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Lab # 1

An Introduction

To MatLAB &

Simulink

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Basic MatLAB Commands

MatLAB Syntax:

Do Not Display Results: Comma

after command

Matrix Creation: [1 2; 3 4] =

43

21

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Basic MatLAB Plotting

Plotting x and y: plot(x(),y())

Transfer Function

Tf([ Numerator Coefficients],[ Denominator Coefficients])

i.e. sys = tf([1],[1 3 2]);

23

1

2

!

sssys

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Basic MatLAB Commands

Conversions

Transfer Function To State Space [A,B,C,D] = tf2ss([Num],[Den]);

State Space To Transfer Function [Num, Den] = ss2tf(A,B,C,D);

Transfer Function To Zero/Poles [z,p,k] = tf2zp([Num],[Den]);

Zero/Poles To Transfer Function [Num, Den] = zp2tf(z,p,k);

State Space To Zero/Poles [z,p,k] = ss2zp(A,B,C,D,iu);

Zero/Poles To State Space [A,B,C,D] = zp2ss(z,p,k);

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Basic MatLAB Commands

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Basic MatLAB Commands

Symbolic Variables syms variable;

i.e. syms t

Laplace Transforms laplace(function);

i.e. syms t;

f = sin(t);

laplace(f)

Inverse Laplace Transforms ilaplace(function);

i.e. syms s;

f = (s+1)/(s^2+3s+2);

ilaplace(f)

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Basic MatLAB Commands

Integration int(function, variable)

i.e. syms x;

f = sin(x);

int(f,x)

Differentiation diff(function, variable)

i.e. syms x;

f = sin(x);

diff(f,x)

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Basic MatLAB Commands:

Examples

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MatLAB:

SpecialCharacters

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Basic MatLAB Plots

For the next three plots and simulink models,

this is the system used:

Spring-Dashpot Mass Systemm=1 Input Sine

b=4 Amp=50

k=2 Freq=5

Fkxxbxm !

24

1

2

!

sssF

sX

? A ? A

? A? A Fxy

Fxx

001

1/1

0

1/41/2

10

!

!

M

k

F

b

x

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Basic MatLAB Plots Bode Diagrams

A graphical way

of representing

systems through

a magnitude and

phase plot. Using

the frequency domain

these plots can be

obtained. These

can be used in:Control Systems

Dynamics

Electronics

MatLAB Command: bode(sys) or bode(tf([Num],[Den]))

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Basic MatLAB Plots Root Locus

Diagram

A diagram of

the poles and

zeros of a system,

using a real and

imaginary axes.

rlocus(sys) or

rlocus(tf([Num],[Den]))

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Basic MatLAB Plots Nyquist

DiagramThis allows the

prediction of

stability andPerformance

using the systems

open loop form.

nyquist(sys) or

nyquist(tf([Num],[Den]))

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Introduction To Simulink

Simulink is a graphical representation of

systems, differential equations, or problems

encountered in engineering fields. Blocks

can be assembled to reproduce almost

anything as long as it can be modeled

mathematically. Simulink has become an

important part of aeronautical, astronautical,computer, electrical, and mechanical

engineering programs and industries.

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Simulink: Computer Integrated

Simulink can be used to control systems

with the correct hardware and software.

Texas Instruments and other electronic

equipment manufacturers creates circuit

boards for integration with a PC running

Simulink. Output can be directly saved to

a computer and analyzed to improve themodel or write the report, more efficiently

than in the past.

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Simulink Toolboxes

These are some of the

toolboxes simulink has.

We will use only the first

toolbox Simulink and

Simulink Extras furtherdown.

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Simulink: Most Commonly Used

Blocks

These are the most commonly used blocks

for Mechanical Engineers.

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Simulink: Most Commonly Used

Blocks

These are

the mostcommonly

used blocks

for Electrical

Engineers.

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Simulink: Creation Of A Model

1. A mathematical model has to be finished or aprior simulation had to been performed.

2. Create the block diagram by opening a newmodel sheet and grabbing and dropping theblocks onto the model sheet.

3. Arrange blocks in the order that the modelshows and connect them by dragging thearrow coming out of the block to the next block

or clicking on both blocks while holding downcontrol.

4. Make sure the model is correct before runningthe simulation. Then run the simulation.

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Simulink: Creation Of A Model

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Simulink: Model Parameters

Changing

the

simulation

parameters

will help or

hurt your

model

depending

on what ischanged.

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Simulink: Output Of The Model

There are

several

ways to use

or view the

data

received

from the

model.

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Simulink: Example 1 & 2

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Simulink: Example 3

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Simulink: Lab 2 Diagram

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Simulink: Moderate to Advanced

Models

Research Model: Modeling and

control of swimming robotic fish

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An Introduction To MatLAB

& Simulink