This document provides an introduction to Simulink, which is an extension of MATLAB that allows engineers to model dynamic physical systems using block diagrams. It defines key concepts like systems, block diagrams, and modeling approaches. The document explains that Simulink uses block diagram representations of mathematical models to simulate and analyze dynamic systems. It provides examples of modeling spring-mass systems in Simulink and discusses how Simulink can be used for rapid prototyping and application development.

1. Introduction to Simulink K. Craig 1
Introduction to Simulink
Physical &
Mathematical
Modeling
Engineering
Measurement
Engineering
Analysis &
Computing
Engineering
Discovery
Physics
Mathematics
SocialScience
Hands-On Minds-On
Technical
Communications
Teamwork Professionalism
Engineering System Investigation Process
Engineering System Design Process
Mechanical
Engineering
Electrical &
Computer
Engineering
Civil &
Environmental
Engineering
Biomedical
Engineering
SelectionofEngineeringMaterials
ProcessestoMakeProducts

2. Introduction to Simulink K. Craig 2
What is a System?
• A system is an assemblage of components or elements
intended to act together to accomplish an objective.
• The view of a system as a set of interconnected elements is
what has been called the “systems approach” to problem
solving.
• The behavior of a system is specified by its input-output
relation, which is a description – usually mathematical – of
how the output is affected by the input.
• There are two types of systems: static and dynamic.
• Engineering dynamic systems can be small-scale and
large-scale.

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What is a Block Diagram?
• Block Diagram
– A block diagram of a system is a pictorial
representation of the functions performed by each
component and of the flow of signals. It describes a
set of relationships that hold simultaneously.
– A block diagram contains information concerning
dynamic behavior, but it does not include any
information on the physical construction of the
system.
– Many dissimilar and unrelated systems can be
represented by the same block diagram.
– A block diagram of a given system is not unique.

4. Introduction to Simulink K. Craig 4
Electro-Pneumatic Transducer:
An Engineering System
Note the three methods of
engineering communication:
picture, schematic, & block
diagram!

5. Introduction to Simulink K. Craig 5
Temperature Feedback
Control System:
A Larger-Scale
Engineering System

6. Introduction to Simulink K. Craig 6
What is Simulink?
• Simulink is an extension to MatLab that allows engineers to
rapidly and accurately build computer models of dynamic
physical systems using block diagram notation.
– linear and nonlinear systems
– continuous-time and discrete-time components
– graphical animations are possible
• Previously, a block diagram of the dynamic system
mathematical model was created and then the block
diagram was translated into a programming language.
• In Simulink, the computer program is the block diagram and
this eliminates the risk that the computer program may not
accurately implement the block diagram.

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Engineering System Investigation Process
Physical
System
System
Measurement
Measurement
Analysis
Physical
Model
Mathematical
Model
Parameter
Identification
Mathematical
Analysis
Comparison:
Predicted vs.
Measured
Design
Changes
Is The
Comparison
Adequate ?
NO
YES
START HERE
Focus
of
Our Attention Here
Simulink uses the
Mathematical Model
represented in Block
Diagram form and
predicts the dynamic
response (solves the
equations) of the
physical model (not
the actual physical
system).

8. Introduction to Simulink K. Craig 8
F ma
Ma Bv Kx F(t)
Ma Bv Kx F(t)
1
a ( Bv Kx F(t))
M
• Rigid support
• Pure and ideal spring
• Pure and ideal viscous damper
• One degree-of-freedom motion; x direction
• Rigid attached mass
• System is vertical; g acts down in +x direction
Physical System Simplifying Assumptions
Mathematical Model

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Simulink Block Diagram
1/s means
integration
in Simulink
Gain Block
multiplies the input
by the gain value
To Workspace
Block sends
selected output
to workspace
for plotting,
analysis, etc.

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• Numerical Integration
– Rectangle Approximation
• Assumes the function has a constant value within each interval
• Break the interval into a number of pieces of equal width, T
• Evaluate the function at x, the start of each piece, i.e., f(x)
• Calculate the area of a rectangle for each piece
– Area = T • f(x)
• Add up the areas of all the rectangles
T
f(x)

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– Trapezoid Approximation
• Assumes the function may change linearly within each interval
• Break the interval into a number of pieces of equal width, T
• Evaluate the function at x1, the start of each piece, i.e., f(x1)
• Evaluate the function at x2, the end of each piece, i.e., f(x2)
• Calculate the area of a box with a linearly sloping top for each
piece
– Area = T • ½ [f(x1) + f(x2)]
• Add up the areas of all the boxes
f(x1)
f(x2)
T

12. Introduction to Simulink K. Craig 12
• Inputs to a Dynamic System
– Engineers typically use two inputs to evaluate dynamic
systems: a step input and a sinusoidal input.
– By a step input of any variable, we will always mean a
situation where the system is at rest at time t = 0 and we
instantly change the input quantity, from wherever it was
just before t = 0, by a given amount, either positive or
negative, and then keep the input constant at this new
value forever. This leads to a transient response called
the step response of the system.
– When the input to the system is a sine wave, the steady-
state response of the system, after all the transients have
died away, is called the frequency response of the system.
– These two input types lead to the two views of dynamic
system response: time response and frequency response.

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Step Response
blue mass is placed on mass
M at t = 0 and left there

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Why is Simulink Important?
• The potential productivity improvement and cost savings
realized from the block diagram approach to programming
is dramatic.
• There are two principal strategies for Simulink employment.
– Rapid Prototyping
• This is the application of productivity tools to develop
working prototypes in the minimum amount of time.
Here we optimize for development speed, rather than
execution speed or memory use. A hierarchy of
physical models is used in this phase. Physical
system design and control design are optimized
simultaneously.

15. Introduction to Simulink K. Craig 15
– Rapid Application Development
• Here the final computer program is the Simulink
model or is derived from the Simulink model
through automatic C-code generation.

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MatLab Desktop
Command WindowCurrent Directory / Workspace
Command History
Simulink Icon

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File → New → Model

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Simulink Block Diagram Manipulations

20. Introduction to Simulink K. Craig 20
• Some Simulink Block Diagram Suggestions
– Careful arrangements of blocks and signal lines can
make relationships easier to follow.
– Naming blocks and signal lines and adding
annotations to the model can make the purpose of the
model elements easier to understand.
– The Best Way to ensure that your Simulink Block
Diagram accurately represents your mathematical
model equations is to write your mathematical model
equations directly from the Simulink Block Diagram
and then compare your result to the actual equations.
This will uncover any errors before you start to use
your block diagram to investigate model behavior.

21. Introduction to Simulink K. Craig 21
F ma
Ma Bv Kx F(t)
dv dx
a v
dt dt
Ma Bv Kx F(t)
1
a ( Bv Kx F(t))
M
Spring-Mass System Mathematical Model
a v v x
a v
v x

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Initial Conditions
a v v x

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1
a ( Bv Kx F(t))
M

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1
a ( Bv Kx F(t))
M

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1
a ( Bv Kx F(t))
M

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1
a ( Bv Kx F(t))
M

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1
a ( Bv Kx F(t))
M

28. Introduction to Simulink K. Craig 28
1
a ( Bv Kx F(t))
M

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1
a ( Bv Kx F(t))
M

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1
a ( Bv Kx F(t))
M

31. Introduction to Simulink K. Craig 31
Simulation → Configuration Parameters → Solver

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Simulation → Configuration Parameters → Data Import/Export

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M-File for Parameters
Start
Simulation

34. Introduction to Simulink K. Craig 34

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