ECEN/MAE 3723 – Systems I
MATLAB Lecture 2
Lecture Overview
What is Simulink?
How to use Simulink
 Getting Start with Simulink
 Building a model
Example 1 (Differential Equations )
Example 2 (Transfer Function)
Creating Subsystems
Useful Information
What is Simulink? (1)
A software package for modeling,
simulating, and analyzing dynamic systems.
Supports linear and nonlinear systems,
modeled in continuous time, sample time, or
a hybrid of the two.
Systems can also be multirate (i.e. different
parts that are sampled or updated at
different rates)
What is Simulink? (2)
 For modeling, it provides a graphical user
interface (GUI) for building models as block
diagrams (using click-and-drag mouse
operations)
 Can build models in hierarchical fashion
(using both top-down and bottom-up
approaches)
 You can simulate, analyze the output results,
explore, revise your models and have FUN!
Lecture Overview
What is Simulink?
How to use Simulink
 Getting Start with Simulink
 Building a model
Example 1 (Differential Equations )
Example 2 (Transfer Function)
Creating Subsystems
Useful Information
Start a Simulink Session
Click on the SIMULINK icon on toolbar
Type simulink
on Matlab command window
Simulink Library Browser
CREAT NEW MODEL icon
SEARCH window
BLOCK set
for model construction
LIBRARY
Create a New Model
CREAT NEW MODEL icon
Workspace where you
construct your model
Lecture Overview
What is Simulink?
How to use Simulink
 Getting Start with Simulink
 Building a model
Example 1 (Differential Equations )
Example 2 (Transfer Function)
Creating Subsystems
Useful Information
Building a Model
 Simulink Block Diagram – pictorial model of a
dynamic system
 Each block represents an elementary dynamic
system that produces an output (either
continuous or discrete output)
 Lines represent connections of block inputs to
block outputs
u
(Input)
x
(states)
y
(Output)
Building a Model (2)
The following steps will guide you to construct
a system/model:
STEP 1: Creating Blocks
STEP 2: Making connections
STEP 3: Set Parameters
STEP 4: Running Simulation
Building a Model (3)
 Step 1: Creating Blocks
Save this model
This is the
Sine Wave block is
from the Sources library
Sources library
Click-Drag-Drop the Sine Wave block to Workspace Window
Building a Model (4)
 Step 1: Creating Blocks
The Gain
block is
from the
Math library
The Mux block is from
the Signals &Systems library
These are
from the
Sinks library
Building a Model (5)
 Step 2: Making connections
To make connection: left-click while holding down control key (on keyboard)
and drag from source port to a destination port
A connected Model
Building a Model (6)
 Step 3: Set Parameters
Double click the Gain block to set the parameter for the Gain block
Name the output
parameter as “out1”
Gain value = 5
Building a Model (7)
 Step 4: Running Simulation
Click here to run the simulation
click “simulation parameters” to set
up the desired parameters
You can change the “stop time” and
then click the “OK button”
Building a Model (8)
 View output via Scope block
Output of the scope
To fit graph to frame
Yellow: Input sine wave
Purple: Output (sine wave with gain of 5
Double click on Scope block to display output of the scope
Note: Scope block is similar to oscilloscope!
Building a Model (9)
 View output (workspace)
You can plot the output using the plot function
Three outputs show here
Lecture Overview
What is Simulink?
How to use Simulink
 Getting Start with Simulink
 Building a model
Example 1 (Differential Equations )
Example 2 (Transfer Function)
Creating Subsystems
Useful Information
Example 1:Differential Equations (1)
 Example of a dynamic system: A massspring-damper system
f t 
The Mathematical model of the system
is describe by:
x
1
x
 Bx  Kx  f  t  

M
M
Lets M=2kg; B = 2 Ns/m; K=2 N/m
K
B
1
x   2 x  2 x  f  t  
2
Example 1:Differential Equations (2)
 Use Simulink to simulate the step response
of the system, i.e.
f(t), N Unit Step Input
1
x   2 x  2 x  f  t  
1
2
STEP 1: Creating Blocks
0
Time, s
Select BLOCK set
Location in Simulink Library
Step
Sources
Sum
Math Operation
Gain
Math Operation
Integrator
Continuous
Scope & To Workspace
Sinks
Example 1:Differential Equations (2)
STEP 2: Making connections
x
x
x
Example 1:Differential Equations (3)
STEP 3: Set Parameters
Set Step time =0
x
Note: Assume all initial conditions = 0
x
x
Example 1:Differential Equations (4)
STEP 4: Running Simulation
1
Open “simulation parameters” window
2
Set “Stop time” = 30
RUN
Simulation
Example 1:Differential Equations (5)
Step Response for the mass-spring-damper
system example
Output from Scope block
Plot system response
Lecture Overview
What is Simulink?
How to use Simulink
 Getting Start with Simulink
 Building a model
Example 1 (Differential Equations )
Example 2 (Transfer Function)
Creating Subsystems
Useful Information
Example 2: Transfer Function (1)
 Use the same mass-spring-damper system
example and simulate the response using
transfer function approach
1
x   2 x  2 x  f  t  
2
The transfer function of the equation
(assume all initial conditions =0)
X ( s)
1
 2
F ( s) 2s  2s  2
Example 2: Transfer Function (2)
STEP 1: Creating Blocks
Select BLOCK set
Location in Simulink Library
Step
Sources
Transfer Function
Continuous
Scope & To Workspace
Sinks
Example 2: Transfer Function (3)
STEP 2: Making connections
x
Example 2: Transfer Function (4)
STEP 3: Set Parameters
Set Step time =0
x
Example 2: Transfer Function (5)
STEP 4: Running Simulation
1
Open “simulation parameters” window
2
Set “Stop time” = 30
RUN
Simulation
Example 2: Transfer Function (6)
Same output as before (Slide 21)
Output from Scope block
Plot system response
Lecture Overview
What is Simulink?
How to use Simulink
 Getting Start with Simulink
 Building a model
Example 1 (Differential Equations )
Example 2 (Transfer Function)
Creating Subsystems
Useful Information
Creating Subsystems (1)
Subsystem – similar to “Subroutine”
Advantage of Subsystems:
Reduce the number of blocks display on the
main window (i.e. simplify the model)
Group related blocks together (i.e. More
organized)
Can create a hierarchical block diagram (i.e.
you can create subsystems within a subsystem )
Easy to check for mistakes and to explore
different parameters
Creating Subsystems (2)
Create Subsystem using model in Example 1
STEP 1: Creating Blocks (Main window)
This is the Subsystem block is
from the Subsystems library
Creating Subsystems (3)
STEP 2: Double click Subsystem block and
create a model in the Subsystem block
Inport
(named from “sum”
Outport
(three outports)
Creating Subsystems (4)
STEP 3: Making connections (Main window)
Creating Subsystems (5)
STEP 4: Set Parameter (Main window)
STEP 5: Running Simulation
Then view output response
Output from Scope block
Lecture Overview
What is Simulink?
How to use Simulink
 Getting Start with Simulink
 Building a model
Example 1 (Differential Equations )
Example 2 (Transfer Function)
Creating Subsystems
Useful Information
Useful Information (1)
Ramp Function
Set Slope
Set Start time for Ramp function
Set initial value
Useful Information (2)
Input(t)
Unit Step Function or Impulse
5
0
Start at 0 s
Start at 5.01 s
5
t(s)
Useful Information (3)
To run programs, have to be in the current
active directory or in a directory in the path
(goto File  Set path... )
To copy the SIMULINK Model from
Simulink Workspace and add to report
(Edit  Copy model to clipboard)
Need help on SIMULINK (At Simulink
Library Browser  Click Help)