lab 01 intro to matlab

8/7/2019 LAB 01 Intro to Matlab

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Control Systems

INTRODUCTION TO MATLAB

LAB# 01


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Introduction to Matlab

What is Matlab?

Matlab is a commercial MATrix LABoratory package by

Mathworks, which operates as an interactive programming

environment with graphical output.

The MATLAB programming language is exceptionally straight

forward since almost every data object is assumed to be an Array.

In engineering MATLAB is displacing popular programminglanguages, due to its interactive interface, reliable algorithmic

foundation, fully extensible environment and availability of

different tool boxes.


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Introduction to MATLAB

Entering and Running MATLAB

On a system running Microsoft Windows double click on the

Matlab icon to launch Matlab.

A command window will appear with the prompt >> you are now

in MATLAB.

Leaving Matlab

A MATLAB session may be terminated by simply typing

>> quit or by typing >>exit at the MATLAB prompt.

Online HelpOnline help is available from the MATLAB prompt both generally and

for specific commands.

>> help

>> help demo


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Desktop Tools (Matlab v7)

Command Window

type commands

Workspace

view program variables clear to clear

double click on a variable to see it in the Array Editor

Command History

view past commands

save a whole session using diary


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Variables

MATLAB is case sensitive, that is

a is not the same as A

MATLAB has built in variables like pi, eps and ans.

The variable ans will keep track of the last output which was not

assigned to another variable.

Variable Assignment:

The equality sign is used to assigned values to variables.

>> x = 3 y = x ^ 2

Out put can be suppressed by appending a semicolon to thecommand lines.

>> x = 3 ; y = x 2 ;


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Variables

Active Variables:

Who

Removing Variables Clear x

Clear

Saving and RestoringVariables

Save filename

Load filename


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Variable Arithmetic

Operator precedence

2 + 3 *4 ^ 2

Double Precision Arithmetic Normally the results will be displayed in a shorter form.

a = sqrt( 2 ) >> a = 1.4142

Format long

b = sqrt ( 2 ) >> b = 1.41421356.

Format short

Command Line Editing

The arrow keys allow command line editing


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Built in Mathematical Functions

Functions Meaning Examples

Sin sine sin ( pi )=0.0

Cos cosine cos ( pi )=1.0

Tan tangent tan ( pi / 4)=1.0

Exp exponential exp(1.0)=2.7183

log natural log log(2.7183)=1.0

Arguments to trigonometric functions are given in radians.

x= pi / 3; sin( x ) 2 + cos ( x ) ^ 2 = ?


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Matrices

The element within a row of a matrix may be separated by a commas

as well as a blank.

The elements of a matrix being created are enclosed by brackets.

A matrix is entered in row major order [i.e. all of the first row, then

all of the second row; etc];

Rows are separated by semicolon [or a new line], and the elements of

the row may be separated by either a comma or space.

The following commands will create a 3 x 3 matrix and assigned it to

the variable A.

>> A = [1 2 3; 4 5 6; 7 8 9]; or A = [1,2,3;4,5,6;7,8,9]

>> A = [ 1 2 3

4 5 6

7 8 9 ]


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Matrices

The matrix element located in the i-th row and j-th column

of A is referred to in the usual way:

>> A (1 , 2), A ( 2 , 3)

Matrices can be easily modified:

A ( 2 , 3 ) = 10;

Building Matrices from a Block:

Large matrices can be assembled from smaller matrix blocks i.e.

C = [A;10 11 12];

[A; A; A] [A, A, A]

>> B = [A, zeros(3,2); zeros(2,3), eye( 2 ) ] ?


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Built in Matrix Functions

Function Description

diag return diagonal M.E as a vector

eye identity matrixmagic magic squares

ones matrix of ones

rand randomly generated matrix

zeros matrix of zeros


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Built in Matrix Functions

Matrices of Random Entries: >> rand ( 3 )

>> rand ( m , n )

Magic Squares: A magic square is a square matrix which has equal sums along all its rows

and columns. >> magic ( 4 )

Matrix of Ones: >> eye ( m , n )

>> eye ( n )

Matrices of Zeros:

>> zeros ( m , n ) >> zeros ( n )

Diagonal Matrices: >> diag (A)

diag ( diag ( A ) ) ?


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Matrix Operations

+ Addition

- Subtraction

* Multiplication

^ Power

Transpose

/ Division

* If the sizes of the matrices are incompatible for the matrix

operation, an error message will result.

.* element-by-element mul

./ element-by-element div

.^ element-by-element power

. transpose


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Matrix Operations

Matrix Transpose: >> A

Matrix Addition / Subtraction:

A + B, A B

Matrix Multiplication;

A * B , B * A.

Round Floating Point Numbers to Integers: >> f = [-.5 .1 .5 ]

round (f)

ceil (f)

floor (f)

sum (f)

prod (f) Matrix Element Level Operations:

The matrix operation of addition and subtraction are already operates onan element by element basis but other operation given above do not.

Matlab has a convention in which a dot in front of the operations is used.

i.e [1 , 2 , 3 , 4 ] . * [ 1 , 2 , 3 , 4 ]

[ 1 , 2 , 3 , 4 ] . 2


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Operators (relational, logical)

== equal

~= not equal

< less than greater than

>= greater than or equal

& AND

| OR

~ NOT


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Branching Constructs

If end Construct:

if < condition >,

< program >

end

If - else - end Construct:

if < condition 1 >,

< program 1>

else

< program2 >

end

If - elseif - end Construct:

if < condition1 >,

< program 1>

elseif

< program2 >

end


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Looping Constructs

For Loops:

for i = 1 : n ,

< program>,

end

While Loops:

while < condition >,

< program >,

end

Nested For Loops:

for i = 1 : n ,

for j = 1 : n ,

A(i,j) = i/j ;

end

end


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Matlab M-files

Matlab commands can be run from one file without having

to enter each command one by one at Matlab prompt.

In order to use the programs later in Matlab they are to be

saved first. For this purpose programs should be written in the editor /

debugger.

In command window go to File menu, new and select M-file.

Code your algorithm

Execute it from the command window by typing file name


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Matlab User Defined Function

Matlab User Defined Function can have an input and output.

Arguments can be passed to a function for computation

For this purpose programs should be written in the editor / debugger.

In command window go to File menu, new and select M-file. function add

x = 3; y = 5;

z = x + y

Save the file and write add at the command prompt

function addv (x,y)

Z = x + y

Save the file and write addv(5,6) at the command prompt

% is used for commenting in front of a statement


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Input/ Output

Request User Input

data=input(message);

data=input(message,s)

Ouput Data

disp(message)

disp(variable_name)


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Matlab Graphics

x = 0:pi/100:2*pi;

y = sin(x);

plot(x,y)

xlabel('x = 0:2\pi')

ylabel('Sine of x')

title('Plot of the

Sine Function')


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Multiple Graphs

t = 0:pi/100:2*pi;

y1=sin(t);

y2=sin(t+pi/2);

plot(t,y1,t,y2)

grid on


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Multiple Graphs

x = 0 : .01 : 2 * pi;

y1= sin(x);

y2 =sin(2*x);

y3 = sin(4*x);

plot(x,y1,--',x,y2,-,x,y3,+')

grid

title('Dashedlineanddotted

linegraph')


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Multiple Plots

t = 0:pi/100:2*pi;

y1=sin(t);

y2=sin(t+pi/2);

subplot(2,2,1)

plot(t,y1)

subplot(2,2,2)

plot(t,y2)


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Three Dimensional Graphics

x = -1:.1:1;

y = -1:.1:1;

fori=1:1:length(x)

for j=1:1:length(y)

z(i,j)=x(i)^2+y(j)^2;

end

end

mesh(z);


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Graph Functions (summary)

plot (x,y) linear plot

plot (x,y1,x,y2) multiple plots on the same graph

mesh(z) 3-D graph

stem (x) discrete plot

xlabel (X-axis label ) add X-axis label

ylabel (Y-axis label ) add Y-axis label

title (title of plot) add graph title

subplot (m,n,p) divide figure window

grid add grid lines

hold hold current graph in the figure

zoom allow zoom in/out using mouse

figure create new figure window

pause wait for user response

lab 01 intro to matlab

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