1) Matlab_Miniguide

7/31/2019 1) Matlab_Miniguide

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Chemical Engineering Department

University of Florida

Oscar D. Crisalle 1997-2009 File Name: Matlab_Miniguide_Rev_7.3.doc

MATLAB MINIGUIDEby Prof. Oscar D. Crisalle

CONTENTS

1.1 MATLAB Manuals and Literature ..............................................................................................11.1.1 Manuals and Tutorials Available at CIRCA ..................................... 1

1.2 Introduction to MATLAB .............................................................................21.2.1 Modes of Using MATLAB ..............................................................21.2.2 Executing the MATLAB Program....................................................21.2.3 Exiting from the MATLAB Program ............................................... 21.2.4 Obtaining On-Line Help .................................................................. 21.2.5 Useful Keyboard Commands ...........................................................31.2.6 Adjusting the Format of Numbers Displayed....................................3

1.3 List of Essential Commands and Operators .................................................41.4 Overview of MATLAB Operations ...............................................................5

1.4.1 Defining Vectors, Matrices and Polynomials....................................51.4.2 Defining Three Useful Functions ones, zeros, eye ........................ 61.4.3 Defining Transcendental Functions sin, cos, log, exp ...................71.4.4 Defining Basic Operations det, eig, conv, poly.............................8

1.5 Advanced MATLAB Commands ..................................................................101.5.1 Plotting............................................................................................101.5.2 Displaying to the Screen .................................................................. 111.5.3 Operating with Strings of Characters................................................121.5.4 Appending Results to a Vector or a Matrix.......................................131.5.5 Taking Input from the Keyboard ......................................................141.5.6 Creating a Diary File........................................................................ 151.5.7. Creating an M-File.......................................................................... 151.5.8

If Structure.......................................................................................16

1.5.9 While Structure................................................................................161.5.10 For Structure..................................................................................171.5.11 Break Command ............................................................................171.5.12 M-Functions...................................................................................181.5.13 Quadrature/Numerical Integration.................................................. 201.5.14 ODE23/ODE45..............................................................................21


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Oscar D. Crisalle 1997-2009 - 1 - MATLAB Miniguide

1.1 MATLAB MANUALS AND LITERATURE

Program name:

MATLAB (personal computers)

PRO-MATLAB (workstations)

Note: Manuals may be titledMATLAB or PRO-MATLAB.

Basic manuals an documentation:

a. MATLAB user's guide (tutorial and reference)

b. Control Toolbox manual

c. SIMULINK Manual

d. Various manuals for each toolbox

1.1.1 Manuals and Tutorials Available at CIRCA

a. CIRCA Lab:

Room: CSE 211 - Phone: 392-2446

Hours: M-F 8:00 AM - midnight Sat. Noon - Midnight

b. CIRCA consultants office

Room: CSE 520 - Phone: 2-HELP (2-4357)

Hours: M-F 9:00 AM - 5:00 PM


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1.2 INTRODUCTION TO MATLAB

MATLAB is a high-level computer language with powerful commands that emphasize

numerical operations with matrices. The word MATLAB itself is derived from the words

MATrix LABoratory. Originally MATLAB carried out only linear algebra calculations (matrix

operations) but has now been extended to include operations useful for signal processing, control

analysis and design, nonlinear differential equations, and many others. These extensions are

done by a number of routines collected under directories called Toolboxes, such as the following:

Control toolbox Robust control toolbox

Identification toolbox MFD (multivariable frequency design) toolbox

Optimization toolbox Splines toolbox

The related program SIMULINK includes MATLAB plus additional capabilities for

simulating nonlinear dynamic systems. MATLAB is available in almost all computer platforms

(IBM, Macintosh, HP, Sun, DEC). All commands remain unchanged from one computer to

another.

1.2.1 Modes of Using MATLAB

a. Interactive (commands issued using a keyboard).

b. M-files (programs) , which can be of three types: (1) M-scripts (also called M-files),

(2) M-functions, and (3) SIMULINK M-files.

1.2.2 Executing the MATLAB Program

Type: matlab

The prompt >> appears, indicating that MATLAB is ready to receive interactive

commands.

1.2.3 Exiting from the MATLAB Program

Type: >> quit

Note that you only need to type the word quit; the symbol >> is the MATLAB prompt.

1.2.4 Obtaining On-Line Help

Type: >> help to get a list of commands


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Example: to get help on the command dir type: >> help dir

Type: >> demo to get a demonstration of some of MATLAB's features.

1.2.5 Useful Keyboard Commands

Repeats previous command

Advances to next command

Move left on command line

Move right on command line

^a Move to beginning of command line

^e Move to end of command line

^d Delete next character

Backspace Delete previous character

1.2.6 Adjusting the Format of Numbers Displayed

format short shows 5 digits

format short e shows 5 digits in exponential form

format long shows 15 digits

format long e shows 15 digits in exponential form

format compact does not display extra blank line after each answer is

echoed


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1.3 LIST OF ESSENTIAL COMMANDS AND OPERATORS

The following commands must be thoroughly studied from the MATLAB manual (or

tutorial) so you may carry out the essential operations available.

diary

save, load

help

who, whos, size, dir, clear

inv

eig

zeros, ones, eye

conv

roots

format short, format compact, format short e

plot, hold, axis, title, text, shg, clg, semilog, loglog, subplot

%

' (apostrophe)

: (colon)

; (semicolon)

, (comma)

All of these commands must be typed in lowercase (MATLAB is case-sensitive).

To learn more about a command, type help. Example: >> help whos


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1.4 OVERVIEW OF MATLAB OPERATIONS

1.4.1 Defining Vectors, Matrices and Polynomials

>> x = [ 123]

x =

123

Defines column vectorx =

1

2

3

!

"

###

$

%

&&&

Echo displayed on the screen

>> x = [1; 2; 3]

x =1

23

Defines column vectorx =

1

2

3

!

"

###

$

%

&&&

The semicolon indicates that the next element ison a new row (the semicolon is an end-of-row

marker)

>>x = [1 2 3]

x =

1 2 3

Defines row vector x = [1 2 3]

Echo printed on screen

>> x = [1, 2, 3]

x =

1 2 3

Defines row vector x = [1 2 3 ]

The comma indicates that the next element is on

a new column ( the comma is an end-of-columnmarker)

>> A = [5 67 8]

A =5 6

7 8

Defines matrix A

>> A = [5, 6; 7, 8]

A =

5 67 8

Defines matrix A

The comma separates elements on the same row,

and the semicolon separates elements ondifferent rows

>> b = A(2, 2)b =

8

Denotes the element (2, 2) of matrix A

>> b = A(2, :)

b =7 8

Denotes row 2 ofA and all columns of matrix A

>> b = A(:, 2)

b =6

8

Denotes all rows ofA and column 2 of matrix A


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>> b = A(1, 1) + A(2, 2)

b =

13

Sum of elements (1, 1) and (2, 2) of matrix A

>> A(1, 1) + A(2, 2)

ans =

13

Sum of elements (1, 1) and (2, 2) of matrix A

The result is written to the default variable ans>> p = [1 0.9 0.3]

p =1 0.9 0.3

Denotes the polynomial

p(s) = s2 + 0.9s + 0.3

Polynomials are represented as row vectors.>> size(A)

ans =2 2

Finds the number of rows and columns

of matrix A

>> poly2sym([1 0.9 0.3], s)

ans =

s2

+ 0.9s + 0.3

Transforms a row-vector polynomial

representation into a standard symbolic

representation shown the powers of the variable s

and all the terms in the polynomial (requires thatthe Symbolic Toolbox be installed)

>> size(p)

ans =

1 3

Finds the number of rows and columns

of vector p

>> who

Your variables are:A ans b p x

List all variables currently defined

1.4.2 Defining Three Useful Functions ones, zeros, eye

>> B = ones(2, 2)

B =1 1

1 1

Create a matrix consisting of 2 rows and 2columns, and whose entries are all equal to 1

>>B = ones(2, 1)

B =

11

Create a matrix consisting of 2 rows and 1column, and whose entries are all equal to 1

>> A = [5 6 9; 7 8 10], ...

B = ones(size(A))

A =5 6 9

7 8 10B =

1 1 1

1 1 1

More than one command can be given on a line,by separating each individual command with acomma. Commands can also be embedded into

other commands.

The ellipsis (...) indicates that the command

continues on the next line

>> B = ones(3) When only one number is given, the function


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B =1 1 1

1 1 11 1 1

ones returns a square matrix.

>> C = zeros(2, 2)

C =0 00 0

Creates a matrix whose entries are all zeros.

>> C = zeros(2, 1)

C =0

0

>> C = zeros(size(A))

C =0 0 0

0 0 0

>> C = zeros(3)

C =0 0 0

0 0 00 0 0

>> D = eye(2, 2)

D =

1 00 1

Creates an identity matrix of order 2

>> D = eye(2, 3)

D = 1 0 00 1 0

The matrix does not have to be square for eye towork

>> D = eye(size(A))

D =1 0 00 1 0

>> D = eye(3)

D =1 0 0

0 1 00 0 1

1.4.3 Defining Transcendental Functions sin, cos, log, exp

>> pi = 4 * atan(1)

pi =3.1416

Defines = 4 arctan(1).


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>> d = cos(pi)

d =

-1

cosine function

>> d = log10(100)

d =

2

Logarithm to base 10

>> d = log(100)

d =4.6052

Natural logarithm (base e)

1.4.4 Defining Basic Operations det, eig, conv, poly

>> A

A =

5 67 8

Displays matrix A

>> B = A'

B =

5 76 8

Transpose of matrix A. The apostrophe is usedto denote transposition, since it is common in

mathematics to use the nomenclature A to

denote AT>> C = A + B

C =10 13

13 16

Sum of two matrices

>> det(A)

ans =

-2

Determinant of matrix

>> C = inv(A)

C =-4 3

3.5 -2.5

Matrix inversion

>> C * A

ans =1 0

0 1

Matrix multiplication

>> D = abs( [-3, 4] )

D =

3 4

Absolute value of elements of row vector [-3, 4]

>> C = A^2

C =67 78

91 106

Find the second power of matrix A (i.e. A2)

>> eig(A) Finds the eigenvalues of matrix A


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ans =-0.1521

13.1521

>> [H, L] = eig(A)

H =

-0.7587 -0.59280.6515 0.8054

L =

-0.1521 00 13.1521

Eigenvalues ofA are written in diagonal matrix

L =!1 0

0 !2

"

#$

%

&'

and eigenvectorsv1

andv2

arewritten in the columns of matrix H = v1 v2[ ],

where v1 =!0.7587

0.6515

"

#$%

&'and v2 =

-0.5928

-0.8054

!

"#

$

%&

>> b = [10; 20], C = [A, b]

b =1020

C =5 6 107 8 20

Augments matrix A with vector b to obtain C

>> i = sqrt(-1)

i =0 + 1i

Defines the imaginary unit i =!1

>> z = 3 + 4 * iz =

3 +4i

Defines a complex number z = 3 + 4 i.

>> z + (1 + 10 * i )

ans =

4 + 14i

Addition of complex numbers

>> p1 = [1, 0.3], ...

p2 = [1, 0.1]

p1 =1 0.3

p2 =

1 0.1

Defines polynomialsp1(s) = s + 0.3 and p2(s) = s + 0.1

The ellipsis (...) indicates that the commandcontinues on the next line

>> p3 = conv(p1, p2)

p3 = 1 0.4 0.03

Product of two polynomials (convolution)

p3(s) = p1(s) p2(s) = s2 + 0.4s + 0.03

>> p = [1 -6 11 -6], ...r = roots(p)

p =

1 -6 11 6r =

32

1

Define p(s) = s3 - 6s2 + 11s - 6 and find itsroots (s1 = 3, s2 = 2, and s3 = 1). The roots are

stored in column-vector r.

>> q = poly(r)

q =1 -6 11 -6

Creates polynomial q(s) which has roots

indicated by the entries of vector r = [3 2 1]T.

Here q(s) = s3 6s2 + 11s - 6


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1.5 ADVANCED MATLAB COMMANDS

1.5.1 Plotting

x = [0:0.1:10];

y = sin(x);

plot(x, y);

Generates vector x with first component equal to

0 and last component equal to 10. Intermediate

components are spaced at intervals equal to 0.1

Calculates vector y

Generates a plot ofx versus y

0 2 4 6 8 10-1

-0.5

0

0.5

1

plot(x, y, '--') Generates a plot ofx versus y using dashed lines

0 2 4 6 8 10-1

-0.5

0

0.5

1

title('sine plot')xlabel('x')


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ylabel('sin(x)')grid

0 2 4 6 8 10-1

-0.5

0

0.5

1s ne p o

x

s

n

x

help plot

Provides help on the "plot" command. See also:loglog, semilog, polar, text

print -dpdf FileName Saves the figure that is currently displayed as aPDF (portable document format) file with name

FileName.pdf

print -deps -tiff -r300 FileName Saves the figure that is currently displayed as a

color EPS (encapsulated PostScript) file withname FileName.eps that will print in a PostScript

printer with a resolution of 300 dpi. The default

resolution is 150 dpi. The option -tiffcreaters a 72 dpi preview that can be displayed in

a computer screen by many word processors that

import the file.

print -depsc -tiff -r300 FileName Same as above, except that the file is saved in acolor EPS format.

print dill FileName Saves the figure that is currently displayed to a

file with the name FileName.ai that is compatiblewith the Adobe Illustrator graphical software

package.

1.5.2 Displaying to the Screen

disp('Result') Displays the string "Result" on the screen


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Result

disp('Result'),disp('------')

Result------

Displays the string "Result" on the screen

followed by a dashed underline

A = [1,2;3,4]

A =

1 23 4

Defines matrix A and echoes the result to the

screen

disp(A)1 23 4

Displays the entries of matrix A but does not

display the header line "A ="

1.5.3 Operating with Strings of Characters

s = 'This is a string'

s =

This is a string

Defines a string of characters and stores it in

variable s

disp(s)

This is a string

s1 = 'This is';s2 = ' a string';

s3 = [s1 s2]

s3 =

This is a string

Defines string s1Defines string s2

Defines string s3 as the concatenation of s1 and

s2

s1 = 'x is equal to ';

x = 17;s2 = num2str(x);

s3 = [s1 s2]

s3 =

Defines string s1Assigns a value to variable x

Changes the value numeric variable x to a string

of characters. NOTE: num2str only converts

only to four decimal places


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x is equal to 17

disp(s3)

x is equal to 17

help disp See also: sprintf, fprintf, num2str, int2str

1.5.4 Appending Results to a Vector or a Matrix

x = []

x =

[]

x1 = [10;20]

x1 =

10

20

x2 = [100;200]

x2 =

100

200

x = [x; x1]

x =

10

20

x = [x;x1]

x =

102010

20

x = [x;x2;x2]

x =

1020

Defines an empty vector

Defines vector x1

Defines vector x2

Appends columns of x1 to x

Appends again columns of x1 to x


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1020100

200100200

Appends columns of x2 twice to x

z = [1;10;100;1000]

z =1

10

1001000

y = log10(z);

y =

012

3

t = [z, y]

t =

1 010 1

100 21000 3

disp(' t y'); ...

disp('---- ---'); disp(t)

t y---- ---

1 010 1

100 2

1000 3

Creates a two-column matrix

1.5.5 Taking Input from the Keyboard

n = input('Give value of n ')

Give value of n

n =

3

Asks the user to give a value for n

If user enters "3" followed by return, the value of

n is displayed on the screen


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1.5.6 Creating a Diary File

diary exercise1

x = [1 10 100]

x =

1 10 100

y = log10(x)

y =

0 1 2

diary off

Creates a file named 'exercise1' with the

following contents that contains all the linesdisplayed to the screen following the command

"diary". The file exercise1 has the followingcontents:

x = [1 10 100]

x =

1 10 100

y = log10(x)

y =

0 1 2

diary off

1.5.7. Creating an M-File

An M-file (or M-script) is a text file that contains MATLAB commands, and has the extension

.m. Create this text file using a text editor. Common text editors are: xedit, vi, and emacs.

x = [1 10 100]

y = log10(x)

Use a text editor to create and save a file (M-file)containing the two lines shown on the left

column. Save the file under the name 'test1.m'

test1

x =

1 10 100

y =

0 1 2

Execute 'test1.m' from the MATLAB command

window


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1.5.8 If Structure

x = input('value of x ')

if x < 0

disp('x negative')

elseif x == 0

disp('s is equal to 0')

else

disp('s is positive')

end

Create an M-file entitled 'test2.m' containing the

lines shown on the left column.

The relational operators are:

== equal ~= not equal

< less than greater than >= greater than or equal

| logic or & logic and

To get help on these operators type

help relop

>>test2

value of x

x =3

x is positive

Execute 'test2.m' from the MATLAB command

window and input the value "3" in response to

the query.

1.5.9 While Structure

x = 1000

while x > 1

x = x / 10

end

Create an M-file entitled 'test3.m' containing thelines shown on the left column.

>>test3

x =1000

x =

100

x =

10

x =

Execute 'test3.m' from the MATLAB commandwindow


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1

1.5.10 For Structure

for i = 5:-1:1

disp(i)

end


>>test4

5

432

1


1.5.11 Break Command

The break command forces the termination of a for loop or awhile loop.

x = [0:0.001:10]';y = sin(x);

n = length(y);

for i = 1 : n

if y(i) >= 0.95

x1 = x(i);break

end

end

disp(['sine is equal to 0.95 at

x = ' num2str(x1)])


The break command exits the loop whenever the

line containing the word "break" is executed.

>>test5

sine is equal to 0.95 at x = 1.254



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1.5.12 M-Functions

M-functions are M-files that take inputs and return outputs.

function f = sqlog(x)

f = x^2 * log10(x);

return

Create an M-file entitled 'sqlog.m' containing the

lines shown on the left column.

The variable "f" appearing to the left of the equal

sign of the first line is the output, while the

variable "x" appearing on the right hand side isthe input to the function.

>>x = 1;

>>sqlog(x)

ans =

0

>>x=10; sqlog(x)

ans =

100

Assign the value of 1 to variable x.

Execute 'sqlog.m' from the MATLAB command

window.

function f = xsqylog(x, y) ;

f = x^2 * log10(y)

return

Create an M-file entitled 'xsqylog.m' containingthe lines shown on the left column. M-functions

can have multiple inputs.

>>xsqylog(3,100)

ans =

18

Execute 'xsqylog.m' from the MATLAB

command window.

function [f, g] = fsqglog(x)

f = x^2;g = log10(x);

return

Create an M-file entitled 'fsqglog.m' containing

the lines shown on the left column. M-functionscan have multiple outputs.

>>[f, g] = fsqglog(10)

f =100

g =

Execute 'fsqglog.m' from the MATLAB

command window.


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1


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1.5.13 Quadrature/Numerical Integration

The integration of functions can be done using the gaussian-quadrature function QUAD. This

function requires that the user define an M-function that calculates the integrand for any value of

the dummy integration variable. The example below calculates the integral (2x +1)ab! dx .

function f = integrand(x)

f = 2 * x + 1;

return

Create an M-file entitled 'integrand.m' containingthe lines shown on the left column.

>>a = 0; b = 1 ;>>quad('integrand', a, b)

ans =

2

Define integration limits

Call the QUAD function to integrate the functionintegrand.m between limits a to b

See also: quad8


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1.5.14 ODE23/ODE45

ODE23/ODE45 are differential equation solvers. This section describes solvers that appeared in

earlier versions of MATLAB; consequently, these commands may be obsolete. On the other

hand, the newer solvers retain the basic ideas of the functions ODE23 or ODE45 described

below. The differential equation solved is of the form

dx/dt = f(t, x)

where f(t, x) is known informally as the right-hand-side function. The functions ODE23 and

ODE45 are ordinary differential equation solvers of variable orders 2-3 and 4-5, respectively.

They require that the user define an M-function that calculates the values of the right-hand-side

function f(x, t). The example below calculates the solution to the equation

dx/dt = t2 log(x)

with initial value xo = 2. The result is obtained for values of t ranging from to = 0 to tf= 4.

function f = dxdt(t,x)

f = -t^2 * log(x)

return

Create an M-file entitled 'dxdt.m' containing thelines shown on the left column.

>>t0 = 0; tf = 4;>>x0 = 2;

>>[t,x] = ode23('dxdt',t0,tf,x0);>>plot(t,x)>>xlabel('t')

>>ylabel('x')

0 1 2 3 40.8

1

1.2

1.4

1.6

1.8

2

t

x

Define initial and final times to and tf

Define initial condition xo

Call the ODE23 solver

Plot the solution

Documents

1) Matlab_Miniguide