10-05-2014, 03:20 PM
Introduction to Control Systems
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.
Modern Control Methods, instead of changing domains to avoid the complexities of time-domain ODE
mathematics, converts the differential equations into a system of lower-order time domain equations called State
Equations, which can then be manipulated using techniques from linear algebra (matrices). This book will
consider Modern Methods second.
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.
How is this Book Organized?
This book will be organized following a particular progression. First this book will discuss the basics of system
theory, and it will offer a brief refresher on integral transforms. Section 2 will contain a brief primer on digital
information, for students who are not necessarily familiar with them. This is done so that digital and analog
signals can be considered in parallel throughout the rest of the book. Next, this book will introduce the state-space
method of system description and control. After section 3, topics in the book will use state-space and transform
methods interchangably (and occasionally simultaneously). It is important, therefore, that these three chapters be
well read and understood before venturing into the later parts of the book.
System Identification
Physical Systems can be divided up into a number of different catagories, depending on particular properties that
the system exhibits. Some of these system classifications are very easy to work with, and have a large theory base
for studying. Some system classifications are very complex, and have still not been investigated with any degree
of success. This book will focus primarily on linear time-invariant (LTI) systems. LTI systems are the easiest
class of system to work with, and have a number of properties that make them ideal to study. In this chapter, we
will discuss some properties of systems, and we will define exactly what an LTI system is.