The Engineering Projects

Roots of Quadratic Equations in MATLAB

Hello friends, hope you all are fine and enjoying good health. In today's tutorial, I am going to share How to find Roots of Quadratic Equations in MATLAB. It's quite a quick tutorial in which I will give you the code and will explain it a little. Benefit of this project is that when you are learning MATLAB then you must design such small codes so that you know more about the behavior of MATLAB.

Today two of my juniors came to me for a simple MATLAB term project. It's quite an easy project but i thought to share it for those students who are dealing with basics of MATLAB. Mostly such projects are offered to students in first or second semester when they have very basic knowledge of MATLAB coding and they feel helpless while solving such problems as is the case with those two students. So, let's get started with How to find Roots of Quadratic Equations in MATLAB.

Roots of Quadratic Equations in MATLAB

• This finding Roots of Quadratic Equations in MATLAB takes three inputs from user.
  • Variables of Quadratic Equation.
  • Domain limit.
  • Variable to choose whether to show roots of the equation or minimum of function or both.
• After taking these inputs the function calculates the roots of the quadratic equations.
• After that finds the minimum of the function within the domain limit.
• And finally show both of them on the graph.

Code of the Project

MATLAB is  a really amazing tool and I really love to do coding in it.The code for this project is given below. I didn't give description of the code because its a simple project and second thing I want the young students to search these commands themselves so that they could learn something. Second thing MATLAB has a very strong help section, if you are having problem with any command simply enter doc [Command] or help [Command] in the main window and MATLAB will give you everything you need related to that command. Here's the code :

%==== Code Starts Here(www.TheEngineeringProjects.com) ==== clc clf % ============ Taking Inputs From User ============== handle = input('Enter the handle of the function : '); limit = input('Enter the domain limits : '); initial = input('Enter the initial solution estimate : '); k = input('Enter 1 for min, 2 for roots & 3 for both  : '); syms x; a1 = 100000; %====== Calculating Roots of the Quadratic Equation ========= func = @(x)handle(1,1)*x^2 + handle(1,2)*x + handle(1,3); root1 = (-handle(1,2) + sqrt((handle(1,2)^2)-(4*handle(1,1)*handle(1,3))))/(2*handle(1,1)); root2 = (-handle(1,2) - sqrt((handle(1,2)^2)-(4*handle(1,1)*handle(1,3))))/(2*handle(1,1)); roots=[root1,root2]; %====== Calculating Minimum Value Within Domain Limits ========= for x = limit(1,1):0.1:limit(1,2) a = func(x); if (a < a1) a1 = a; x1 = x; end if(k==1 || k==3) plot(x,a,'--rs','LineWidth',2,... 'MarkerEdgeColor','k',... 'MarkerFaceColor','g',... 'MarkerSize',10) hold on; end end min = a1; %====== Displaying Roots & Minimum Values ========= if ( k == 1) min end if ( k == 2) roots plot(x,root1,'--rs','LineWidth',2,... 'MarkerEdgeColor','k',... 'MarkerFaceColor','r',... 'MarkerSize',10) hold on; plot(x,root2,'--rs','LineWidth',2,... 'MarkerEdgeColor','k',... 'MarkerFaceColor','r',... 'MarkerSize',10) end if ( k == 3) min roots plot(x,root1,'--rs','LineWidth',2,... 'MarkerEdgeColor','k',... 'MarkerFaceColor','r',... 'MarkerSize',10) hold on; plot(x,root2,'--rs','LineWidth',2,... 'MarkerEdgeColor','k',... 'MarkerFaceColor','r',... 'MarkerSize',10) end %==== Code Ends Here(www.TheEngineeringProjects.com) =======

Test Input

• For the testing purposes, use the below values as a testing input :

• First input  = [1 5 6]
• Second input  = [-1 1]
• Third input = 0
• Fourth input = 3

• The Code is self explanatory but if anyone having any problem in it may ask in comments.

That's all for today. I hope you now have the idea How to Find Roots of Quadratic Equations in MATLAB. I will meet you guys in the next lecture. Till then take care.

Protect Simulink Design in MATLAB

Hello friends hope you all are healthy and enjoying good health. In today's tutorial, I am going to share How to Protect Simulink Design in MATLAB and in order to do so I have used S Function method. In my previous post I have explained How to Protect your m-file Codes in MATLAB by converting it to p-file so that no one can reach to your code and now I am gonna explain how to protect your simulations in MATLAB which you create in Simulink so that your intellectual work wont go waste.There are many methods to protect the Simulink simulations and the easiest of them is using S-function. Now follow these simple steps and it won't be much difficult.

Protect Simulink Design in MATLAB

• Open the simulation which you want to protect. Make sure you are done with the simulation and don't need any more editing. As after conversion you wont be able to edit it.
• Now select whole of your simulation and right click on it.
• Click on the Create Subsystem in right click listing.This will create a single block for your whole system.If you double click click this block a new window will pop up and you can see your whole model again.
• Now right click on this newly created subsystem block and then in the listing click on Real Time Workshop and the Generate S-Function.

• On clicking a new window will pop-up add variables if you want to control any otherwise just tick the corner which says Use Embedded Coder and hit Build.
• It will take few seconds to build the S-function for your simulation and when its done Hurrah your simulation is now protected.
• Now double click on your subsytem and you won't be able to open your design, instead a window pops up which will give some description.
• You can add the complete description while generating your simulation.
• Now start your simulation , it will work fine but no one could find your design.

Note :

• This method is mostly used by the developers to protect their simulations.
• Users can use their simulation but couldn't get the design of it, the design got fully protected.

Convert m File into p File in MATLAB

Hello friends, I hope you all are doing great. In today's tutorial, I am going to show you How to Convert m File into p File in MATLAB. Now the question arises that why we need to do that? & the answer is if you want to protect your code and don't want anyone to access it then you need to your Convert m File into p File. P File is like an encrypted file which performs the same functionality as your original m file but no one can get the code out of it. Like me explain it with an example, suppose you are some sort of developer and you have created some code for a company and now you want to protect your code and just send the company some sort of software. MATLAB has a function in which you convert your m-file into p-file and no one can open that p file code. P-file functionality is as same as of m-file but no one can check what's inside p-file.

Convert m File into p File in MATLAB

• Suppose you have created your m-file and you are now want to protect your code and the send the rest to your employer so that he can use it without knowing the code inside it.
• Use these command to do this :

pcode(fun) pcode(fun1,...,funN)

• If fun is the name of the m-file then MATLAB will conver the fun.m to fun.p and create it in the same folder.
• If fun is the name of the folder then MATLAB will convert all the m-files within that folder into p-files.
• If you want to convert more than one m-file into p-file then use the second code and place all the m-files there.
• You can also convert more than one folder using the second command.

So, that's all for today. In my next post I will tell you a way of protecting your simulink model in the same way as we protected our m-file. Till then take care & stay blessed .... :))

Pure Sine Wave Inverter Design With Code

Hello guys, in the last post I have explained the Basics of Inverters along with its types and also the inverters topology in other words working of inverters, then we discussed the Major Components of Inverters. Now in this post I am gonna explain the pure sine wave inverter and how to create it. I have used AVR microcontroller int his project. The reason I am using random microcontrollers is that so you guys get a taste of each one. Before starting on sine wave inverter read this article again and again as I have also mentioned the problem i got while making it. You should also read the Modified Sine Wave Design with Code.

I have divided this tutorial into four parts which are shown below. This is a step by step guide to design and build an inverter and I hope at the end of this tutorial you guys will be able to design your own inverter. I tried my best to keep it simple but still if you guys got stuck at any point ask in comments and I will remove your query. This project is designed by our team and they put real effort in getting this done so that's why we have placed a small fee on its complete description. You can buy the detailed description of this project along with the complete code and circuit diagram, by clicking on the below button:

Buy This Project Note:

• I have also posted a Pure SineWave Inverter Simulation in Proteus, which will be quite helpful if you are designing a pure sine wave inverter.

Pure Sine-Wave Inverter

• Pure Sine wave inverter consist of a microcontroller unit which generates a switching signal of 15 KHz, an H-bridge circuit to convert the signal into AC, a low pass LC filter circuit to block the high frequency components and the transformer unit to step-up the voltages.
• Block diagram of sine wave circuit is given below:

FIGURE 1 : Block diagram of pure sine wave inverter

AVR Micro-Controller Unit

• Microcontroller unit is a multi-purpose control unit which can handle multiple tasks simultaneously.
• We have used it just to generate a switching signal of 15 KHz.
• I am using AVR micro-controller unit for this pure sine wave inverter.

Explanation for PWM in AVR

• AVR is acting as the brain of Pure Sine Wave Inverter.
• Below is the program for atmega16 microcontroller with a clock frequency of 8 MHz (Fcpu = 8MHz). We have worked on a compiler named AVR GCC.
• Initially we included AVR libraries,then we initialized sine table in which the values of a complete sine wave are stored (we generated a sin table in range 0-359 degrees whereas, zero of sine wave is set at decimal 128(0x80 in Hex).

• Then in the next chunk of the code, we used timer0 (8-bit) which starts from 0 and peaks to 255 (it gives a saw tooth output).
• The constant float step = (2*180)/256 = 1.40625 For i=0; s = sin (0*1.40625) = 0 For i = 255 s = sin (255*1.40625) = 358.5937 = 359deg approx.
• This is how the sine wave is generated from 0-359deg.
• When timer reaches 255 then interrupt over flow is generated (Refer the sine wave code, at the end).
• The next part of the code shows that we have used the clock select bits as pre-scalar.
• TIMSK| = (1<<TOIE0) means we are enabling timer overflow interrupt enable 0.
• The last part of the code is the most important part of pure sine wave generator.
• OCR0 is output compare register for timer 0 and it continuously compares timer0 values i.e. 0, 1, 2.......255, and for each value of timer the value from sine wave table is computed then sample++increases the pointer of sine wave table to the next i.e. the value at the second index of sine table and that is computed for the output until samples equals to 255.
• Then we used the command sample = 0 the cycle is repeated again and again.
• Here's the programming code for Pure Sine Wave Inverter:

    #include <stdlib.h>

    #include <avr/io.h>

    #include <util/delay.h>

    #include <avr/interrupt.h>

    #include <avr/sleep.h>

    #include <math.h>

    #include <stdio.h>

    0x80, 0x83, 0x86, 0x89, 0x8C, 0x90, 0x93, 0x96,

    0x99, 0x9C, 0x9F, 0xA2, 0xA5, 0xA8, 0xAB, 0xAE,

    0xB1, 0xB3, 0xB6, 0xB9, 0xBC, 0xBF, 0xC1, 0xC4,

    0xC7, 0xC9, 0xCC, 0xCE, 0xD1, 0xD3, 0xD5, 0xD8,

    0xDA, 0xDC, 0xDE, 0xE0, 0xE2, 0xE4, 0xE6, 0xE8,

    0xEA, 0xEB, 0xED, 0xEF, 0xF0, 0xF1, 0xF3, 0xF4,

    0xF5, 0xF6, 0xF8, 0xF9, 0xFA, 0xFA, 0xFB, 0xFC,

    0xFD, 0xFD, 0xFE, 0xFE, 0xFE, 0xFF, 0xFF, 0xFF,

    0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFE, 0xFE, 0xFD,

    0xFD, 0xFC, 0xFB, 0xFA, 0xFA, 0xF9, 0xF8, 0xF6,

    0xF5, 0xF4, 0xF3, 0xF1, 0xF0, 0xEF, 0xED, 0xEB,

    0xEA, 0xE8, 0xE6, 0xE4, 0xE2, 0xE0, 0xDE, 0xDC,

    0xDA, 0xD8, 0xD5, 0xD3, 0xD1, 0xCE, 0xCC, 0xC9,

    0xC7, 0xC4, 0xC1, 0xBF, 0xBC, 0xB9, 0xB6, 0xB3,

    0xB1, 0xAE, 0xAB, 0xA8, 0xA5, 0xA2, 0x9F, 0x9C,

    0x99, 0x96, 0x93, 0x90, 0x8C, 0x89, 0x86, 0x83,

    0x80, 0x7D, 0x7A, 0x77, 0x74, 0x70, 0x6D, 0x6A,

    0x67, 0x64, 0x61, 0x5E, 0x5B, 0x58, 0x55, 0x52,

    0x4F, 0x4D, 0x4A, 0x47, 0x44, 0x41, 0x3F, 0x3C,

    0x39, 0x37, 0x34, 0x32, 0x2F, 0x2D, 0x2B, 0x28,

    0x26, 0x24, 0x22, 0x20, 0x1E, 0x1C, 0x1A, 0x18,

    0x16, 0x15, 0x13, 0x11, 0x10, 0x0F, 0x0D, 0x0C,

    0x0B, 0x0A, 0x08, 0x07, 0x06, 0x06, 0x05, 0x04,

    0x03, 0x03, 0x02, 0x02, 0x02, 0x01, 0x01, 0x01,

    0x01, 0x01, 0x01, 0x01, 0x02, 0x02, 0x02, 0x03,

    0x03, 0x04, 0x05, 0x06, 0x06, 0x07, 0x08, 0x0A,

    0x0B, 0x0C, 0x0D, 0x0F, 0x10, 0x11, 0x13, 0x15,

    0x16, 0x18, 0x1A, 0x1C, 0x1E, 0x20, 0x22, 0x24,

    0x26, 0x28, 0x2B, 0x2D, 0x2F, 0x32, 0x34, 0x37,

    0x39, 0x3C, 0x3F, 0x41, 0x44, 0x47, 0x4A, 0x4D,

    0x4F, 0x52, 0x55, 0x58, 0x5B, 0x5E, 0x61, 0x64,

    0x67, 0x6A, 0x6D, 0x70, 0x74, 0x77, 0x7A, 0x7D

    void InitSinTable()

    {

    Page | 42

    //sin period is 2*Pi

    const float step = (2*M_PI)/(float)256;

    float s;

    float zero = 128.0;

    //in radians

    for(int i=0;i<256;i++)

    {

    s = sin( i * step );

    //calculate OCR value (in range 0-255, timer0 is 8 bit)

    wave[i] = (uint8_t) round(zero + (s*127.0));

    }

    }

    void InitPWM()

    {

    /*

    TCCR0 - Timer Counter Control Register (TIMER0)

    -----------------------------------------------

    BITS DESCRIPTION

    NO: NAME DESCRIPTION

    --------------------------

    BIT 7 : FOC0 Force Output Compare

    BIT 6: WGM00 Wave form generartion mode [SET to 1]

    BIT 5: COM01 Compare Output Mode [SET to 1]

    BIT 4: COM00 Compare Output Mode [SET to 0]

    BIT 3: WGM01 Wave form generation mode [SET to 1]

    BIT 2: CS02 Clock Select [SET to 0]

    BIT 1: CS01 Clock Select [SET to 0]

    BIT 0: CS00 Clock Select [SET to 1]

    Timer Clock = CPU Clock (No Pre-scaling)

    Mode = Fast PWM

    PWM Output = Non Inverted

    */

    TCCR0|=(1<<WGM00)|(1<<WGM01)|(1<<COM01)|(1<<CS00);

    TIMSK|=(1<<TOIE0);

    //Set OC0 PIN as output. It is PB3 on ATmega16 ATmega32

    DDRB|=(1<<PB3);

    }

    ISR(TIMER0_OVF_vect)

    {

    OCR0 = wave[sample];

    sample++;

    if( sample >= 255 )

    sample = 0;

    }

 

H-Bridge Circuit

• H-Bridge Circuit is acting as the main core of Pure sine Wave Inverter.
• H-bridge circuit is basically enables a voltage to be applied across a load in either direction.
• In inverters, it is used to amplify the input square wave coming from the micro-controller.
• We are giving modulated square wave at the input of the H-bridge because if we give sine wave to the MOSFET or any other switching device like the BJT or IGBT, very high switching losses occur. This is because when we give sinusoidal waveform to any of these devices, they start operating in the linear region, and power loss occurs in devices operating in linear region.
• When we give a square waveform to them, they operate on either saturation or cut-off regions thus having minimum power loss.
• We used IRF5305 and IRFP150 MOSFETs. These are high power MOSFETs with maximum current rating of 31 Amp and 42 Amp respectively.
• IFR5305 is a Pchannel MOSFET whereas IRFP150 is an N-channel MOSFET.
• The circuit configuration of H-bridge is given below:

FIGURE 2 : H-Bridge Circuit

Working

• Working of an H-bridge for pure sine wave inverter can be divided into two modes.
• In Mode1, the input signal at the gate of M1 is high and at the gate of M4 it is low.This causes conduction from M1-M4 and we achieve a +12V signal at the output.
• In Mode2, the input signal at the gate of M3 is high and at the gate of M2 it is low.This causes conduction from M3-M2 and we achieve a -12V signal at the output.
• And thus we obtain a 24Vpeak-peak signal at the output.
• The working of H-Bridge in both conduction modes can be easily understood by the following figure:

FIGURE 3 : H-Bridge Conduction Modes (A) FIGURE 3 : H-Bridge Conduction Modes (B)  

• Due to the conduction of half part of the bridge at +ve half cycle and the other half part of the bridge at –ve half cycle, we obtain a square waveform of 24 Vpeak-peak at the output.
• In figure below is the Proteus simulation showing the waveform output of bridge circuit during each conduction cycle.

FIGURE 4 : Wave-forms of H-bridge conduction cycle

Observations

• In the H-bridge circuit we have observed that input signal"s frequency does not change at the output that means the frequency remains un-altered.
• Only the power of the signal increase in terms of current.

Problems

• Initially we used all the MOSFETs of same type (i-e. n-channel MOSFETs). This caused the shorting of the MOSFETs during the conduction mode. This phenomenon is known as shooting over of the MOSFET.
• Despite the duration of this shooting over was quite small, it caused loading on the MOSFETs.
• The MOSFETs started heating up due to this, and eventually they burned out.
• Another problem occurred while using the MOSFETs of same channel was that the upper MOSFETs (M1 and M3) did not turn on properly.
• After studying, we learned that they required 18V to turn on thus; we needed a MOSFET driver that was IR2110.
• We worked on it but it did not working properly too, because according to the formula for bootstrap capacitor given in datasheet, the driver must have given 18V output but it was not working so we had to search for an alternate.
• Then after extended study we came to know that replacing the upper two n channel MOSFETs with p channel MOSFET is the solution. We applied this technique and it worked.
• Using this technique also solved the problem of MOSFET shooting over by inducing a dead time/delay in the MOSFET switching.

LC Filter

• We have determined inductance of the inductor using LC resonant band stop filter as LC meters were not available in the lab.

FIGURE 5 : LC filter

Working

• Understanding the working of H-Bridge is very essential, if you want to work on Pure sine Wave Inverter.
• The method to determine L or C is simple. Suppose we are required to determine the inductance, then by above circuit,

• V1 signal from function generator is set to 1Vrms using multi-meter.
• At resonance frequency the LC combination will have very low impedance so it will short out the signal and will drop across resistor R1 and prevents the signal to reach the load.
• Using this principle we have varied signal frequency from function generator and we are detecting output voltage at load using multi-meter.
• At resonance frequency multi-meter will show ideally zero volts.
• So by using formula we have :

Problems

• First we designed an RC circuit but we observed that the Resistance R in the circuit acts as a load and dissipates power.
• After studying, we decided to use an LC filter.
• The main problem with the LC filter was the designing of the inductor as the inductor of desired value was not available in the market, thus we had to make it by hand.
• LC meter was not available also thus we had to repeatedly calculate the inductance value mathematically.

Working of Pure Sine Wave Inverter

• Let's have a look at the working of Pure Sine Wave Inverter.
• A 50Hz sin wave is generated with the help of a lookup table within the AVR microcontroller and is modulated over a switching frequency signal of 15KHz.
• As this signal has very weak current, so it is amplified by a BC 547 transistor.
• The amplified signal is given at the gates of M1 and M2 MOSFETs.
• The output of the microcontroller is given to another BC 547 which is working as an inverting amplifier.
• By this, the signal from the microcontroller gets inverted as well as amplified.
• This signal is given at the gates of M3 and M4 MOSFETs.
• Now what happens is that, when the input signal at the gate of M1 of the H-bridge is high and at the gate of M4 of the H-bridge is low, conduction from M1-M4 occurs and we achieve a +12V signal.
• When the input signal at the gate of M3 goes high and at the gate of M2 goes low, conduction from M3-M2 occurs and we achieve a -12V signal.
• Thus at the output we receive a waveform of 12Vpeak or 24Vpeak-peak.
• The output of the H-bridge is then fed into a low pass LC filter which filters the high frequency components of 15 KHz and gives the 50 Hz sine output.
• This output is then fed into a transformer which steps up this 12 Volts AC waveform into 220Volts AC.

So, that's all for today. I hope you guys have enjoyed this Pure Sine Wave Inverter Project. You should also look at Proteus simulation of Pure sine wave and Introduction to Multilevel Inverters, because simulations help a lot in designing hardware projects. So, take care and have fun !!! :)