control&simulink

7/30/2019 Control&Simulink

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Application Software Course

Control

&Simulink

By: Mahdi Akbari

09,November
http://elecdl.com/


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Roots

>> roots([1,2,3,4,5,6])

ans =0.5517+ 1.2533i

0.5517- 1.2533i

-1.4918

-0.8058+ 1.2229i

-0.8058- 1.2229i

2

65432)( 2345 ssssssG


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Symbolic Mathematic

Sym: Create symbolic object

>> x=sym(x)

Syms: Shortcut for creating multiple symbolic objects

>> syms x,y


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Symbolic Mathematic


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>> syms s

>>f= (5*s^2 + 3*s +6)/(s^4 + 3*s^3 + 7*s^2 + 9*s +12);

>> ilaplace(f )

Example


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Transfer Functions

>> num=[1,5];

>> den=[1,2,3,4,5];

>> G=tf(num,den)

6

5432

5)(

234

ssss

ssG


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Transfer Functions

>> den=conv(conv(conv([1,3,1],[1,3,1]),[1,6]),[1,6,5,3]);

>> num=6*[1,5];

>> G=tf(num,den)


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Transformation of System Model

(Steady State)

>> G=ss(A,B,C,D)

8

DuCxy

BuAxx.


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Example

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>> A=[2.25, -5, -1.25, -0.5; 2.25, -4.25, -1.25, -0.25; 0.25, -0.5, -1.25,-1; 1.25, -1.75, -0.25, -0.75];

>> B=[4, 6; 2, 4; 2, 2; 0, 2];

>> C=[0, 0, 0, 1; 0, 2, 0, 2];

>> D=zeros(2,2);

>> G=ss(A,B,C,D)


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Transformation of System Model

[A,B, C,D] = tf2ss (num, den)

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

DuCxy

BuAxx.

DBASICden

num

su

sY

1)(

)()(


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Zero-pole-gain Description

>> KGain=6;

>> Z=[-1.9294; -0.0353+0.9287j; -0.0353-0.9287j];

>> P=[-0.9567+1.2272j; -0.9567-1.2272j; 0.0433+0.6412j; +0.0433-

0.6412j];

>> G=zpk(Z,P,KGain)

11


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step responses

>> step (num,den)

>> step (A,B,C,D)

for find:

MP

Rise time Fall time

Over shoot


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Form 3:

>> [y,x,t] = step (num,den,t)

>> plot(t,y)

13


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impulse responses

For impulse responses:

R(s)=1

Step ( s G(s) )

11

)()(

ssRsC

11

)(

)(

1)

1(

1

1)()(

s

s

ssu

sC

ss

s

ssGsC


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impulse responses

>> impulse (num, den)

15


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Ramp responses

Step ( G(s)/S )

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Feedback

>> Gt=feedback(G,H)

>> syms g1 g2 % declare symbolic variables>> Gt=feedback(g1,g2,1); %Defult: negative feedback

>> pretty(Gt)


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Example:

>> G1=tf(1,[1,2,1]);

>> G2=tf(1,[1,1]);>> G=feedback(G1,G2) %for negative feedback

>> G=feedback(G1,G2,+1) % for positive feedback

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>>[r, p, k] = residue(num, den)


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Root Locus Plots

[r, k] = rlocus (num, den)

[r, k] = rlocus (num, den, k)

[r, k] = rlocus (A,B, C,D)

[r, k] = rlocus (A,B, C,D, K)


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Example

>> num = [0 0 0 1];

>> den = [1 5 9 0];

>> rlocus(num, den);


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Bode Diagrams

bode(num, den)

bode(num, den, W)

bode(A,B, C,D) (3.36)

bode(A,B, C,D, W)

[mag, phase, w] = bode (num, den)

[mag, phase, w] = bode (num, den, w)

[mag, phase, w] = bode (A, B, C, D)[mag, phase, w] = bode (A, B, C,D, w)

[mag, phase, w] = bode (A, B, C, D, iu, w)


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Example

>> %Bode diagram

>> num= [29.125 33.2025 9.4627];

>> den= [0 1 0];

>> bode (num, den)


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Nyquist Plots

nyquist (num, den, w)

nyquist (A,B, C,D)

nyquist (A,B, C,D, w)

nyquist (A,B, C,D, iu, w)

[re, im, w] = nyquist (num, den)

[re, im, w] = nyquist (num, den, w)

[re, im, w] = nyquist (A,B, C,D)[re, im, w] = nyquist (A,B, C,D, w)

[re, im, w] = nyquist (A,B, C,D, iu, w)


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Example

>>z = [13 + 7*i37*i];

>>p = [1353 + 7*i37*i];

>> k= 30;

>> nyquist (num, den)


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What Is Simulink?

Simulink is a software package formodeling, simulating, and analyzingdynamical systems.

It supports linear and nonlinear systems,modeled in continuous time, sampled time,

or a hybrid of the two.


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How to open simulink

Click on this item


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create a model

To create the model, first

type simulink in the MATLAB

command window. On

Microsoft Windows, the

Simulink Library Browserappears.


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Open new window

Simulink opens a new model window.

Click on NewModel button


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Model Editor


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View Command History

Back =(Displays theprevious view in theview history.Forward )

forward=(Displaysthe next view in theview history.Go ToParent )

Go To Parent=Opens, if

necessary, the parent of thecurrent subsystem andbrings its window to the topof the desktop.


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Building a Simple Model

This example shows you how to build a model using

many of the model building

commands and actions you will use to build your own

models

The model integrates a sine wave and displays the

result, along with the sine wave. The block diagram of

the model looks like this


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Create example model

To create this model, you will need to copy blocks into

the model from the following Simulink block libraries:

1. Sources library (the Sine Wave block)

2. Sinks library (the Scope block)

3. Continuous library (the Integrator block)

4. Signals & Systems library (the Mux block)


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first expand the LibraryBrowser tree to display theblocks in the Sourceslibrary. Do this by

clicking first on theSimulink node to displaythe Sources node

Sources node to displaythe Sources library blocks.

Finally right click on the

Sine Wave node to selectthe Sine Wave


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Copy the rest of the

blocks in a similar

manner from their

respective libraries into

the model window


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With all the blocks copied into the model window, the model should

look

something like this.

Now its time to connect the blocks.

Hold down the mouse button and move the cursor to the top input

port of the Mux block. Notice that the line is dashed while the mouse

button is down and that the cursor shape changes to double-lined

cross hairs as it approaches the Mux block.


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Now release the mouse button. The blocks areconnected

Press and hold down the Ctrl key. Press the mousebutton, then drag the pointer to the Integrator blocksinput port or over the Integrator block itself.


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Finish making block connections. When youre done,

your model should look something like this.


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Now, open the Scope block to view the simulation output. Keepingthe Scope

window open, set up Simulink to run the simulation for 10 seconds.

the simulation parameters by choosing Parameters from theSimulation menu. On

the dialog box that appearsnotice that the Stop time

is set to 10.0

(its default value)


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Choose Start from the Simulation menu and watch thetraces of the Scope blocks input.


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Model Viewing Shortcuts


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Zooming Block Diagrams

Select Zoom In from the View menu (or type r) to enlarge theview.Select Zoom Out from the View menu (or type v) to shrink

the view.

Select Fit System To View from the View menu (or press the space

bar) to fit the diagram to the view. Select Normal from the View menu

(or type 1) to view the diagram at

actual size.


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colors

Simulink allows you to specify the foreground and

background colors of any block

select Screen color from the Simulink Format menu


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Connecting Blocks Connecting Two Blocks To auto connect two blocks: Select

the source block. Hold down Ctrl and left-click the destination block.Simulink

connects the source block to the destination block

When connecting two blocks, Simulink draws as manyconnections as possible between the two blocks as illustrated

in the following example.


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Connecting Groups of Source Blocks

Simulink can connect a group of source blocks to a destination block

or a source block to a group of destination blocks.To connect a

group of source blocks to a destination block:

Select the source blocks.

Hold down Ctrl and left-click the destination block.

bl k f


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connect a source block to a group of

destination blocks

Select the destination blocks.

Hold down Ctrl and left-click the source block.


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Moving a Line Segment

To move a line segment: Position the pointer on the segment you want to move.

Press and hold down the left mouse button.

Drag the pointer to the desired location.


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Inserting Blocks in a Line

To insert a block in a line:

Position the pointer over the block and press the left mouse button.

Drag the block over the line in which you want to insert the block.

Release the mouse button to drop the block on the line.

Simulink inserts the block where you dropped it.


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Disconnecting Blocks

To disconnect a block from its connecting

lines, hold down the Shift key, then drag

the block to a new location.


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Creating Subsystems

As your model increases in size and complexity, you

can simplify it by grouping blocks into subsystems.

Using subsystems has these advantages:

It helps reduce the number of blocks displayed in

your model window.

It allows you to keep functionally related blocks

together

C ti S b t b Addi th


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Creating a Subsystem by Adding the

Subsystem Block

To create a subsystem before adding the blocks

Copy the Subsystem block from the Ports & Subsystems

library into your model.

Open the Subsystem block by double-clicking it. In the empty Subsystem window, create the subsystem.

For example, the subsystem shown includes a Sum block

and inport and Outport blocks to represent input to and

output from the subsystem.

C ti S b t b G i


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Creating a Subsystem by Grouping

Existing Blocks If your model already contains the blocks you want to convert to a

subsystem, you can create the subsystem by grouping those blocks:

Enclose the blocks and connecting lines that you want to include in

the subsystem within a bounding box. You cannot specify the blocks

to be grouped by selecting them individually or by using the Select

All command.

Choose Create Subsystem from the Edit menu.

If you open the Subsystem block, Simulink displays the underlying

system, as shown below.

control&simulink

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