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105
Chapter 6
Introduction to Systems
Chapter Outline
6.1 DEFINITION OF A SYSTEM.
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6.1.1 Definitions.
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6.1.2 Representations of Systems .
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6.2 SYSTEM REPRESENTATIONS.
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6.2.1 Introduction to System Representations.
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6.2.2 Differential Equations .
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6.2.3 Laplace Transfer Functions.
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6.2.4 Convolution Integral .
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6.2.5 Fourier Transfer Function.
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6.2.6 Response to Standard Inputs.
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6.3 ELECTRICAL NETWORKS .
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6.3.1 System Representations.
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6.3.2 The Step and Impulse Responses.
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6.4 MASSSPRINGDAMPER SYSTEM.
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6.4.1 System Representations.
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6.4.2 The Step and Impulse Responses.
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6.5 PROOFMASS ACTUATORS .
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6.5.1 Linear Motors as Actuators .
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6.5.2 System Representations.
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6.5.3 The Step and Impulse Responses.
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6.6 CHAPTER SUMMARY.
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6.6.1 Definitions.
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6.6.2 Comparison of Impulse and Step Responses for the Three Systems.
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6.7 HOMEWORK FOR CHAPTER 6.
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In Chapter 5 we introduced the concept of a signal.
This concept is one of the most
fundamental concepts in system theory.
In this chapter we use the concept of a
signal to define the second fundamental concept of system theory: a system.
As
described in Chapter 1, the input signal to a system produces an output signal.
This definition is very general, and it allows us great flexibility in applying it to
a variety of physical processes.
At the same time there are a number of very
powerful system theoretic tools available that we can use to analyze very complex
systems.
It is the purpose of this text to begin the development of the concepts and
tools related to systems.
A system is given concrete
mathematical
expression by an
explicit
mathematical description of the system called a
model
.
The premise of system
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Chapter 6
Introduction to Systems
theory is that a mathematical model can be used to gain insight into a physical
processes.
Implied in this statement is that: (1) we can find a model that adequately
describes the physical process, (2) this model is suitable for analysis, and (3) this
model is suitable for design (if applicable).
It is important to recognize that a model
can accurately describe the physical observations, but be too complicated for
analysis or design.
Or a model that lends itself to analysis and design can be too
simplistic to accurately describe the observations.
In order to choose an appropriate
model, it is important to understand what system analysis techniques exist, and to
what kinds of system models these analysis techniques apply.
These analysis
techniques include both mathematical tools and computeraided design packages.
It
is the purpose of this text to develop this background.
It is the purpose of this
chapter to introduce several different kinds of models, called representations, that we
will study in the coming chapters.
In order to firmly fix the concept of a system, we will also introduce several
systems that we will use to illustrate the concepts in the coming chapters.
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 Spring '09
 MEEHAN

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