Kevin M. Passino
Department of Electrical Engineering
The Ohio State University
Department of Electrical Engineering
The Ohio State University
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MATLAB is a registered trademark of The MathWorks, Inc.
Library of Congress Cataloging-in-Publication Data
Passino, Kevin M.
Fuzzy control / Kevin M. Passino and Stephen Yurkovich.
Includes bibliographical references and index.
1. Automatic control. 2. Control theory. 3. Fuzzy systems.
I. Yurkovich, Stephen. II. Title.
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Fuzzy control is a practical alternative for a variety of challenging control applica-
tions since it provides a convenient method for constructing nonlinear controllers
via the use of heuristic information. Such heuristic information may come from
an operator who has acted as a “human-in-the-loop” controller for a process. In
the fuzzy control design methodology, we ask this operator to write down a set of
rules on how to control the process, then we incorporate these into a fuzzy con-
troller that emulates the decision-making process of the human. In other cases, the
heuristic information may come from a control engineer who has performed exten-
sive mathematical modeling, analysis, and development of control algorithms for a
particular process. Again, such expertise is loaded into the fuzzy controller to au-
tomate the reasoning processes and actions of the expert. Regardless of where the
heuristic control knowledge comes from, fuzzy control provides a user-friendly for-
malism for representing and implementing the ideas we have about how to achieve
In this book we provide a control-engineering perspective on fuzzy control.
We are concerned with both the construction of nonlinear controllers for challeng-
ing real-world applications and with gaining a fundamental understanding of the
dynamics of fuzzy control systems so that we can mathematically verify their prop-
erties (e.g., stability) before implementation. We emphasize engineering evaluations
of performance and comparative analysis with conventional control methods. We
introduce adaptive methods for identiﬁcation, estimation, and control. We exam-
ine numerous examples, applications, and design and implementation case studies
throughout the text. Moreover, we provide introductions to neural networks, ge-
netic algorithms, expert and planning systems, and intelligent autonomous control,
and explain how these topics relate to fuzzy control.
Overall, we take a pragmatic engineering approach to the design, analysis,
performance evaluation, and implementation of fuzzy control systems. We are not
concerned with whether the fuzzy controller is “artiﬁcially intelligent” or with in-
vestigating the mathematics of fuzzy sets (although some of the exercises do), but
rather with whether the fuzzy control methodology can help solve challenging real-
Overview of the Book
The book is basically broken into three parts. In Chapters 1–4 we cover the basics of
“direct” fuzzy control (i.e., the nonadaptive case). In Chapters 5–7 we cover adap-
tive fuzzy systems for estimation, identiﬁcation, and control. Finally, in Chapter 8
we brieﬂy cover the main areas of intelligent control and highlight how the topics
covered in this book relate to these areas. Overall, we largely focus on what one
could call the “heuristic approach to fuzzy control” as opposed to the more recent
mathematical focus on fuzzy control where stability analysis is a major theme.
In Chapter 1 we provide an overview of the general methodology for conven-
tional control system design. Then we summarize the fuzzy control system design
process and contrast the two. Next, we explain what this book is about via a simple
motivating example. In Chapter 2 we ﬁrst provide a tutorial introduction to fuzzy
control via a two-input, one-output fuzzy control design example. Following this
we introduce a general mathematical characterization of fuzzy systems and study
their fundamental properties. We use a simple inverted pendulum example to illus-
trate some of the most widely used approaches to fuzzy control system design. We
explain how to write a computer program to simulate a fuzzy control system, using
either a high-level language or Matlab1. In the web and ftp pages for the book we
provide such code in C and Matlab. In Chapter 3 we use several case studies to
show how to design, simulate, and implement a variety of fuzzy control systems.
In these case studies we pay particular attention to comparative analysis with con-
ventional approaches. In Chapter 4 we show how to perform stability analysis of
fuzzy control systems using Lyapunov methods and frequency domain–based sta-
bility criteria. We introduce nonlinear analysis methods that can be used to predict
and eliminate steady-state tracking error and limit cycles. We then show how to
use the analysis approaches in fuzzy control system design. The overall focus for
these nonlinear analysis methods is on understanding fundamental problems that
can be encountered in the design of fuzzy control systems and how to avoid them.
In Chapter 5 we introduce the basic “function approximation problem” and
show how identiﬁcation, estimation, prediction, and some control design problems
are a special case of it. We show how to incorporate heuristic information into the
function approximator. We show how to form rules for fuzzy systems from data pairs
and show how to train fuzzy systems from input-output data with least squares,
gradient, and clustering methods. And we show how one clustering method from
fuzzy pattern recognition can be used in conjunction with least squares methods to
construct a fuzzy model from input-output data. Moreover, we discuss hybrid ap-
proaches that involve a combination of two or more of these methods. In Chapter 6
we introduce adaptive fuzzy control. First, we introduce several methods for auto-
matically synthesizing and tuning a fuzzy controller, and then we illustrate their
application via several design and implementation case studies. We also show how
1. MATLAB is a registered trademark of The MathWorks, Inc.
to tune a fuzzy model of the plant and use the parameters of such a model in the
on-line design of a controller. In Chapter 7 we introduce fuzzy supervisory control.
We explain how fuzzy systems can be used to automatically tune proportional-
integral-derivative (PID) controllers, how fuzzy systems provide a methodology
for constructing and implementing gain schedulers, and how fuzzy systems can be
used to coordinate the application and tuning of conventional controllers. Follow-
ing this, we show how fuzzy systems can be used to tune direct and adaptive fuzzy
controllers. We provide case studies in the design and implementation of fuzzy
In Chapter 8 we summarize our control engineering perspective on fuzzy control,
provide an overview of the other areas of the ﬁeld of “intelligent control,” and
explain how these other areas relate to fuzzy control. In particular, we brieﬂy cover
neural networks, genetic algorithms, knowledge-based control (expert systems and
planning systems), and hierarchical intelligent autonomous control.
Examples, Applications, and Design and Implementation Case Studies
We provide several design and implementation case studies for a variety of appli-
cations, and many examples are used throughout the text. The basic goals of these
case studies and examples are as follows:
• To help illustrate the theory.
• To show how to apply the techniques.
• To help illustrate design procedures in a concrete way.
• To show what practical issues are encountered in the development and implemen-
tation of a fuzzy control system.
Some of the more detailed applications that are studied in the chapters and their
accompanying homework problems are the following:
• Direct fuzzy control: Translational inverted pendulum, fuzzy decision-making sys-
tems, two-link ﬂexible robot, rotational inverted pendulum, and machine schedul-
ing (Chapters 2 and 3 homework problems: translational inverted pendulum, au-
tomobile cruise control, magnetic ball suspension system, automated highway sys-
tem, single-link ﬂexible robot, rotational inverted pendulum, machine scheduling,
motor control, cargo ship steering, base braking control system, rocket velocity
control, acrobot, and fuzzy decision-making systems).
• Nonlinear analysis: Inverted pendulum, temperature control, hydrofoil controller,
underwater vehicle control, and tape drive servo (Chapter 4 homework problems:
inverted pendulum, magnetic ball suspension system, temperature control, and
hydrofoil controller design).
• Fuzzy identiﬁcation and estimation: Engine intake manifold failure estimation,
and failure detection and identiﬁcation for internal combustion engine calibra-
tion faults (Chapter 5 homework problems: tank identiﬁcation, engine friction
estimation, and cargo ship failures estimation).
• Adaptive fuzzy control: Two-link ﬂexible robot, cargo ship steering, fault toler-
ant aircraft control, magnetically levitated ball, rotational inverted pendulum,
machine scheduling, and level control in a tank (Chapter 6 homework problems:
tanker and cargo ship steering, liquid level control in a tank, rocket velocity con-
trol, base braking control system, magnetic ball suspension system, rotational
inverted pendulum, and machine scheduling).
• Supervisory fuzzy control: Two-link ﬂexible robot, and fault-tolerant aircraft con-
trol (Chapter 7 homework problems: liquid level control, and cargo and tanker
Some of the applications and examples are dedicated to illustrating one idea from
the theory or one technique. Others are used in several places throughout the text
to show how techniques build on one another and compare to each other. Many of
the applications show how fuzzy control techniques compare to conventional control
World Wide Web Site and FTP Site: Computer Code Available
The following information is available electronically:
• Various versions of C and Matlab code for simulation of fuzzy controllers, fuzzy
control systems, adaptive fuzzy identiﬁcation and estimation methods, and adap-
tive fuzzy control systems (e.g., for some examples and homework problems in
• Other special notes of interest, including an errata sheet if necessary.
You can access this information via the web site:
or you can access the information directly via anonymous ftp to
For anonymous ftp, log into the above machine with a username “anonymous” and
use your e-mail address as a password.
Organization, Prerequisites, and Usage
Each chapter includes an overview, a summary, and a section “For Further Study”
that explains how the reader can continue study in the topical area of the chapter.
At the end of each chapter overview, we explain how the chapter is related to the