SIMULINK
Prepared by :
Ehab Naser Abd_Elmonem Sowaidan
Introduction to Simulink
• Simulink is a graphical, “drag and drop” environment for
building simple and complex signal and system dynamic
simulations
• It allows users to concentrate on the structure of the
problem, rather than having to worry (too much) about a
programming language
• The parameters of each signal and system block is
configured by the user
Advantages of Simulink
 Model and Simulate Your System : explore a wide design
space by modeling the system under test and the
physical plant
 Test Early and Often : reduce expensive prototypes by
testing your system under conditions that are otherwise
too risky or time-consuming to consider
 Automatically Generate Code : instead of writing
thousands of lines of code by hand, automatically
generate production-quality C and HDL code that
behaves the same way as the model you created in
Simulink. Then deploy it directly onto your embedded
processor or FPGA/ASIC
Advantages of Simulink
 One of the main advantages of Simulink is the ability to
model a nonlinear system, which a transfer function is
unable to do
 Another advantage of Simulink is the ability to take on
initial conditions where in transfer function the initial
conditions are assumed to be zero
SIMULINK BASICS
 A systems is represented by a block diagram
 You select the block from a library of blocks
 You need to know the library that contains the block
that you need
 click on the library name and you will see a list of blocks
in that library
 click on the block that you want and drag it to the work
file
 click on the block to select its parameters
 Connect it to other blocks
Launch Simulink
First launch MATLAB.
To open Simulink, type simulink at the MATLAB command
window or click on the Simulink icon on the MATLAB toolbar
Simulink Block Libraries
Simulink block libraries
Simulink provides a library browser that allows you to
select blocks from libraries of standard blocks :
Continuous - blocks that describe linear functions
Discontinuities - blocks that describe nonlinear functions
Discrete - blocks that describe discrete-time components
logic and bit operations - blocks that describe logic operation
Math operations - blocks that describe general mathematics functions
Sinks - blocks that display or write block output
Look up Tables
Model Verification
Model Wide Utilities
Ports & Subsystems
Signal Attributes
Signal Routing
User Defined Functions
Additional Math & Discrete
Create a new model
• Click the new-model
icon in the upper left
corner to start a new
Simulink file
Your workspace
Library of elements
Model is created in this window
Example 1
• Build a Simulink model that solves the differential
equation
x  3 sin 2t 
• Initial condition
x(0)  1
Simulation diagram
• Input is the function 3sin(2t)
• Output is the solution of the differential
equation x(t)
x(0)  1
3sin(2t)
(input)
x
1
s
x
x(t)
(output)
integrator
• Now build this model in Simulink
Select an input block
Drag a Sine Wave block
from the Sources library
to the model window
Select an operator block
Drag an Integrator block
from the Continuous library
to the model window
Select an output block
Drag a Scope block from the
Sinks library to the model
window
Connect blocks with signals
• Place your cursor on the
output port (>) of the
Sine Wave block
• Drag from the Sine Wave
output to the Integrator
input
• Drag from the Integrator
output to the Scope
input
Arrows indicate the
direction of the signal flow
Select simulation parameters
Double-click on
the Sine Wave
block to set
amplitude = 3
and freq = 2
This produces the
desired input of
3sin(2t)
Select simulation parameters
Double-click on
the Integrator
block to set
initial condition
= -1
This sets our IC
x(0) = -1
Run the simulation
In the model
window, from the
Simulation pulldown menu,
select run
View the output
x(t) in the Scope
window.
Simulation results
To verify that this
plot represents the
solution to the
problem, solve the
equation analytically
The analytical result,
x(t )  12  32 cos2t 
matches the plot
(the simulation
result) exactly
Example 2
 Build a Simulink model to get the response
of the system
•
•
•
•
2nd-order mass-spring-damper system
zero initial conditions
put f(t) is a step with magnitude 3
parameters: m = 0.25, c = 0.5, k = 1
mx  cx  kx  f (t )
From equation the system model
f(t)
input
+
-
mx 1
m
x
cx
kx
1
s
x
1
s
x
x
c
k
x
x(t)
output
Drag a Sum block from
the Math library
Double-click to change the
block parameters to
rectangular and + - -
Drag a Gain block from
the Math library
Double-click to change the
block parameters The gain
is 4 since 1/m=4
add a title
Drag Integrator blocks from
the Continuous library
ICs on the integrators are
zero.
Add a scope from the Sinks library
Connect output ports to input ports
Label the signals by double-clicking on the leader line
Drag new Gain blocks
from the Math library
To flip the gain block, select it
and choose Flip Block in the
Format pull-down menu.
 Double-click on gain blocks to
set parameters
c=0.5
,
k=1.0
 Connect from the gain block
input backwards up to the
branch point
 Re-title the gain blocks
Double-click on Step block
to set parameters. For a
step input of magnitude 3,
set Final value to 3
Final Simulink model
Results
Underdamped response.
Overshoot of 0.5.
Final value of 3
Is this expected?
Analysis
based on the equations of motion
• Standard form
• Natural freq
• Damping ratio
• Static gain
x
k
m
c
1
 x  x  f (t )
k
k
k
n 
 2.0
m
2
c

   0.5
n k
1
K  1
k
Check simulation results
• Damping ratio of 0.5 is less than 1
– Expect the system to be underdamped
– Expect to see overshoot
• Static gain is 1
– Expect output magnitude to equal input magnitude
– Input has magnitude 3, so does output
• Simulation results conform to expectations