11-07-2012, 03:21 PM
Control Systems
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Introduction
What are Control Systems?
The study and design of automatic Control Systems, a field known as control engineering, is a large and
expansive area of study. Control systems, and control engineering techniques have become a pervasive part of
modern technical society. From devices as simple as a toaster, to complex machines like space shuttles and
rockets, control engineering is a part of our everyday life. This book will introduce the field of control
engineering, and will build upon those foundations to explore some of the more advanced topics in the field. Note,
however, that control engineering is a very large field, and it would be foolhardy of any author to think that they
could include all the information into a single book. Therefore, we will be content here to provide the foundations
of control engineering, and then describe some of the more advanced topics in the field.
Classical and Modern
Classical and Modern control methodologies are named in a misleading way, because the group of techniques
called "Classical" were actually developed later then the techniques labled "Modern". However, in terms of
developing control systems, Modern methods have been used to great effect more recently, while the Classical
methods have been gradually falling out of favor. Most recently, it has been shown that Classical and Modern
methods can be combined to highlight their respective strengths and weaknesses.
Classical Methods, which this book will consider first, are methods involving the Laplace Transform domain.
Physical systems are modeled in the so-called "time domain", where the response of a given system is a function
of the various inputs, the previous system values, and time. As time progresses, the state of the system, and it's
response change. However, time-domain models for systems are frequently modeled using high-order differential
equations, which can become impossibly difficult for humans to solve, and some of which can even become
impossible for modern computer systems to solve efficiently. To counteract this problem, integral transforms,
such as the Laplace Transform, and the Fourier Transform can be employed to change an Ordinary
Differential Equation (ODE) in the time domain into a regular algebraic polynomial in the transform domain.
Once a given system has been converted into the transform domain, it can be manipulated with greater ease, and
analyzed quickly and simply, by humans and computers alike.
Who is This Book For?
This book is intended to accompany a course of study in under-graduate and graduate engineering. As has been
mentioned previously, this book is not focused on any particular discipline within engineering, however any
person who wants to make use of this material should have some basic background in the Laplace transform (if
not other transforms), calculus, etc. The material in this book may be used to accompany several semesters of
study, depending on the program of your particular college or university. The study of control systems is
generally a topic that is reserved for students in their 3rd or 4th year of a 4 year undergraduate program, because it
requires so much previous information. Some of the more advanced topics may not be covered until later in a
graduate program.
What are the Prerequisites?
Understanding of the material in this book will require a solid mathematical foundation. This book does not
currently explain, nor will it ever try to fully explain most of the necessary mathematical tools used in this text.
For that reason, the reader is expected to have read the following wikibooks, or have background knowledge
comparable to them:
Calculus
Algebra
Linear Algebra
Differential Equations
Engineering Analysis
Branches of Control Engineering
Here we are going to give a brief listing of the various different methodologies within the sphere of control
engineering. Oftentimes, the lines between these methodologies are blurred, or even erased completely.
Classical Controls
Control methodologies where the ODEs that describe a system are transformed using the Laplace, Fourier,
or Z Transforms, and manipulated in the transform domain.
Modern Controls
Methods where high-order differential equations are broken into a system of first-order equations. The
input, output, and internal states of the system are described by vectors called "state variables".
Robust Control
Control methodologies where arbitrary outside noise/disturbances are accounted for, as well as internal
inaccuracies caused by the heat of the system itself, and the environment.