panel in the direction in which the sun’s intensity is maximum.

Fig. 12 Single-Axis Tracker

The main disadvantage of the single axistracker is that it can only track the daily movement of the sun and not the yearly movement. The efficiency of the single axis tracking system is also reduced during cloudy days since it can only track the east-west movement of the sun.

3.2 Dual-axis trackers

Dual axis tracking system uses the solar panel to track the sun from east to west and north to south using two pivot points to rotate. The dual axis tracking system uses four LDR’s, two motors and a controller. The four LDR’s are placed at four different directions. One set of sensors and one motor is used to tilt the tracker in sun’s east - west direction and the other set of sensors and the other motor which is fixed at the bottom of the trackeris used to tilt the tracker in the sun’s north-south direction. The controller detects the signal from the LDR’s and commands the motor to rotate the panel in respective direction.

Fig. 13 Dual axis tracking system

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3.3 Advantage of solar trackers

The main reason to use a solar tracker is to reduce the cost of the energy you want to capture. A tracker produces more power over a longer time than a stationary array with the same number of modules. This additional output or “gain” can be quantified as a percentage of the output of the stationary array. Gain varies significantly with latitude, climate, and the type of tracker you choose as well as the orientation of a stationary installation in the same location.Climate is the most important factor. The more sun and less clouds, moisture, haze, dust, and smog, the greater the gain provided by trackers. At higher latitudes gain will be increased due to the long arc of the summer sun.

IV. System Modeling

The photovoltaicsolar trackinger system requires movement in different directions, and uses electric motors as prime mover, based on this; photovoltaic tracking solar tracker system motion control is simplified to an electric motor motion control. In solar tracking system design, any light sensitive device can be used as input sensor unit to detect and track the sun position, based on sensors readings, and generated sun tracking error, the control unit generates the voltage used to command the circuit to drive the motor, that outputs the rotational displacement of electric motor, which is the motion of solar tracking system. Simplified block diagram representation of solar tracking system is shown in Fig. 14below:

Figure. 14 Simplified block diagram representation of solar tracking system

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Fig. 15 two axis solar tracker system arrangements.

4.1 Light sensor selection and circuit

Light dependenttecting resistor sensor (LDR) that may used to built photovoltaic trackersolar tracker include; phototransistors, photodiodes Depending on particular application and required maximum energy receiving of solar panel, two main photovoltaicsolar tracking system arrangements; one-axis (one directional) sun tracking system using two light detectors and dualtwo-axis (two directional) sun tracking system using four light sensitive sensors, in both cases, sensors are mounted on the solar panel and placed in an enclosure, the LDRs are screened from each other by opaque surfaces. For dualtwo axis system, fFigure .14 can be modified to have the arrangement shown in fFigure. 176. For one-axis photovoltaicsun tracking system, one light tracking circuit consisting of two sensors, and one electric motor are used, meanwhile, for two-axisdual axis photovoltaicsun tracking.

[(a)] One-axis photovoltaicsun tracking system (b) Two-axis sun photovoltaic tracking system.

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(c) LDR comparator

Figure. 156 light detecting and tracking circuit and arrangements.

Figure. 16 Dual5 two axis photovoltaicsolar tracker system arrangements.

4.2 Actuator and drive selection

Electric motors most used for solar tracker are permanent magnet DC motor (PMDC motor) and stepper motors, the proper selection of motor and drive combination can save energy and improve performance. A suitable, available, easy to control and interface selection is PMDC motor. For bidirectional driving, a motor can be driven via H-bridge drive.

The PMDC motor directly provides rotary motion and, coupled with wheels or drums and cables, can provide translational motion. The electric equivalent circuit of the armature and the free-body diagram of the rotor are shown in the following figure 17.

Fig.17 A Model of PMDC motor

For this example, we will assume that the input of the system is the voltage source (V) applied to the motor's armature, while the output is the rotational speed of the shaft d(theta)/dt. The rotor and shaft are assumed to be rigid. We further assume a viscous friction model, that is, the friction torque is proportional to shaft angular velocity.

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Table 4 PMDC motor characteristics:The physical parameters for our example are:(J) moment of inertia of the rotor 0.01 kg.m2 (b) motor viscous friction constant 0.1 N.m.s(Ke) electromotive force constant 0.01 V/rad/sec(Kt) motor torque constant 0.01 N.m/Amp(R) electric resistance 1 Ohm(L) electric inductance 0.5 H

Parameter Value Unit(J) moment of inertia of the rotor 0.1 kg.m2 (b) motor viscous friction constant 0.01 N.m.s(Ke) electromotive force constant 0.01 V/rad/sec(Kt) motor torque constant 0.01 N.m/Amp(R) electric resistance 1 Ohm(L) electric inductance 0.5 Henry

V.Mathematical Modeling

In general, the torque generated by a PMDC motor is proportional to the armature current and the strength of the magnetic field. In this example we will assume that the magnetic field is constant and, therefore, that the motor torque is proportional to only the armature current i by a constant factor Kt as shown in the equation below. This is referred to as an armature-controlled motor.

T =K t i (3.1)The back emf, e, is proportional to the angular velocity of the shaft by a constant factor Ke.

e = K e θ̇ (3.2)

In SI units, the motor torque and back emf constants are equal, that is, K t= K e; therefore, we will use K to represent both the motor torque constant and the back emf constant.

From the figure 17, we can derive the following governing equations based on Newton's 2nd law and Kirchhoff's voltage law.

J θ̈+b θ̇=¿❑❑i (3.3)

Ldidt

+Ri=V −❑❑θ̇ (3.4)

Applying the Laplace transform for equations (3.3) and (3.4). it can be expressed in terms of the Laplace variable s.

s (Js+b )θ ( s)=T (s )=❑❑ I (s ) (3.5)

(Ls+R) I (s)=V (s)−❑❑sθ (s) (3.6)

5.1 Tranfer function

From equation (3.1) tThe transfer function from the input armature current to the resulting motor torque is:

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T (s )I ( s )

=K t ( s)(3.7) From equation (3.5) the transfer function from the input motor

torque to rotational speed changes is:

θ̇ (s )T (s )

= 1/Js+b/ J

(3.8) From equations (3.64) .tThe transfer function from the current to the

input vVoltage source is:

I (s)V (s )

= 1/ LS+R /L

(3.9)

We arrive at the following open-loop transfer function by eliminating I(s) between equations (3.5) and (3.6), where the output angular displacementis considered the output and the armature voltage is considered the input ( third order e q ation ) :

.

G (s )= θ(s)V (s)

= Ks [(Js+b)(Ls+ R)+K 2]

[ rad /secV

]

Or

G (s )= θ(s)V (s)

= KLJ s3+ (RJ+ Lb ) s2+(Rb+K2) s [ rad /sec

V ](3.8)

5.2 Block Diagram

Combininge equations (3.72), (3.85) and (3.97) together. The overall transfer function from the input armature voltage to the resulting angular displacement velocity can be represented by the closed loop block diagram shown below:

Fig.18 Block diagram of PMDC motor.

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VI. Controller Design In this system we used the PD controller to optained the desired output. PD controller also known as Proportional-Derivative control is a motivated derivative control system inherent in a motor system. It is a very useful and fast response regulator.

Fig.19 A PD controller using operational amplifiers.

Specify how to set the parameters (gains) of PID controller (which principle or theory that you are based on)

PID control is by far the most common way of using feedback in natural and man-made systems. PID controllers are commonly used in industry and a large factory may have

thousands of them, in instruments and laboratory equipment. In engineering applications the controllers appear in many different forms: as a stand alone controller, as part of hierarchical, distributed control systems, or built into embedded components. Most controllers do not use derivative action. In this chapter we discuss the basic ideas of PID control and the methods

for choosing the parameters of the controllers.

Fig.19 A PID controller takes control action based on past, present andprediction of future control errors.

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T the PID controller is given by the formula:

u (t )=k P e (t )❑❑∫❑

❑

()+k Ddedt

The transfer function of PID control is given by:

G (s )=K P

❑❑

❑ +KD s

Tohere are several methods to find determine the gain K P ,❑❑ K D,but they require some experiments to get the exact values. In this case study, we used PIID Automatic Tuner in matlab simulinkMATLAB/SIMULINK to obtain a desired behavior That we can analyze the design using a variety of response plots, and interactively adjust the design to meet the performance requirements.

VII. Simulation and Result

From block diagram of PMDC motor (Fig.18). we can convert it in simulink:

Figure 20 block diagram of PMDC motor produced with Simulink

Figure 21 shows the step response of the PMDC motor using a set of values for the motor parameters (see table 4). It takes about 3 seconds to reach the new steady state rotor speed following a unit increase in applied voltage.

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We made model of PMDC motor became a subsytem in MATLAB/SIMULINK, and then built the Photovoltaic tracking model system with PD controller.

Fig.22 Photovoltaic tracking model system in matlap/simulink

To test the proposed overall system model, first, The light position value of π2

step

input, will be applied and analyzed. Then we used the auto tuner of MATLAB/SIMULINK to find P, D elements of the system. So we get the results below:

Proportional (P): -44.221

Derivative (D): -16.697

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Running the model, The PD controller will optimize the system, result in response curves shown in Figure 21 and 22.

Speed vs time(Radian/s)

Finally, the calculated altitude angle will be considered as the input signal to the overall system model, tested and analyzed .

Fig.21 The Response curves show the changing speed of motor 1.7 seconds

Also, try the dual axis systems for better result and demonstrationAngle vs time

Fig.22 The Response curves show the system reaches desired angular position (θ =- π /2)

in 1.6 seconds with zero steady state error.

To test the proposed overall system model, first, step input, will be applied and analyzed. Finally, the calculated altitude angle will be considered as the input signal to the overall system model, tested and analyzed .

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The photovoltatic tracking system model with the PD controller running in the ideal case has fast response. In practical, the system may contain disturbance and torque of the load so it may take a longer time to get the desired output behavior.

Fig.20 A solar tracking model system in matlap/simulink

We can find the P, I, D elements. running the model, with step input, will result in response of the proposed solar tracker model shown in Fig.21

Proportional (P): 4349.0144369549

Intergral (I): 133.330842093994

Derivative (D): 1682.85210870196

Filter coefficient: 37.1993217775763

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Fig.21 Response curves show the system reaches desired output position (θ = π /6) in 1.7 seconds with zero steady state error.

Conclusion

In this research paperwork, we approached a review of the literature of calculating the altitude angle and solar declination to determine the tilt angle for single-axissingle –axis photovoltaic module. and then designing controller for both single-axis tracker and dual- axis photovoltaicsun tracker by using PID controller which gives us a larg benefit of using solar energy. It also developed the defining equations for a PMDC motor, performed some simple testing of the model and illustrated the model-building capability of the Simulink tool box and showed how to include a complete system (the dc motor) as one component of a larger system (the photovoltaic tracking system).

Reference - http://en.wikipedia.org/wiki/PID_controller

- Author name, “Book, journal paper and conference paper title”, Journal name, Vol. , pp. , Month, year of publication.

- Deepthi.S, Ponni.A, Ranjitha.R, R Dhanabal, “Comparison of Efficiencies of Single-Axis Tracking System and Dual-Axis Tracking System with Fixed Mount”, International Journal of Engineering Science and Innovative Technology (IJESIT),Volume 2, Issue 2, March 2013

- THIẾT KẾHỆTHỐNG THU NĂNG LƯỢNG MẶT TRỜI TỰXOAY THEO HƯỚNG TIA NẮNG – NGUYỄN VĂN DỰ

- http://en.wikipedia.org/wiki/PID_controller

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