# Microsoft PowerPoint - Simulink 3

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```					Introduction to Simulink

Design of Mechanical Systems
650:486
• Simulink is an extension to Matlab that
allows engineers to rapidly and accurately
build computer models of dynamical
systems using block diagram notation.
• Block diagram notation is a graphical
means to represent dynamical systems.
Block Diagram Vs Flowchart
• A flowchart describes a     • A block diagram
sequence of operations,       describes a set of
so only one block in the      relationships that holds
flow chart is active at a     simultaneously, all blocks
time.                         in a block diagram may
be active at once. So
block diagram can be
thought of being
represented by a set of
simultaneous equations.

• At the command prompt for matlab type
simulink. This will open up the window for

create a new model or
click the “new” button      open an existing one

Continuous System
• Most physical systems are modeled as
continuous system since they can be
described by using differential equations.
• Simple models are linear and time
invariant.
Four fundamental blocks
• The four primitive blocks used to represent
continuous linear systems are
• Gain block
• Sum block
• Derivative block
• Integrator block.
Continuous system
Using source and sink blocks
Gain Block
• The simplest block
diagram element is the
gain block. The output of
the gain block is the input
multiplied by a constant.
• y(t)= kx(t) is represented
by the following block
diagram
Sum Block
• The sum block permit
us to add two or more
inputs.
• The expression
• c=a – b is represented
by the following
block diagram
Integrator Block
• The integrator block
computes the time
integral of its input
from the starting time
to the present.
Derivative block
• The derivative block
computes the time
rate of change of its
input.
y = dx/dt
Example 1
• Solving for a second order constant
coefficient linear differential equation
d2y/dt2 +c1dy/dt + c0y = b0f(t)

For a response to a ‘step’ command
Get an equivalent block diagram for the system

use mouse to drag blocks into
the model window and to
connect blocks with arrows

use integrators to get dy/dt and y

d2y/dt2 +c1dy/dt + c0y =
b0f(t)

Introducing the stepping function

Now, double click the blocks to open and set the block’s parameters

set gain value

set initial condition

set variable name
set output format to “array”
To set the simulation parameters….

select Simulation -> Simulation Parameters

set Start and Stop time (in seconds)
set numerical integration type
Time to run the simulation

click the “run” button to begin the simulation

when the simulation is complete, “Ready” appears at the bottom
Example

Simulink will automatically save a variable named “tout” to the
workspace.

This variable contains the time values used in the simulation, important
for variable time integration types

Simulink also will create the output variable(s) you specified

>>plot(tout,yoft)
Example #2
• The block diagram
denotes a cart of mass
m, on a frictionless
surface denoted by the
equation of motion :
d2x/dt2 = F/m
Cart Continued
• The block diagram of
the cart position
computation.
Simulation
• Simulating the cart: Using
a sine function as force
input, mass as 100 kg.
Problem #1
• Consider a spring-mass-
dashpot system
represented by the
equation of motion:
m(d2x/dt2) + c(dx/dt) + kx =
F
where m=100, c=10, k =5.
Simulate the position of the
mass.
Solution #1
Problem #2
• Represent the
differential equation
given by

dx/dt = bx – px2
where b =1 and p = 0.5

Hint: use product block
Solution #2

```
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