4. x=0.1:0.1:10;
4
b=sin(x);
Plot(x,b)
------ no
computational
complexity
5. 5
That is the beauty we have as an
engineer.
Name is
MATLAB
6. Recent Trends in Computational
techniques for Engineering
6
Use of MATLAB in
Engineering
Prof. Ashish M. Kothari
Department of Electronics & Communication Engineering
Atmiya Institute of Technology & Science, Rajkot
7. Topics..
7
What is MATLAB ??
Basic Matrix Operations
Script Files and M-files
Some more Operations and Functions
Plotting functions ..
8. Topics..
8
What is MATLAB ??
Basic Matrix Operations
Script Files and M-files
Some more Operations and Functions
Plotting functions
9. MATLAB
9
“MATrix LABoratory”
Powerful, extensible, highly integrated
computation, programming, visualization, and
simulation package
Widely used in engineering, mathematics, and
science
11. MATLAB- Starting & Quiting
11
Starting MATLAB
On a Microsoft Windows platform, to start MATLAB, double-click the
MATLAB shortcut icon on your Windows desktop.
On Linux, to start MATLAB, type matlab at the operating system prompt.
After starting MATLAB, the MATLAB desktop opens – see “MATLAB
Desktop”.
You can change the directory in which MATLAB starts, define startup
options including running a script upon startup, and reduce startup time in
some situations.
12. MATLAB- Starting & Quiting
12
Quiting MATLAB
To end your MATLAB session, select Exit MATLAB from the
File menu in the desktop, or type quit in the Command
Window.
15. MATLAB Variable
15
Variable names ARE case sensitive
Variable names can contain up to 63 characters (as of
MATLAB 6.5 and newer)
Variable names must start with a letter followed by letters,
digits, and underscores.
16. MATLAB Variable
16
>> 16 + 24 no declarations needed
ans =
40
>> product = 16 * 23.24 mixed data types
product =
371.84
semi-colon suppresses output of
>> product = 16 *555.24; the calculation’s result
>> product
product =
8883.8
17. MATLAB Variable
17
>> clear clear removes all variables;
>> product = 2 * 3^3;
>> comp_sum = (2 + 3i) + (2 - 3i); clear x y removes only x and y
>> show_i = i^2;
complex numbers (i or j) require
>> save three_things
no special handling
>> clear
>> load three_things
>> who
save/load are used to
Your variables are:
comp_sum product show_i retain/restore workspace variables
>> product
product =
54
use home to clear screen and put
>> show_i
cursor at the top of the screen
show_i =
-1
18. MATLAB Special Variables
18
ans Default variable name for results
pi Value of π
eps Smallest incremental number
inf Infinity
NaN Not a number e.g. 0/0
i and j i = j = square root of -1
realmin The smallest usable positive real number
realmax The largest usable positive real number
19. Topics..
19
What is MATLAB ??
Basic Matrix Operations
Script Files and M-files
Some more Operations and Functions
Plotting functions ..
20. Math & Assignment Operators
20
Power ^ or .^ e.g a^b or a.^b
Multiplication * or .* e.g a*b or a.*b
Division / or ./ e.g a/b or a./b
or or . e.g ba or b.a
NOTE: 56/8 = 856
- (unary) + (unary)
Addition + a+b
Subtraction - a-b
Assignment = a=b (assign b to a)
21. Other MATLAB symbols
21
>> prompt
... continue statement on next line
, separate statements and data
% start comment which ends at end of line
; (1) suppress output
(2) used as a row separator in a matrix
: specify range
22. MATLAB Relational Operators
22
MATLAB supports six relational operators.
Less Than <
Less Than or Equal <=
Greater Than >
Greater Than or Equal >=
Equal To ==
Not Equal To ~=
23. MATLAB Logical Operators
23
MATLAB supports three logical operators.
not ~ % highest precedence
and & % equal precedence with or
or | % equal precedence with and
24. MATLAB Matrices
24
MATLAB treats all variables as matrices. For our purposes
a matrix can be thought of as an array, in fact, that is how
it is stored.
Vectors are special forms of matrices and contain only one
row OR one column.
Scalars are matrices with only one row AND one column
25. MATLAB Matrices
25
A matrix with only one row AND one column is a scalar. A
scalar can be created in MATLAB as follows:
» a_value=23
a_value =
23
26. MATLAB Matrices
26
A matrix with only one row is called a row vector. A row
vector can be created in MATLAB as follows (note the
commas):
» rowvec = [12 , 14 , 63]
rowvec =
12 14 63
27. MATLAB Matrices
27
A matrix with only one column is called a column vector.
A column vector can be created in MATLAB as follows
(note the semicolons):
» colvec = [13 ; 45 ; -2]
colvec =
13
45
-2
28. MATLAB Matrices
28
A matrix can be created in MATLAB as follows (note the
commas AND semicolons):
» matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]
matrix =
1 2 3
4 5 6
7 8 9
29. Extracting a Sub-Matrix
29
A portion of a matrix can be extracted and stored in a
smaller matrix by specifying the names of both matrices
and the rows and columns to extract. The syntax is:
sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ;
where r1 and r2 specify the beginning and ending rows
and c1 and c2 specify the beginning and ending columns
to be extracted to make the new matrix.
30. MATLAB Matrices
30
A column vector can be Here we extract column 2
extracted from a matrix. of the matrix and make a
As an example we create a column vector:
matrix below:
» matrix=[1,2,3;4,5,6;7,8,9] » col_two=matrix( : , 2)
matrix = col_two =
1 2 3
4 5 6 2
7 8 9 5
8
31. MATLAB Matrices
31
A row vector can be Here we extract row 2 of
extracted from a matrix. the matrix and make a
As an example we create row vector. Note that
a matrix below: the 2:2 specifies the
second row and the 1:3
» matrix=[1,2,3;4,5,6;7,8,9] specifies which columns
of the row.
matrix =
» rowvec=matrix(2 : 2 , 1 :
3)
1 2 3
4 5 6 rowvec =
7 8 9
4 5 6
32. Topics..
32
What is MATLAB ??
Basic Matrix Operations
Script Files /M-files and Function Files
Some more Operations and Functions
Plotting functions ..
33. Use of M-File
33
There are two kinds of M-files:
Scripts, which do not accept input
arguments or return output arguments. They
operate on data in the workspace.
Functions, which can accept input
arguments and return output arguments.
Internal variables are local to the function.
Click to create
a new M-File
34. M-File as script file
34
Save file as filename.m
Type what you want to
do, eg. Create matrices
If you include “;” at the
end of each statement,
result will not be shown
immediately
Run the file by typing the filename in the command window
35. MATLAB Function File
35
function [a b c] = myfun(x, y) Write these two lines to a file myfun.m
b = x * y; a = 100; c = x.^2; and save it on MATLAB’s path
>> myfun(2,3) % called with zero outputs
ans =
100
>> u = myfun(2,3) % called with one output
u =
100
>> [u v w] = myfun(2,3) % called with all outputs
u =
100
v = Any return value which is not stored in
6 an output variable is simply discarded
w =
4
36. Topics..
36
What is MATLAB ??
Basic Matrix Operations
Script Files and M-files
Some more Operations and Functions
Plotting functions ..
37. Some Useful MATLAB commands
37
who List known variables
whos List known variables plus their size
help >> help sqrt Help on using sqrt
lookfor >> lookfor sqrt Search for
keyword sqrt in m-files
what >> what a: List MATLAB files in a:
clear Clear all variables from work space
clear x y Clear variables x and y from work space
clc Clear the command window
38. Some Useful MATLAB commands
38
what List all m-files in current directory
dir List all files in current directory
ls Same as dir
type test Display test.m in command window
delete test Delete test.m
cd a: Change directory to a:
chdir a: Same as cd
pwd Show current directory
which test Display directory path to ‘closest’
test.m
39. MATLAB Logical Functions
39
MATLAB also supports some logical functions.
xor (exclusive or) Ex: xor (a, b)
Where a and b are logical expressions. The xor
operator evaluates to true if and only if one
expression is true and the other is false. True is
returned as 1, false as 0.
any (x) returns 1 if any element of x is nonzero
all (x) returns 1 if all elements of x are nonzero
isnan (x) returns 1 at each NaN in x
isinf (x) returns 1 at each infinity in x
finite (x) returns 1 at each finite value in x
40. Matlab Selection Structures
40
An if - elseif - else structure in MATLAB.
Note that elseif is one word.
if expression1 % is true
% execute these commands
elseif expression2 % is true
% execute these commands
else % the default
% execute these commands
end
41. MATLAB Repetition Structures
41
A for loop in MATLAB for x = array
for ind = 1:100
b(ind)=sin(ind/10)
end
while loop in MATLAB while expression
while x <= 10
% execute these commands
end
43. Scalar - Matrix Addition
43
» a=3;
» b=[1, 2, 3;4, 5, 6]
b=
1 2 3
4 5 6
» c= b+a % Add a to each element of b
c=
4 5 6
7 8 9
44. Scalar - Matrix Subtraction
44
» a=3;
» b=[1, 2, 3;4, 5, 6]
b=
1 2 3
4 5 6
» c = b - a %Subtract a from each element of b
c=
-2 -1 0
1 2 3
45. Scalar - Matrix Multiplication
45
» a=3;
» b=[1, 2, 3; 4, 5, 6]
b=
1 2 3
4 5 6
» c = a * b % Multiply each element of b by a
c=
3 6 9
12 15 18
46. Scalar - Matrix Division
46
» a=3;
» b=[1, 2, 3; 4, 5, 6]
b=
1 2 3
4 5 6
» c = b / a % Divide each element of b by a
c=
0.3333 0.6667 1.0000
1.3333 1.6667 2.0000
47. The use of “.” – “Element” Operation
47
Given A:
Divide each element of Multiply each Square each
A by 2 element of A by 3 element of A
48. MATLAB Toolboxes
48
MATLAB has a number of add-on software modules, called
toolbox , that perform more specialized computations.
Signal Processing
Image Processing
Communications
System Identification
Wavelet Filter Design
Control System
Fuzzy Logic
Robust Control
-Analysis and Synthesis
LMI Control
Model Predictive Control
…
49. MATLAB Demo
49
Demonstrations are invaluable since they give an indication
of the MATLAB capabilities.
A comprehensive set are available by typing the command
>>demo in MATLAB prompt.
demo
51. Topics..
51
What is MATLAB ??
Basic Matrix Operations
Script Files and M-files
Some more Operations and Functions
Plotting functions ..
52. Plot
52
Example
PLOT Linear plot.
x = [-3 -2 -1 0 1 2 3];
PLOT(X,Y) plots vector Y y1 = (x.^2) -1;
versus vector X
plot(x, y1,'bo-.');
PLOT(Y) plots the columns of
Y versus their index
PLOT(X,Y,S) with plot
symbols and colors
See also SEMILOGX,
SEMILOGY, TITLE,
XLABEL, YLABEL, AXIS,
AXES, HOLD, COLORDEF,
LEGEND, SUBPLOT...
52
53. Plot Properties
53
Example
XLABEL X-axis label. ...
xlabel('x values');
XLABEL('text') adds text ylabel('y values');
beside the X-axis on the
current axis.
YLABEL Y-axis label.
YLABEL('text') adds text
beside the Y-axis on the
current axis.
53
54. Hold
54
Example
HOLD Hold current graph. ...
hold on;
HOLD ON holds the current
y2 = x + 2;
plot and all axis properties so
plot(x, y2, 'g+:');
that subsequent graphing
commands add to the existing
graph.
HOLD OFF returns to the
default mode
HOLD, by itself, toggles the
hold state.
54
55. Subplot
55
SUBPLOT Create axes in tiled
positions.
SUBPLOT(m,n,p), or
SUBPLOT(mnp), breaks the Figure
window into an m-by-n matrix of
small axes
Example
x = [-3 -2 -1 0 1 2 3];
y1 = (x.^2) -1;
% Plot y1 on the top
subplot(2,1,1);
plot(x, y1,'bo-.');
xlabel('x values');
ylabel('y values');
% Plot y2 on the bottom
subplot(2,1,2);
y2 = x + 2;
plot(x, y2, 'g+:');
55
56. Figure
56
FIGURE Create figure window.
FIGURE, by itself, creates a
new figure window, and
returns its handle.
Example
x = [-3 -2 -1 0 1 2 3];
y1 = (x.^2) -1;
% Plot y1 in the 1st Figure
plot(x, y1,'bo-.');
xlabel('x values');
ylabel('y values');
% Plot y2 in the 2nd Figure
figure
y2 = x + 2;
plot(x, y2, 'g+:');
56
63. MATLAB Applications
63
Control Systems
Transfer Function
p1 s n + p 2 s n −1 + ... + p n +1
H (s ) =
q1 s m + q1 s m −1 + ... + q m +1
where
p1 , p 2 ... p n +1 numerator coefficients
q1 , q1 ... q m +1 denominator coefficients
63
64. MATLAB Applications
64
Control Systems
Transfer Function
Consider a linear time invariant (LTI) single-
input/single-output system
y ''+ 6 y '+ 5 y = 4u '+ 3u
Applying Laplace Transform to both sides with
zero initial conditions
Y ( s) 4s + 3
G ( s) = = 2
U ( s) s + 6s + 5
64
65. MATLAB Applications
65
Control Systems
Transfer Function
>> num = [4 3]; >> [num,den] =
>> den = [1 6 5]; tfdata(sys,'v')
>> sys = tf(num,den) num =
Transfer function: 0 4 3
4s+3 den =
----------------- 1 6 5
s^2 + 6 s + 5
65
66. MATLAB Applications
66
Control Systems
Zero-pole-gain model (ZPK)
(s − p1)(s − p2 ) +... + (s − pn )
H (s ) = K
(s −q1)(s −q2 ) +... + (s −qm )
where
p1 , p2 ... pn+1 the zeros of H(s)
q1,q1 ... qm+1 the poles of H(s)
66
67. MATLAB Applications
67
Control Systems
Zero-pole-gain model (ZPK)
Consider a Linear time invariant (LTI) single-
input/single-output system
y ''+ 6 y '+ 5 y = 4u '+ 3u
Applying Laplace Transform to both sides with
zero initial conditions
Y (s) 4s + 3 4( s + 0.75)
G (s) = = 2 =
U ( s ) s + 6 s + 5 ( s + 1)( s + 5)
67
68. MATLAB Applications
68
Control Systems
>> G=tf([4 3],[1 6 5]) >> [z,p,k]=zpkdata(G)
Transfer function: z=
4s+3 [-0.7500]
-------------
s^2 + 6 s + 5 p=
[-5;-1]
k=
4
68
77. Reference Books
77
Mastering MATLAB 7, D. Hanselman and B. Littlefield,
Prentice Hall, 2004
Getting Started with MATLAB 7: A Quick Introduction
for Scientists and Engineers, R. Pratap, Oxford University
Press, 2005.
77
78. Some More Web Resources
78
MATLAB Educational sites:
http://www.eece.maine.edu/mm/matweb.html
Yahoo! MATLAB Web site:
dir.yahoo.com/Science/mathematics/software/matlab/
Newsgroup:
comp.soft-sys.matlab
78
