-stability bode nyquist pdf-

An Introduction To MatLAB &

Simulink

Basic MatLAB CommandsMatLAB Syntax:Do Not Display Results: Comma

after command

Matrix Creation: [1 2; 3 4] = ⎥⎦

⎤⎢⎣

⎡4321

Basic MatLAB PlottingPlotting x and y: plot(x(),y())

Transfer FunctionTf([ Numerator Coefficients],[ Denominator Coefficients])

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

231

2 ++=

sssys

Basic MatLAB CommandsConversionsTransfer 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);

Basic MatLAB Commands

Basic MatLAB CommandsSymbolic Variables syms variable;

i.e. syms tLaplace 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)

Basic MatLAB CommandsIntegration 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)

Basic MatLAB Commands: Examples

MatLAB: Special

Characters

Basic MatLAB Plots

For the next three plots and simulink models, this is the system used:

Spring-Dashpot Mass Systemm=1 Input Sineb=4 Amp=50k=2 Freq=5

Fkxxbxm =++ &&&

( )( ) 24

12 ++

=sssF

sX

[ ] [ ]

[ ][ ] Fxy

Fxx

0011/1

01/41/2

10

+=

⎥⎦

⎤⎢⎣

⎡+⎥

⎦

⎤⎢⎣

⎡−−

=&

M

k

F

b

x

Basic MatLAB Plots – Bode Diagrams

A graphical wayof representingsystems througha magnitude andphase plot. Usingthe frequency domainthese plots can beobtained. Thesecan be used in:

Control Systems DynamicsElectronics

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

Basic MatLAB Plots – Root Locus Diagram

A diagram of the poles andzeros of a system,using a real andimaginary axes.

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

Basic MatLAB Plots – NyquistDiagram

This allows the prediction ofstability and Performanceusing the systemsopen loop form.

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

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.

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 the model or write the report, more efficiently than in the past.

Simulink Toolboxes

These are some of the toolboxes simulink has.

We will use only the firsttoolbox ‘Simulink’ and‘Simulink Extras’ furtherdown.

Simulink: Most Commonly Used Blocks

These are the most commonly used blocks for Mechanical Engineers.

Simulink: Most Commonly Used Blocks

These are the most commonly used blocks for Electrical Engineers.

Simulink: Creation Of A Model1. A mathematical model has to be finished or a

prior simulation had to been performed.2. Create the block diagram by opening a new

model sheet and grabbing and dropping the blocks onto the model sheet.

3. Arrange blocks in the order that the model shows and connect them by dragging the arrow coming out of the block to the next block or clicking on both blocks while holding down ‘control’.

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

Simulink: Creation Of A Model

Simulink: Model ParametersChanging the simulation parameters will help or hurt your model depending on what is changed.

Simulink: Output Of The Model

There are several ways to use or view the data received from the model.

Simulink: Example 1 & 2

Simulink: Example 3

Simulink: Lab 2 Diagram

Simulink: Moderate to Advanced Models

Research Model: Modeling and control of swimming robotic fish

An Introduction To MatLAB& Simulink