Using matlab simulink

What is Simulink
•  Simulink is an input/output device GUI block diagram
simulator.
•  Simulink contains a Library Editor of tools from which we
can build input/output devices and continuous and
discrete time model simulations.
•  To open Simulink, type in the MATLAB work space
–  >>simulink

The Library Editor
•  >>simulink
•  Simulink opens with
the Library Browser
•  Library Browser is
used to build
simulation models

Continuous Elements
•  Contains continuous
system model
elements

Discontinuous Elements
•  Contains
discontinuous system
model elements

Math Operations
•  Contains list of math
operation elements

Signal Routing
•  Signal Routing
elements

Sink Models
•  Sinks: sink device
elements. Used for
displaying simulation
results

Signal Routing
•  Sources: provides list of
source elements used for
model source functions.

Signal Routing
•  Simulink Extras: additional
linear provide added block
diagram models. The two
PID controller models are
especially useful for PID
controller simulation.

Building Models
•  Creating a New Model
•  To create a new model, click the New button on the
Library Browser’s toolbar
•  This opens a new untitled model window.

Building Models (2)
•  Model elements are added by selecting the appropriate
elements from the Library Browser and dragging them
into the Model window. Alternately, they may be copied
from the Library Browser and pasted into the model
window.
•  To illustrate lets model the capacitor charging equation:

Modeling the Capacitor System (2)
Unconnected system model

Connecting the System Blocks
System blocks are connected in to ways; one way is the auto
connect method which is done by 1st selecting the source block
and holding down the Cntr key and selecting the destination
block.
Simulink also allows you to draw lines manually between blocks
or between lines and blocks. To connect the output port of one
block to the input port of another block: Position the cursor over
the first block’s output port. The cursor shape changes to
crosshairs. Right click and drag the crosshairs to the input of the
destination block to make the connection.
The next slide shows the connected model

The Connected Capacitor Model
Connected system model

Editing the Capacitor Model
Now that we have connected the model, we need to edit it. This
is done by selecting and double clicking to open the appropriate
models and then editing. The blocks we need to edit are the
step function, the two gain blocks, and the summing junction
block.

Editing the Capacitor Model (2)
In editing the blocks note that we have set the height of the step
function at 10, left R and C as variable (we will enter these from
the workspace), and changed the sign of the summing junction
input from + to -.

Controlling the Simulation
Simulation control is fixed by
selecting Configuration
Parameters

Controlling the Simulation - Solver
Simulink uses numerical integration to solve dynamic system
equations. Solver is the engine used for numerical integration.
Key parameters are the Start and Stop times, and the Solver
Type and methods.

Solver Parameters
The Start and Stop times set the start and stop times for the
simulation.
Solver Type sets the method of numerical integration as variable
step or fixed step. Variable step continuously adjusts the
integration step size so as to speed up the simulation time.
I.E., variable step size reduces the step size when a model’s
states are changing rapidly to maintain accuracy and increases
the step size when the system’s states are changing slowly in
order to avoid taking unnecessary steps.
Fixed step uses the same fixed step size throughout the
simulation. When choosing fixed step it is necessary to set the
step size.

Setting Fixed Step Size
The following example illustrates setting the fixed step size to a
value of 0.01 seconds.

Setting the Integration Type
The list of integration type solvers are shown below. For more
information on fixed and variable step methods and integration
types consult the MATLAB Simulink tutorial.

Running the Simulation
To run the simulation we 1st need to enter the values of R and
C. Note we could have entered these directly in the gain blocks
but we chose to enter these from the work space. To do this in
the work space we type
>>R = 1; C = 1;
This will fix the gain block’s as K = 1/(R*C)
Now select and click
the run button to run
the simulation

Viewing the Simulation with the Scope
To view the simulation results double click on the Scope block to
get. To get a better view left click and select Autoscale

Setting the Scope Axis Properties
We can adjust the Scope axis properties to set the axis limits:

Setting the Scope Parameters
The default settings for the Scope is a Data History of 5000 data
samples. By selecting Parameters an un-clicking the Limit
data points to last 5000 we can display an unlimited number of
simulation samples. Especially useful for long simulations or
simulations with very small time steps.

Saving Data to the Work Space
Often we wish to save data to the work space and use the
MATLAB plot commands to display the data. To do this we can
use the Sink Out1 block to capture the data we wish to display.
In this example we will connect Out blocks to both the input and
the output as shown below:

Where does the Output Data get Saved
To see where the output data gets saved we open Solver and
select Data Import/Export and unclick the Limit data points to
last box. As shown time is stored as tout, and the outputs as
yout.

Where does the Output Data get Saved
Now run the simulation and go to the workspace and type whos
Note that yout is a 1001 by 2 vector, that means that yout(:,
1)=input samples, and yout(:,2)=output samples.
To plot the data execute the M-File script shown on the next
slide.

M-File Script to Plot Simulink Data
' M-File script to plot simulation data '
plot(tout,yout(:,1),tout,yout(:,2)); % values to plot
xlabel('Time (secs)'); grid;
ylabel('Amplitude (volts)');
st1 = 'Capacitor Voltage Plot: R = '
st2 = num2str(R); % convert R value to string
st3 = ' Omega'; % Greek symbol for Ohm
st4 = ', C = ';
st5 = num2str(C);
st6 = ' F';
stitle = strcat(st1,st2,st3,st4,st5,st6); % plot title
title(stitle)
legend('input voltage','output voltage')
axis([0 10 -5 15]); % set axis for voltage range of -5 to 15

The SIM Function
Suppose we wish to see how the capacitor voltage changes for
several different values of C. To do this we will use the sim
command.
To use the sim command we must 1st save the model. To do
this select the File Save As menu and save the file as
capacitor_charging_model. Make sure you save the model to a
folder in your MATLAB path.
Next execute the M-File script on the next slide. The for loop
with the sim command runs the model with a different capacitor
value each time the sim command is executed. The output data
is saved as vc(k,:)
The plot command is used to plot the data for the three different
capacitor values. Note the use of string’s to build the plot
legend.

M-Code to Run and Plot the Simulation data
R = 1; % set R value;
CAP = [1 1/2 1/4]; % set simulation values for C
for k = 1:3
C = CAP(k); % capacitor value for simulation
sim('capacitor_charging_model'); % run simulation
vc(k,:) = yout(:,2); % save capacitor voltage data
end
plot(tout,vc(1,:),tout,vc(2,:),tout,vc(3,:)); % values to plot
st1 = 'R = '
st2 = num2str(R); % convert R value to string
st3 = ' Omega'; % Greek symbol for Ohm
st4 = ', C = ';
st5 = num2str(CAP(1));
st6 = ' F';
sl1 = strcat(st1,st2,st3,st4,st5,st6); % legend 1

M-Code to Run and Plot the Simulation data
title('Capacitor Voltage Plot Using SIM')
legend(sl1,sl2,sl3); % plot legend

SIM script to run RLC Circuit Model
R = 1; % set R value;
L = 1; % set L
CAP = [1/2 1/4 1/8]; % set simulation values for C
for k = 1:3
C = CAP(k); % capacitor value for simulation
sim('RLC_circuit'); % run simulation
vc(k,:) = yout; % save capacitor voltage data
end
plot(tout,vc(1,:),tout,vc(2,:),tout,vc(3,:)); % values to plot
st1 = 'C = ';
st3 = ' F';
sl1 = strcat(st1,st2,st3); % legend 1

SIM script to run RLC Circuit Model
st1 ='Capacitor Voltage Plot, R = ';
st2 = num2str(R); st3 = 'Omega';
st4 = ',L = '; st5 = num2str(L);
st6 = ' H';
stitle = strcat(st1,st2,st3,st4,st5,st6);
title(stitle)
legend(sl1,sl2,sl3); % plot legend

Modifying the Series RLC Circuit

Modifying the Series RLC Circuit (2)

Running the Simulation
' MATLAB script for RLC simulation '
R = 1; C = 1/8; L = 1/2; % set circuit parameters
sim('RLC_circuit_Mod'); % run simulation
vC = yout(:,1); % capacitor voltage drop
vR = yout(:,2); % resistor voltage drop
vL = yout(:,3); % inductor voltage drop
plot(tout,vR,tout,vC,tout,vL); % plot individual voltage drops
legend('v_R','v_C','v_L'); % add plot legend
grid; % add grid to plot
xlabel('Time (sec)'); % add x and y labels
% Build plot title
st1 ='RLC Circuit Voltage Plot, R = ';
st2 = num2str(R); st3 = 'Omega';
st4 = ',L = '; st5 = num2str(L);
st6 = ' H'; st7 = ', C = ';
st8 = num2str(C); st9 = ' F';
stitle = strcat(st1,st2,st3,st4,st5,st6,st7,st8,st9);
title(stitle)

Using matlab simulink

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