introdução ao simulink

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Simulink and block diagram

2 0 1 5 B R A Z I L S T U DY A B R O A D P R O G R A M

T E X A S A & M U N I V E R S I T Y - U N I V E R S I T Y O F S A O PA U L O

E L M E R A L E X I S G A M B O A P E Ñ A LO Z A

R O D O L P H O V I L E L A A LV E S N E V E S

M I C H E L B E S S A N I

R A FA E L F E R N A N D O Q U I R I N O M A G O S S I

D E PA R TA M E N TO D E E N G E N H A R I A E L É T R I C A U S P - S Ã O C A R L O S

2 0 1 5

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Simulink and block diagram

Matlab has a tool called Simulink. Simulink allows you to create block diagram, modelling, model analysis and construction functions.

To access Simulink, type:

>> simulink

3

Simulink and block diagramSimulink’s interface

4

Simulink and block diagramSimulink’s interface

5

Simple RC circuit example

iu

Sensor

idtC

vc

1

C

i

dt

dvc

R

vui c

cvx 1

dt

dvx c1'

RC

u

RC

xx 1

1'

R

u

R

xy

1

RC

vu

dt

dv cc

iy

If then

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Simple RC circuit exemple

This is the simulink library. You can type what you want. For example:

Gain

Sum

Integrator

7

Simple RC circuit exemple

8


RC

u

RC

xx 1

1'

To create the first equation, you can use:

9


To use the integrator with external initial

condition, give a double click on integrator

block.

10


To create the second equation you can use

R

u

R

xy

1

11


Before you run your simulation, it’s necessary set theconfigurations in simulink.

12


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%parameters of a RC circuitclear all;close all ;clc;

% constantsR = 1000;C = 1000e-6;alpha = 1;

Create and run a script using the program below before of runthe simulation

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To get the linear model, use the blocks in

and out on the diagram.

Open a new script on matlab and

use this program to create the

linear model.

[A,B,C,D] = linmod(‘rc_circuit’);

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Now, it’s possible get the transfer function of

the system.

Use the tf command on matlab with the

matrices A,B,C,D

[num,den] = ss2tf(A,B,C,D);G = tf(num,den);

16


You got the following function:

>> G

G =

0.001 s

-------

s + 1

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Create a transfer function using

on simulink the transfer fcn block.

18


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To simulate the transfer function use the step and scope on simulink.

Run and give a double click on scope to see the response.

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Hand’s on (simple pendulum example)

State space representation

1xy

22122 xml

bxsen

l

g

ml

ux

1x

2

1

x

xx

1x

2x

cTu

y

21

Simple pendulum example

Vector notation

buxfx

u

mlxsen

l

g

x

x

21

2

10

1xy

22


1xy

22122 xml

bxsen

l

g

ml

ux

1x

23


1xy

22122 xml

bxsen

l

g

ml

ux

1x

24


1xy

22122 xml

bxsen

l

g

ml

ux

1x

u 2ml

u

2ml

u

25


1xy

22122 xml

bxsen

l

g

ml

ux

1x

22122 xml

bxsen

l

g

ml

ux

u 2ml

u

2x

1xsen1x

2x

1xsenl

g

22x

ml

b

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1xsen

22x

ml

b

u 2ml

u

1xsenl

g

2x2x

2x

1x

1xy

22122 xml

bxsen

l

g

ml

ux

1x

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1xsen

22x

ml

b

u

2ml

u

1xsenl

g2x

2x

2x

1x

1xy

22122 xml

bxsen

l

g

ml

ux

1x

2x

2x

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1xsen

22x

ml

b

u

2ml

u

1xsenl

g2x

2x

2x

1x

1xy

22122 xml

bxsen

l

g

ml

ux

1x

2x

2x

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1xsen

22x

ml

b

u2ml

u

1xsenl

g 2x

2x

2x

1x

1xy

22122 xml

bxsen

l

g

ml

ux

1x

2x

2x

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Before you run your simulation, it’s necessary set theconfigurations in simulink.

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%parameters of simple pendulum clear all;close all ;clc;

% constantsl=0.5;m=10;g=9.81;b=4.5;%initial conditionsx20= 0; %initial acelerationx10=30*pi/180; %initial position in rad

Create a script using this program

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Hands on plus!1. Using the function [A,B,C,D]=linmod('SYS') to extract the continuous-time linear state-space model of the

nonlinear pendulum;

Pendulum System

u y

2. Compare the linear system found in step 1 with the nonlinear system built.

Pendulum System

u y

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Simulink and block diagramTransfer Fcn

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RC circuit transfer function

iu

Sensor

)(1

)( sisC

sRisu

)()(

sysi

)(si )(sy)(su)(sG

Kirchhoff

)(1

)( suRCs

Cssi

1

RCs

CssG

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RC circuit transfer function to time

iu

Sensor

1

)()(

)(

RCs

CssG

su

sysK

)(1

)( suRCs

Cssy

)(1

)( suRCs

C

Rsy

RCs

CRRsy

1

1)(

2

RC

t

eCR

tR

ty

2

)()(

0t

)(si )(sy)(su)(sG

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Hands on!

)(si )(sy)(su

1. Built the transfer function of the RC circuit using Simulink:

R=1000 (ohm); C=0.001 (F); alpha=10;;

2. Simulate the step responses.

1RCs

Cs

a)

b)

cvsy )()(su

RCs1

1

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Hands on!

Newton

Kirchhoff

+

-

JBtiK at

eaaaa

a KviRdt

diL

J=3.2284E-6; B=3.5077E-6; Kt=Ke=0.0274; Ra=4; La=2.75E-6;

1. Find the state space representation of the D.C motor whit output

a

a

vu

ix

x

x

3

2

1

2. Build the block diagram using Simulink.

3. Simulate the step response to get: x1, x2 ,x3.

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[1] Matlab Product Help.

[2] Matlab Demystified. A Self-Teaching Guide, David McMahon, McGraw Hill.

[3] Matlab: An Introduction with Applications, Amos Gilat, Fourth Edition, JOHN WILEY & SONS.

References

introdução ao simulink

Documents