Transcript Application Software Course Control & Simulink By: Mahdi Akbari 09,November Roots G(s)  s 5  2s 4  3s 3  4s 2  5s.

Application Software Course
Control
&
Simulink
By: Mahdi Akbari
09,November
1
Roots
G(s)  s 5  2s 4  3s 3  4s 2  5s  6
>> 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
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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
4
Example
>> syms s
>> f = (5*s^2 + 3*s +6)/(s^4 + 3*s^3 + 7*s^2 + 9*s +12);
>> ilaplace(f )
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Transfer Functions
s5
G(s)  4
3
2
s  2 s  3s  4s  5
>> num=[1,5];
>> den=[1,2,3,4,5];
>> G=tf(num,den)
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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)
 .
x  Ax  Bu

 y  Cx  Du
>> G=ss(A,B,C,D)
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Example
>> 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
Y ( s) num

 C ( SI  A) 1 B  D
u ( s) den
 .
x  Ax  Bu

 y  Cx  Du
[A, B, C, D] = tf2ss (num, den)
[num , den] = ss2tf (A, B, C, D)
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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; +0.04330.6412j];
>> G=zpk(Z,P,KGain)
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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)
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impulse responses
C (s)
1

R( s) s  1
For impulse responses:
R(s)=1
1
s 1
C (s)  G(s) 
(
)
s 1 s 1 s
C ( s)
s


1 s 1
u ( s) 
s
Step ( s G(s) )
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impulse responses
>> impulse (num, den)
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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 = [– 1 – 3 + 7*i – 3 – 7*i];
>> p = [– 1 – 3 – 5 – 3 + 7*i – 3 – 7*i];
>> k = 30;
>> nyquist (num, den)
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What Is Simulink?
•Simulink is a software package for
modeling, simulating, and analyzing
dynamical 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 Browser
appears.
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Open new window
• Click on New
Model button
•Simulink opens a new model window.
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Model Editor
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View Command History
•
Back =(Displays the
previous view in the
view history.Forward )
•forward=( Displays
the next view in the
view history.Go To
Parent )
•Go To Parent=Opens, if
necessary, the parent of the
current subsystem and
brings its window to the top
of 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
•
1.
2.
3.
4.
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To create this model, you will need to copy blocks into
the model from the following Simulink block libraries:
Sources library (the Sine Wave block)
Sinks library (the Scope block)
Continuous library (the Integrator block)
Signals & Systems library (the Mux block)
• first expand the Library
Browser tree to display the
blocks in the Sources
library. Do this by
• clicking first on the
Simulink node to display
the Sources node
• Sources node to display
the Sources library blocks.
• Finally right click on the
Sine Wave node to select
the 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 it’s 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 are
connected
• Press and hold down the Ctrl key. Press the mouse
button, then drag the pointer to the Integrator block’s
input port or over the Integrator block itself.
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• Finish making block connections. When you’re done,
your model should look something like this.
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• Now, open the Scope block to view the simulation output. Keeping
the Scope
• window open, set up Simulink to run the simulation for 10 seconds.
• the simulation parameters by choosing Parameters from the
Simulation menu. On
the dialog box that appears
notice that the Stop time
is set to 10.0
(its default value)
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• Choose Start from the Simulation menu and watch the
traces of the Scope block’s 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 the
view.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 many
connections 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.
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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
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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.
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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.
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