an introductory on matlab and simulink

Getting StartedRun MATLAB from Start → Programs → MATLAB Depending on version used, several windows appear • For example in Release 13 Ver 6, there are several windows – command his

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An Introductory on MATLAB and Simulink

Muhamad Zahim Sujod

zahim@kuktem.edu.my

Ext : 2312

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Introduction to MATLAB and Simulink

What can you gain from the course ?

Know basics of MATLAB/Simulink

– know how to solve simple problems

Know what MATLAB/Simulink is

Know how to get started with MATLAB/Simulink

Be able to explore MATLAB/Simulink on

your own !

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Introduction to MATLAB and Simulink

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MATLAB – MATrix LABoratory

– Initially developed by a lecturer in 1970’s to help students learn linear algebra

– It was later marketed and further developed under MathWorks Inc (founded in 1984) – www.mathworks.com

– Matlab is a software package which can be used to perform analysis and solve mathematical and engineering problems

– It has excellent programming features and graphics capability – easy to learn and flexible

– Available in many operating systems – Windows, Macintosh, Unix, DOS

– It has several tooboxes to solve specific problems

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Simulink

– Used to model, analyze and simulate dynamic

systems using block diagrams.

– Fully integrated with MATLAB , easy and fast to

learn and flexible.

– It has comprehensive block library which can be

used to simulate linear, non–linear or discrete

systems – excellent research tools.

– C codes can be generated from Simulink models for embedded applications and rapid prototyping of

control systems.

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Getting Started

Run MATLAB from Start → Programs → MATLAB

Depending on version used, several windows appear

• For example in Release 13 (Ver 6), there are several windows –

command history, command, workspace, etc

• For Matlab Student – only command window

Command window

• Main window – where commands are entered

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Example of MATLAB Release 13 desktop

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Variables – Vectors and Matrices –

ALL variables are matrices

Variables

•They are case–sensitive i.e x ≠ X

•Their names can contain up to 31 characters

•Must start with a letter

Variables are stored in workspace

6 5 1 2

[ ] 4

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Vectors and Matrices

 How do we assign a value to a variable?

R 1x1 8 double array i1 1x1 8 double array v1 1x1 8 double array Grand total is 3 elements using 24 bytes

>>> who Your variables are:

R i1 v1

>>>

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10 B

 How do we assign values to vectors?

separated by spaces

A column vector – values are separated by semi–colon (;)

[ 1 2 3 4 5 ]

A =

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If we want to construct a vector of, say, 100 elements

between 0 and 2 π – linspace

>>> c1 = linspace(0,(2*pi),100);

>>> whos

Name Size Bytes Class

c1 1x100 800 double array Grand total is 100 elements using 800 bytes

>>>

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If we want to construct an array of, say, 100

elements between 0 and 2 π – colon notation

>>> c2 = (0:0.0201:2)*pi;

>>> whos

Name Size Bytes Class

c1 1x100 800 double array c2 1x100 800 double array Grand total is 200 elements using 1600 bytes

>>>

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 How do we assign values to matrices ?

6 5 4

3 2 1

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 How do we access elements in a matrix or a vector?

Try the followings:

>>> A(2,3)ans =

6

>>> A(:,3)ans =

3 6 9

>>> A(1,:)ans =

1 2 3

>>> A(2,:)ans =

4 5 6

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 Some special variables

Inf

>>> pians = 3.1416

>>> ians = 0+ 1.0000i

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 Arithmetic operations – Matrices

Performing operations to every entry in a matrix

Add and subtract

4 5 6

7 8 9

10 11 12

>>> A-2ans = -1 0 1

2 3 4

5 6 7

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Multiply and divide

2 4 6

8 10 12

14 16 18

>>> A/3ans = 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000 2.3333 2.6667 3.0000

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To square every element in A, use

the element–wise operator .^

>>> A.^2ans =

1 4 9

16 25 36

49 64 81

>>> A^2ans =

30 36 42

66 81 96

102 126 150

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Performing operations between matrices

2 2 2

1 1 1

9 8 7

6 5 4

3 2 1

2 x 6 2 x 5 2 x 4

1 x 3 1 x 2 1 x 1

21

12 10

8

3 2

50

32 32

32

14 14

14

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36667

23333

2

0000

35000

20000

2

0000

30000

20000

2 / 6 2 / 5 2 / 4

1 / 3 1 / 2 1 / 1

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343

3625

16

32

3

2 2

2

1 1

1

9 8

7

6 5

4

3 2

1

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Example (cont)

(0.1 + j0.2)V1 – j0.2V2 = -j2

- j0.2V1 + j0.1V2 = 1.5

0 j

2 0 j 2

0 j 1

2 j

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Example (cont)

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Example (cont)

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Built in functions

(commands)

element-wise when applied to a matrix or vector

e.g sin cos tan atan asin log

abs angle sqrt round floor

At any time you can use the command

help to get help

e.g >>>help sin

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Built in functions (commands)

>>> a=linspace(0,(2*pi),10)

a =

Columns 1 through 7

0 0.6981 1.3963 2.0944 2.7925 3.4907 4.1888

Columns 8 through 10

-0.9848 -0.6428 0.0000

>>>

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scalar value

e.g max min mean prod sum length

>>> max(b)ans =

0.9848

>>> max(a)ans =

6.2832

>>> length(a)ans =

10

>>>

>>> a=linspace(0,(2*pi),10);

>>> b=sin(a);

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matrices

>>> help elmat

>>> help matfun

e.g eye size inv det eig

At any time you can use the command

help to get help

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1.0000 0.0000 0.0000 0.0000

0 1.0000 0 0.0000 0.0000 0 1.0000 0.0000

0 0 0.0000 1.0000

>>>

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From our previous example,

0 j

2 0 j 2

0 j 1

2 j

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Data visualisation – plotting graphs

>>> help graph2d

>>> help graph3d

e.g plot polar loglog mesh

semilog plotyy surf

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Example on plot – 2 dimensional plot

Add title, labels and legend

Use ‘copy’ and ‘paste’ to add to your window–based document, e.g MSword

eg1_plt.m

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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

angular frequency (rad/s)

Example on plot – 2 dimensional plot

eg1_plt.m

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Example on mesh and surf – 3 dimensional plot

Supposed we want to visualize a function

Z = 10e(–0.4a) sin (2 π ft) for f = 2

when a and t are varied from 0.1 to 7 and 0.1 to 2, respectively

eg2_srf.m

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eg2_srf.m

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eg2_srf.m

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Solution : use M-files

M-files : Script and function files

When problems become complicated and require re–

evaluation, entering command at MATLAB prompt is

not practical

Collections of commands

Executed in sequence when called

Saved with extension “.m”

User defined commands Normally has input &

output Saved with extension “.m”

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M-files : script and function files (script)

At Matlab prompt type in edit to invoke M-file editor

Save this file

as test1.m

eg1_plt.m

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To run the M-file, type in the name of the file at the prompt e.g >>> test1

Type in matlabpath to check the list of directories

listed in the path

Use path editor to add the path: File → Set path …

It will be executed provided that the saved file is in the known path

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Example – RLC circuit

Exercise 1:

Write an m–file to plot Z, Xc and XLversus

frequency for R =10, C = 100 uF, L = 0.01 H

+ V –

L

eg4.m eg5_exercise1.m

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+

=

C

1 L

j R

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0 200 400 600 800 1000 1200 1400 1600 1800 2000 0

20 40 60 80 100

120

Z Xc Xl

eg4.m eg5_exercise1.m

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For a given values of C and L, plot the following versus the frequency

a) the total impedance ,

L

eg6.m

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-100 -50 0 50

100

Phase

0 20 40 60 80 100

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 Function is a ‘black box’ that communicates with workspace through input and output variables.

– Commands – Functions – Intermediate variables

M-files : script and function files (function)

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Every function must begin with a header:

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 Function – a simple example

function y=react_C(c,f)

%react_C calculates the reactance of a capacitor

%The inputs are: capacitor value and frequency in hz

%The output is 1/(wC) and angular frequency in rad/sy(1)=2*pi*f;

w=y(1);

y(2)=1/(w*c);

File must be saved to a known path with filename the same as the function name and with an extension ‘.m’

Call function by its name and arguments

help react_C will display comments after the header

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 Function – a more realistic example

function x=impedance(r,c,l,w)

%IMPEDANCE calculates Xc,Xl and Z(magnitude) and

%Z(angle) of the RLC connected in series

%IMPEDANCE(R,C,L,W) returns Xc, Xl and Z (mag) and

%Z(angle) at W rad/s

%Used as an example for IEEE student, UTM

%introductory course on MATLAB

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We can now add our function to a script M-file

fprintf('\n The magnitude of the impedance at %.1f

rad/s is %.3f ohm\n', w,y(3));

fprintf('\n The angle of the impedance at %.1f rad/s is

%.3f degrees\n\n', w,y(4));

M-files : script and function files (function) eg7_fun.m

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Used to model, analyze and simulate dynamic

systems using block diagrams.

Provides a graphical user interface for constructing block diagram of a system – therefore is easy to use However modeling a system is not necessarily easy !

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Model – simplified representation of a system – e.g using

mathematical equation

We simulate a model to study the behavior of a system –

need to verify that our model is correct – expect results

Knowing how to use Simulink or MATLAB does not mean that you know how to model a system

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Problem: We need to simulate the resonant circuit and display the current waveform as we change the frequency dynamically.

Observe the current What do we expect ?

The amplitude of the current waveform will become

maximum at resonant frequency, i.e at ω = 1000 rad/s

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1 dt

di L iR

v

Writing KVL around the loop,

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LC

i dt

i

d L

R dt

di dt

dv L

1

2

+ +

=

Differentiate wrt time and re-arrange:

Taking Laplace transform:

LC

I I

s

sI L

R L

+ +

L

R s

I L

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LC

1 s

L

R s

) L / 1 (

s V

I

2

LC

1 s

L

R s

) L / 1 (

s

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Start Simulink by typing simulink at Matlab prompt Simulink library and untitled windows appear

It is here where we construct our model.

It is where we

obtain the blocks to

construct our model

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Constructing the model using Simulink:

‘Drag and drop’ block from the Simulink library window to the untitled window

1s+1Transfer Fcn

simout

To WorkspaceSine Wave

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Constructing the model using Simulink:

LC

1 s

L

R s

) L / 1 (

s

) 100 (

s

× +

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We need to vary the frequency and observe the current

100s

s +1000s+1e62Transfer Fcn1

v

To Workspace3 w

Integrator

sin Elementary Math Dot Product3

Dot Product2 1000

Constant

5 Amplitude

eg8_sim.mdl

…From initial problem definition, the input is 5sin(ωt).

You should be able to decipher why the input works, but

you do not need to create your own input subsystems of

this form.

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1

-0.5 0 0.5 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -5

0 5

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The waveform can be displayed using scope – similar

to the scope in the lab

100s

s +1000s+1e62Transfer Fcn

0.802

Slider Gain

Scope s

1 Integrator

sin

Elementary Math

Dot Product2

5 Constant1

2000

Constant

eg9_sim.mdl

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 Internet – search engine

 Mastering MATLAB 6 (Prentice Hall)

– Duane Hanselman

– Bruce Littlefield

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