Expt 1 - Matlab

7/30/2019 Expt 1 - Matlab

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ELEC 2110 Experiment 1 1 of 19

EXPERIMENT 1

Introduction to MATLAB

The objectives of this experiment are to:Learn to use MATLAB to create, format, analyze, and manipulate dataLearn to use MATLAB for plotting

I. Introduction

This laboratory experiment provides an introduction to the use of MATLAB.

II. MATLAB Basics and Examples

MATLAB is a commercial product of the MathWorks (http://www.mathworks.com), which is anindustry standard software tool in electromagnetics, signal processing, and control systems. A

student version of MATLAB can be purchased at the Auburn University bookstore. The

objective of this lab is to introduce the student to some of the basic features of MATLAB that are

relevant to problem solving in the ECE department and engineering in general. You will receive

additional MATLAB instruction in your other lecture courses.

Access to software

MATLAB is available on all of the computers on the engineering network and the computers in

the laboratory. Students who wish to use MATLAB on their personal computers should

purchase the Student Version of MATLAB.

MATLAB Background and Tutorial

The MATLAB program allows users to do many things that can be found in compiled

programming languages, such as loops, if-then-else structures, and subroutines. The key

differences between MATLAB and common programming languages such as C, C++, Java, or

FORTRAN, are

Declaringvariables - MATLAB does not require variables to be declared.

Variable - the primary type ofMATLABTM variable is an array whose dimensions can be

changed by the user at any time.

Subroutines - For the most part, MATLABTM

requires subroutine functions to be in separatefiles, each ending with .m. These are often calledm-files.

Plotting - MATLABTM has a easy to use plotting function that can be used to plot several

functions, add axis labels, legends, and print these plots for use in other documents.

Trademark MathWorks


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Linear Equations

MATLABs most basic function is the solution of problems in linear algebra. One of the most

common concepts in linear algebra is systems of linear equations. For example, suppose that we

wish to solve for the unknownsx1

andx2

in the equations

3x1 + 2 x2 = 7-3x1 x2 = -1

The equations above are often written in matrix form.

First: Define the vector of unknowns: x=

x

1

x2

.

Then write the matrix form of the equation:

3 2

-3-1

x

1

x2

=

7

-1

Notice that the rows of

3 2

-3-1are the coefficients of the unknowns x

1andx

2. This notation is

important in the study of signals and systems, communications, electromagnetics, control

systems, etc.

Tutorial

Start MATLAB on your machine. A user interface (Figure 1) will appear in which MATLAB

commands can be entered with windows in which MATLAB programs and functions can be

edited.

Figure 1

Variables

MATLAB does not require that variables be declared. At the MATLAB prompt, enter the

command:


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a = 1

You will see the output as shown in Figure 2. Notice that MATLAB prints back the result of this

operation.

Figure 2

Now enter the commands

b = 2

c = a + b

The values forb andc should be printed to the screen (Figure 3).

Figure 3


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Now enter

d = a b;

Notice the semicolon at the end of the command (Figure 4). The variable dwas calculated, but

the semicolon instructs MATLAB not to print its value to the screen. You can see the value ofd

by entering the command:

d

Figure 4

Question 1(Write it in your report) Summarize the use of the semicolon in MATLAB.

MATLAB variables can also be arrays or vectors. Type in the following commands andnotice the results:

a = 1:4

b = 4:8

c = 1:2:9

d = 1:3:10

Check your results with Figure 5.


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Figure 5

Question 2(Write it in your report) Summarize the use of the colon in MATLAB.

There are other ways to initialize variables.

Question 3(Write it in your report) Enter the following commands. Summarize the use of the

commands linspace, zeros, andones.

f1 = linspace(0,1,5)

f2 = linspace(1,2,9)

g1 = zeros(1,4)g2 = zeros(3,4)

h1 = ones(1,4)

h2 = ones(4,2)

You should get Figure 6.


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Figure 6

Finally, MATLAB also has string variables, which are always set off with single quote marks.message = hi there

In MATLAB, you will see Figure 7.

Figure 7


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Notice that variable names follow the same rules as in other programming languages: they must

start with a letter, and otherwise may be composed of any letters, numbers, or the underscore

character _. For example,

elec2010today = a great class

is a legal statement in MATLAB.

Calculations

MATLAB can also perform math operations on array/vector variables.

Question 4(Write it in your report) Enter the following commands and summarize the results

for your report.( We have already saved the values of a, b, c, d into MATLAB, when ?)

w = a + d

x = b + c

y = a + c

You should get the results in Figure 8. The last command gives you an error. Why?

Figure 8


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MATLAB does allow math operations with scalars even if dimensions dont match. Enter the

following command (Figure 9):

z = a + 4

Figure 9

Linear algebra problems

Since MATLAB naturally works with matrices and vectors, the system of equations mentioned

earlier can be solved very easily in MATLAB. Enter the following commands in MATLAB:

A = [ 3 , 2 ; -3 , 1]

B = [ 7 ; -1 ]

x = A\B

check = A*x - B

MATLAB will give you the result in Figure 10.

Figure 10


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Notice how matrices and vectors are entered: entries on rows are separated by (optional) commas

and each row ends with a semicolon. While the commas are optional, they are a good idea, as

are parentheses. Notice the line x = A\B. This line performs the operationx=A-1

B; that is, it

computes the solution ofAx=B.

Question 5 (Write it in your report) Enter the following commands and write yourobservations. Notice that the commas and blanks in each line do make a difference in the result.

x = [ 1, - 2 ]

y = [ 1 - 2 ]

z = [ 1 -2 ]

You can see the difference from what you get (Figure 11).

Figure 11

(It is a good idea to use commas and parentheses in order to be sure that MATLAB correctly

interprets your commands.)


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Loops

MATLAB has loop capabilities like C, C++, etc. However, the syntax for loops in MATLAB is

different. The syntax is:

for varname = row_vector

loop commands go hereend

For example, type in the following commands:

for x = 1:5

thisvar = [x, x^2]

end

You should get a table of powers of two (Figure 12). We illustrate loops further in the next

section.

Figure 12


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Displaying and output

MATLAB can display variables to the screen using the fprintf command, which is similar to

the C commands printf andfprintf. Enter the following commands at the MATLAB

window:

f1 = linspace(0,1,5)for myvar = f1

fprintf(the value is %e\n, myvar);

end

MATLAB will return Figure 13.

Figure 13

Notice that the variable myvar takes each value in the row vectorf1 (or a below). The

tag %e indicates that the value is a number that should be printed in exponential format. If the

values are integers, you can also use the %d tag:

a = 1:4

for myvar = a

fprintf(the value is %d\n,myvar);

end

Check the difference between these two types (Figure 14).


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Figure 14

MATLAB also has if-then-else commands. Type in this example (Figure 15):

for myvar = 1:6

if( myvar < 4 )

fprintf(%d is less than 4\n,myvar);

elseif ( myvar == 4 )

fprintf(%d is equal to 4\n,myvar);

else

fprintf(%d is greater than 4\n,myvar);

endend

Figure 15


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M-files

By now youve noticed that typing in commands in the MATLAB command window can be

tedious. MATLAB allows you to write scripts (programs) calledm-files so that you can write

commands in a separate text file and the run them later.

Use the MATLAB editor (file -> new -> m-file or click ) to open a new m-file. Enter thesecommands in the file: (You will see Figure 16 after you open a new m-file).

Figure 16

M-file 1 myloop.m

for myvar = 1:6

if( myvar < 4 )

fprintf('%d is less than 4\n',myvar);

elseif ( myvar == 4 )

fprintf('%d is equal to 4\n',myvar);

else

fprintf('%d is greater than 4\n',myvar);end

end

It should be the same as Figure 17.


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Figure 17

Save the file as myloop.m. (See Figure 18.)

Figure 18

Notice that MATLAB does not run these commands. Now, in the MATLAB command window,

type in

myloop

You should get Figure 19.


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Figure 19

Notice that you do nottype in the .m at the end of the command.

m-files can be called from other m-files. Write the following commands and save them in

myfile.m.

M-file 2 myfile.m

fprintf('Hi there.\n');

myloop

fprintf('back from myloop\n');

At the MATLAB command prompt, type in

myfile

and observe what MATLAB does.

Plotting

One of the most useful features of MATLAB is its plotting capability. Enter the following

commands in the MATLAB command window, and write what happens as each command is

executed.

t = linspace(0,10,100);

x = exp(-t);

plot(t,x);xlabel(time (s));

ylabel(x(t));

title(plot of e^{-t});

grid on

The output should be Figure 20.


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Figure 20

More than one signal can be plotted at a time. Enter the following commands in the MATLAB

command window:

y = sin(t);

plot(t,x,-, t,y,-.);

legend(x(t)=exp(-t), y(t) = sin(t));

grid on

xlabel(time (s));

title(two plots at once)You can see the two signals in one plot (Figure 21).


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Figure 21

Notice that each plot has three arguments: thex axis values, they axis values, and a string for the

line style. Other plotting options are documented in MATLABs help files. Type in help

command_name to see on-line documentation. For example,

help plot

and you will see Figure 22.


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Figure 22

Functions

A function is an m-file that follows a special format. Enter the following text into an m-file

window and save it as tempC.m.

M-file 3 tempC.m

function tempDegC = tempC(tempDegF)

tempDegC = (tempDegF-32.0)/1.8;

Now type in the following command at the MATLAB prompt

bodyTemp = tempC(98.6)

Your output should be like that shown Figure 23.


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ELEC 2110 E i 1 19 f 19

Figure 23

Question 6(Write it in your report) What is the value ofbodyTemp?

Remark 4 Notice the function tempC does not have a return statement or an end statement.

It only requires that the return variable centigrade be defined somewhere in the file.

Remark 5 Important! Notice that the name of the function, tempC, matches the name of the

file, tempC.m. MATLAB requires this convention. This means that every function must be in

its own m-file.

II. EXERCISES

[1] Create an array for theta varying from 0 to 2 containing at least 20 points. Now plot thesine and cosine functions, both on the same plot as a function of theta, with the grid turned on.

Add appropriate labels and title to the plot. Include this plot in your report. Make a second plot

of the sine and cosine functions as a function of degrees instead of radians and include in your

report.

[2] Given the following temperatures in Fahrenheit, convert them to Centigrade, Kelvin and

Rankine using MATLAB. How are the answers different? Now format them to get 2 decimal

places in both cases and compare your final answers.

-148, 14, 32, 50, 212, 572

[3] Create a plot of the function V = R I for the values ofR = 100 ohms andI = 0 to 100

amperes using at least 12 values ofI. Add labels and a title to your plot and include it in your

report.

[4] Create a plot of i(t) = 10 - 40 e-t

amperes for the values of t = 0 to 10 seconds with

increments of 0.5 seconds. Determine the value of time at which i(t) = 0 from your plot. Also,

determine the maximum value of i(t) from the your plot. Add labels and a title to your plot and

include it in your report.

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Expt 1 - Matlab