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Antonio Visioli
Practical PID Control
With 241 Figures
123

Antonio Visioli, PhD
Dipartimento di Elettronica per l’Automazione
Università degli Studi di Brescia
I-25123 Brescia
Italy
antonio.visioli@ing.unibs.it
www.ing.unibs.it/
˜visioli
British Library Cataloguing in Publication Data
Visioli, Antonio
Practical PID control. - (Advances in industrial control)
1. PID controllers
I. Title
629.8
ISBN-13: 9781846285851
ISBN-10: 1846285852
Library of Congress Control Number: 2006932289
Advances in Industrial Control series ISSN 1430-9491
ISBN-10: 1-84628-585-2 e-ISBN 1-84628-586-0 Printed on acid-free paper
ISBN-13: 978-1-84628-585-1
© Springer-Verlag London Limited 2006
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers,
or in the case of reprographic reproduction in accordance with the terms of licences issued by the
Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to
the publishers.
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a
speciﬁc statement, that such names are exempt from the relevant laws and regulations and therefore free
for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the information
contained in this book and cannot accept any legal responsibility or liability for any errors or omissions
that may be made.
9 8 7 6 5 4 3 2 1
Springer Science+Business Media
springer.com

Advances in Industrial Control
Series Editors
Professor Michael J. Grimble, Professor of Industrial Systems and Director
Professor Michael A. Johnson, Professor (Emeritus) of Control Systems
and Deputy Director
Industrial Control Centre
Department of Electronic and Electrical Engineering
University of Strathclyde
Graham Hills Building
50 George Street
Glasgow G1 1QE
United Kingdom
Series Advisory Board
Professor E.F. Camacho
Escuela Superior de Ingenieros
Universidad de Sevilla
Camino de los Descobrimientos s/n
41092 Sevilla
Spain
Professor S. Engell
Lehrstuhl für Anlagensteuerungstechnik
Fachbereich Chemietechnik
Universität Dortmund
44221 Dortmund
Germany
Professor G. Goodwin
Department of Electrical and Computer Engineering
The University of Newcastle
Callaghan
NSW 2308
Australia
Professor T.J. Harris
Department of Chemical Engineering
Queen’s University
Kingston, Ontario
K7L 3N6
Canada
Professor T.H. Lee
Department of Electrical Engineering
National University of Singapore
4 Engineering Drive 3
Singapore 117576

Professor Emeritus O.P. Malik
Department of Electrical and Computer Engineering
University of Calgary
2500, University Drive, NW
Calgary
Alberta
T2N 1N4
Canada
Professor K.-F. Man
Electronic Engineering Department
City University of Hong Kong
Tat Chee Avenue
Kowloon
Hong Kong
Professor G. Olsson
Department of Industrial Electrical Engineering and Automation
Lund Institute of Technology
Box 118
S-221 00 Lund
Sweden
Professor A. Ray
Pennsylvania State University
Department of Mechanical Engineering
0329 Reber Building
University Park
PA 16802
USA
Professor D.E. Seborg
Chemical Engineering
3335 Engineering II
University of California Santa Barbara
Santa Barbara
CA 93106
USA
Doctor K.K. Tan
Department of Electrical Engineering
National University of Singapore
4 Engineering Drive 3
Singapore 117576
Professor Ikuo Yamamoto
Kyushu University Graduate School
Marine Technology Research and Development Program
MARITEC, Headquarters, JAMSTEC
2-15 Natsushima Yokosuka
Kanagawa 237-0061
Japan

Series Editor’s Foreword
The series Advances in Industrial Control aims to report and encourage tech-
nology transfer in control engineering. The rapid development of control tech-
nology has an impact on all areas of the control discipline. New theory, new
controllers, actuators, sensors, new industrial processes, computer methods,
new applications, new philosophies..., new challenges. Much of this develop-
ment work resides in industrial reports, feasibility study papers and the re-
ports of advanced collaborative projects. The series offers an opportunity for
researchers to present an extended exposition of such new work in all aspects
of industrial control for wider and rapid dissemination.
In February, 2006, IEEE Control Systems Magazine celebrated its first 25
years of publication and the special issue was devoted to the topic of PID
control. It was fascinating to read of PID control developments in many of
the departments of the magazine; these included several specialist PID con-
trol articles, a review of PID patents, software and industrial hardware, a
new design software package for PID control and reviews of four substantial
new books on different aspects of the PID control paradigm. The evidence
from this special issue was that PID control continues to play a significant
and important role in industrial control engineering. When seeking reasons
for this industrial popularity, many cite the simplicity of the control law, the
straight forwardness of its tuning procedures and so on but, perhaps a more
fundamental point is that so many industrial control loops are easy to control
and PID control is all that is needed. Then, the simplicity of the PID con-
trol law and the availability of pro-forma tuning procedures have real benefit
particularly as these have been captured by automated tuning procedures in
widely available software packages.
However, the converse of the above argument is also true and much of the sci-
ence of PID control engineering has emerged from trying to understand and
identify the exceptions, where PID control is not adequate for the complex-
ities of the process, and the remedies that can be followed. One example of
this type of new development is that of performance assessment and monitor-
ing. This emerged from trying to find simple ways of determining whether the
many PID control loops in an industrial plant (and often there are hundreds)
had controller tunings that were fit for purpose. Questions like these on the
practical aspects of PID control continue to motivate new developments for
use in industrial practice.
The Advances in Industrial Control series of monographs has always sought

x Series Editor’s Foreword
to be abreast of developments in theory and applications that have an impact
on the field of industrial control. During the late 1990s, there was a veritable
clutch of titles in the series on PID control. C.C. Yu’s monograph Autotuning
of PID Controllers: Relay Feedback Approach was published in 1999 (and has
since been republished as a second edition (ISBN: 1-84628-036-2) in 2006).
The same year saw K.K. Tan and his colleagues develop, summarise and ex-
tend many new and existing concepts in a volume entitled Advances in PID
Control (ISBN: 1-85233-614-5). This presented new methods for a fundamen-
tal understanding of the properties of PID controller tuning parameters. On
a related subject, the series published the 1999 monograph Performance As-
sessment of Control Loops (ISBN: 1-85233-639-0) by B. Huang and S.L. Shah.
This work grew from the seminal work of Professor Thomas Harris who sought
ways of determining just how good an installed PID controller was. As if to
capture this extensive ongoing research activity, PID control had its own con-
ference event under the auspices of IFAC, for in 2000, a Workshop on Digital
Control, PID 2000 was held at Terrassa, Spain.
As the special issue of IEEE Control Systems Magazine shows, the industrial
and academic interest in PID control continues and to continue the devel-
opment of PID control from the millennium, Advances in Industrial Control
welcomes Practical PID Control by Antonio Visioli of the University of Bres-
cia, Italy. It is a very useful and pertinent addition because it focuses on the
broader practical aspects of PID control other than those of how to select or
tune the controller coefficients.
The new volume opens with an introductory chapter on the basics of PID
controllers that establishes the notation, terminology, and structure of the
controllers to be used in the text. Then Dr. Visioli presents chapters on deriva-
tive filter design, anti-windup strategies, the selection of set-point weightings,
the use of feed-forward control, the implications of model identification and
reduction for PID control, performance assessment procedures and, finally,
the oft-neglected ratio control systems. In what is obviously a comprehensive
set of contributions to PID control, Dr. Visioli also has a chapter on Plug
& Control facilities that are often available in industrial SCADA and DCS
software suites. Throughout the text, developments are illustrated with sim-
ulations and experimental results from two hardware process rigs, namely a
level control system (the double tank apparatus from KentRidge Instruments)
and a temperature control rig based on a laboratory-scale oven.
For those interested in the development of PID control, this monograph
presents new perspectives to inspire new theoretical developments and exper-
imental tests. The industrial engineer can use the book to investigate wider
practical PID control problems and the research engineer will be able to ini-
tiate close study of many problems that often prevent PID control systems
form reaching their full performance potential.
M.J. Grimble and M.A. Johnson
Glasgow, Scotland, U.K.

Preface
Although the new and effective theories and design methodologies being
continually developed in the automatic control field, Proportional–Integral–
Derivative (PID) controllers are still by far the most widely adopted con-
trollers in industry owing to the advantageous cost/benefit ratio they are able
to provide. In fact, although they are relatively simple to use, they are able
to provide a satisfactory performance in many process control tasks. Indeed,
their long history and the know-how that has been devised over the years
has consolidated their usage as a standard feedback controller. However, the
availability of high-performance microprocessors and software tools and the
increasing demand of higher product quality at reduced costs still stimulates
researchers to devise new methodologies for the improvement of performance
and/or for an easier use of them. This is proven by the large number of publi-
cations on this topic (especially in recent years) and by the increasing number
of products available on the market.
Actually, much of the effort of researchers has been concentrated on the devel-
opment of new tuning rules for the selection of the values of the PID parame-
ters. Although this is obviously a crucial issue, it is well-known that a key role
in the achievement of high performance in practical conditions is also played
by those functionalities that have to (or can) be added to the basic PID con-
trol law. Thus, in contrast to other books on PID control, this book focuses
on some of these additional functionalities and on other practical problems
that a typical practitioner has to face when implementing a PID controller
(for scalar linear systems). Recent advances as well as more standard method-
ologies are presented in this context. To summarise, the book tries to answer
the following questions:
• How can an effective filter on the PID action be implemented?
• How can an effective anti-windup strategy be implemented?
• How can the set-point weighting strategy be modified to improve perfor-
mance?

xii Preface
• How can the identification (and model reduction) procedure be selected
for the tuning of the parameters?
• How can an effective feedforward strategy be implemented?
• How can the achieved performance be assessed?
• How can PID-based control structures (ratio control and cascade control)
be implemented effectively?
The aim of the following chapters is therefore to provide a comprehensive
(although surely not exhaustive) review of approaches in the context outlined
above and also aims at stimulating new ideas in the field.
The content of the book is organised as follows.
Chapter 1 provides an introduction to PID controllers, with the aim of making
the book self-contained, of presenting the notation and of describing the prac-
tical issues that will be analysed in the following chapters. In particular, the
three actions are described, the different controller structures are presented
and the tuning issue is discussed.
In Chapter 2 the design of the low-pass filter that is necessary to make the
controller transfer function proper is discussed. It is pointed out that this is
indeed an important issue for the control performance and should be treated
to all intents as a tuning parameter. Methodologies proposed recently in the
literature in this context are described.
Chapter 3 presents and compares the different techniques that can be imple-
mented to counteract the integrator windup effect due to the presence of a
saturating actuator.
Chapter 4 addresses the use of the set-point weighting functionality. In par-
ticular, the standard technique of weighting the set-point for the proportional
action (i.e., of filtering the set-point of the closed-loop system) in order to
reduce the overshoot is first reviewed. Then, the use of a variable set-point
weight is also analysed in detail and it is shown that this might significantly
improve the set-point following performances.
Chapter 5 further focuses on the use of a feedforward action to improve set-
point following performance. In particular, a new design for a (causal) feedfor-
ward action is presented and it is compared to the standard approach. Further,
two methodologies for the design of a noncausal feedforward action, based on
input-output inversion, are explained. The design of feedforward action for
disturbance rejection purposes is also briefly considered.
In Chapter 6 the recently developed Plug&Control strategy is described. It is
shown that it represents a useful tool for the fast tuning of the controller at
the start-up of the process.
Identification and model reduction techniques are analysed in Chapter 7. Dif-
ferent methods based on the open-loop step response or on the relay-feedback
approach for the estimation of the parameters of first-order-plus-dead-time
(FOPDT) or second-order-plus-dead-time (SOPDT) transfer functions are re-
viewed and compared in order to analyse and discuss their suitability of use in
the context of PID control. Further, the use of model reduction techniques to

Preface xiii
be applied for the design of PID control of high-order processes is discussed.
Chapter 8 presents methodologies for the assessment of the (stochastic and
deterministic) performance obtained by a PID controller in the general frame-
work of process monitoring.
Finally, Chapter 9 addresses control structures based on PID controllers. In
particular, standard approaches together with recently proposed methodolo-
gies are presented for cascade control and ratio control.
A large number of simulation and experimental results are shown to anal-
yse better each technique presented. Experimental results are obtained by
means of two laboratory scale setups (described in the appendix), where a
level control task and a temperature control task are implemented. Although
true industrial plant data are not adopted, it is believed that these results are
indeed significant for the evaluation of a methodology in a practical context.
The book is therefore intended to be useful as a comprehensive review for aca-
demic researchers as well as for industrial practitioners who are looking for
new methodologies to improve control systems performance while retaining
their basic know-how and the ease of use and the low cost of the controller.
Readers are assumed to know the fundamentals of linear control systems,
which are typically acquired in a basic course in automatic control at the
university level. In particular, the description of a system through its transfer
function is adopted over the whole book.
This book is a result of almost ten years of research in the field of PID con-
trol. I would like to thank Giovanna Finzi of the University of Brescia for
having encouraged me in pursuing this research topic and for having always
supported me with her friendship. It has been a privilege to work with Aurelio
Piazzi of the University of Parma, I am indeed indebted with him for having
shared his knowledge and experience with me. I am also grateful to Massi-
miliano Veronesi of Yokogawa Italia, Fausto Gorla of Paneutec and Michele
Caselli of ER Sistemi for the useful discussions we had together. A partic-
ular thank is due to Claudio Scali of University of Pisa for having read the
manuscript of the book and for his valuable comments. A special thank is due
also to Leslie Mustoe of Loughborough University for the careful correction of
the manuscript. Many experimental results have been obtained with the help
of many students of the Faculty of Engineering of the University of Brescia.
Their contribution is acknowledged. Many thanks also to Oliver Jackson of
the publishing staff at Springer London, for his help during the preparation
of the manuscript.
Finally, I would like to express my deep gratitude to my beloved wife Silvia
and my dearest daughters Alessandra and Laura for their love, patience and
support.
Dipartimento di Elettronica per l’Automazione Antonio Visioli
University of Brescia

Contents
1 Basics of PID Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Feedback Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 On–Off Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 The Three Actions of PID Control . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.1 Proportional Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.2 Integral Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4.3 Derivative Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Structures of PID Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Modifications of the Basic PID Control Law . . . . . . . . . . . . . . . . 8
1.6.1 Problems with Derivative Action . . . . . . . . . . . . . . . . . . . . 8
1.6.2 Set-point Weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6.3 General ISA–PID Control Law . . . . . . . . . . . . . . . . . . . . . . 13
1.7 Digital Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.8 Choice of the Controller Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.9 The Tuning Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.10 Automatic Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.11 Conclusions and References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Derivative Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 The Significance of the Filter in PID Design . . . . . . . . . . . . . . . . 19
2.3 Ideal vs. Series Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Simulation Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 Four-parameters Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Anti-windup Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Integrator Windup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Anti-windup Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

xvi Contents
3.3.1 Avoiding Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.2 Conditional Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.3 Back-calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.4 Combined Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.5 Automatic Reset Implementation . . . . . . . . . . . . . . . . . . . . 42
3.4 Simulation Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.5.1 Level Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.5.2 Temperature Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4 Set-point Weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 Constant Set-point Weight Design . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 Variable Set-point Weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.1 Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.3.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 Fuzzy Set-point Weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4.1 Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4.2 Tuning Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5 Use of a Feedforward Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2 Linear Causal Feedforward Action . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Nonlinear Causal Feedforward Action . . . . . . . . . . . . . . . . . . . . . . 96
5.4 Noncausal Feedforward Action: Continuous-time Case . . . . . . . . 109
5.4.1 Generalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.4.2 Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5 Noncausal Feedforward Action: Discrete-time Case. . . . . . . . . . . 130
5.5.1 Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.6 Feedforward Action for Disturbance Rejection . . . . . . . . . . . . . . . 140
5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Contents xvii
6 Plug&Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.2 Self-tuning Temperature Control . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.3 Time-optimal Plug&Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.3.1 Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.3.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.3.3 Practical Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7 Identification and Model Reduction Techniques . . . . . . . . . . . . 165
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.2 FOPDT Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.2.1 Open-loop Identification Techniques . . . . . . . . . . . . . . . . . 166
7.2.2 Closed-loop Identification Techniques . . . . . . . . . . . . . . . . 173
7.3 SOPDT Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.3.1 Open-loop Identification Techniques . . . . . . . . . . . . . . . . . 180
7.3.2 Closed-loop Identification Techniques . . . . . . . . . . . . . . . . 191
7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
7.5 PID Control of High-order Systems . . . . . . . . . . . . . . . . . . . . . . . . 193
7.5.1 Internal Model Control Design . . . . . . . . . . . . . . . . . . . . . . 194
7.5.2 Process Model Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
7.5.3 Controller Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
7.5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8 Performance Assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
8.2 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3 Stochastic Performance Assessment . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3.1 Minimum Variance Control . . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3.2 Assessment of Performance . . . . . . . . . . . . . . . . . . . . . . . . . 212
8.3.3 Assessment of PID Control Performance. . . . . . . . . . . . . . 216
8.4 Deterministic Performance Assessment . . . . . . . . . . . . . . . . . . . . . 222
8.4.1 Useful Functionalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
8.4.2 Optimal Performance for Single-loop Systems . . . . . . . . . 232
8.4.3 PID Tuning Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

xviii Contents
9 Control Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
9.2 Cascade Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
9.2.1 Generalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
9.2.2 Relay Feedback Sequential Auto-tuning . . . . . . . . . . . . . . 253
9.2.3 Relay Feedback Simultaneous Auto-tuning . . . . . . . . . . . . 253
9.2.4 Simultaneous Identiﬁcation Based on Step Response . . . 257
9.2.5 Simultaneous Tuning of the Controllers . . . . . . . . . . . . . . 257
9.2.6 Tuning of the General Cascade Control Structure. . . . . . 260
9.2.7 Use of a Smith Predictor in the Outer Loop . . . . . . . . . . 263
9.2.8 Two Degree-of-freedom Control Structure . . . . . . . . . . . . 265
9.3 Ratio Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
9.3.1 Generalities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
9.3.2 The Blend Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
9.3.3 Dynamic Blend Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
9.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
A Experimental Setups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
A.1 Level Control Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
A.2 Temperature Control Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

1
Basics of PID Control
1.1 Introduction
A Proportional–Integral–Derivative (PID) controller is a three-term controller
that has a long history in the automatic control field, starting from the be-
ginning of the last century (Bennett, 2000). Owing to its intuitiveness and its
relative simplicity, in addition to satisfactory performance which it is able to
provide with a wide range of processes, it has become in practice the standard
controller in industrial settings. It has been evolving along with the progress
of the technology and nowadays it is very often implemented in digital form
rather than with pneumatic or electrical components. It can be found in vir-
tually all kinds of control equipments, either as a stand-alone (single-station)
controller or as a functional block in Programmable Logic Controllers (PLCs)
and Distributed Control Systems (DCSs). Actually, the new potentialities
offered by the development of the digital technology and of the software pack-
ages has led to a significant growth of the research in the PID control field:
new effective tools have been devised for the improvement of the analysis and
design methods of the basic algorithm as well as for the improvement of the
additional functionalities that are implemented with the basic algorithm in
order to increase its performance and its ease of use.
The success of the PID controllers is also enhanced by the fact that they often
represent the fundamental component for more sophisticated control schemes
that can be implemented when the basic control law is not sufficient to obtain
the required performance or a more complicated control task is of concern.
In this chapter, the fundamental concepts of PID control are introduced with
the aim of presenting the rationale of the control law and of describing the
framework of the methodologies presented in the subsequent chapters. In par-
ticular, the meaning of the three actions is explained and the tuning issue is
briefly discussed. The different forms for the implementation of a PID control
law are also addressed.

2 1 Basics of PID Control
1.2 Feedback Control
The aim of a control system is to obtain a desired response for a given sys-
tem. This can be done with an open-loop control system, where the controller
determines the input signal to the process on the basis of the reference signal
only, or with a closed-loop control system, where the controller determines
the input signal to the process by using also the measurement of the output
(i.e., the feedback signal).
Feedback control is actually essential to keep the process variable close to the
desired value in spite of disturbances and variations of the process dynamics,
and the development of feedback control methodologies has had a tremen-
dous impact in many different fields of the engineering. Besides, nowadays
the availability of control system components at a lower cost has favoured the
increase of the applications of the feedback principle (for example in consumer
electronics products).
The typical feedback control system is represented in Figure 1.1. Obviously,
the overall control system performance depends on the proper choice of each
component. From the purposes of controller design, the actuator and sensor
dynamics are often neglected (although the saturation limits of the actuator
have to be taken into account) and the block diagram of Figure 1.2 is consid-
ered, where P is the process, C is the controller, F is a feedforward filter, r is
the reference signal, e = r − y is the control error, u is the manipulated (con-
trol) variable, y is the process (controlled) variable, d is a load disturbance
signal and n is a measurement noise signal.
Controller Actuator Process
Sensor
Fig. 1.1. Typical components of a feedback control loop
C P
u y
n
e
d
r F
Fig. 1.2. Schematic block diagram of a feedback control loop

1.4 The Three Actions of PID Control 3
1.3 On–Off Control
One of the most adopted (and one of the simplest) controllers is undoubtedly
the On–Off controller, where the control variable can assume just two values,
umax and umin, depending on the control error sign. Formally, the control law
is defined as follows:
u =

umax if e 0
umin if e 0
, (1.1)
i.e., the control variable is set to its maximum value when the control error is
positive and to its minimum value when the control error is negative. Gener-
ally, umin = 0 (Off) is selected and the controller is usually implemented by
means of a relay.
The main disadvantage of the On–Off controller is that a persistent oscillation
of the process variable (around the set-point value) occurs. Consider for exam-
ple the process described by the first-order-plus-dead-time (FOPDT) transfer
function
P(s) =
1
10s + 1
e−2s
controlled by an On–Off controller with umax = 2 and umin = 0. The result
of applying a unit step to the set-point signal is shown in Figure 1.3, where
both the process variable and the control variable have been plotted.
Actually, in practical cases, the On–Off controller characteristic is modified
by inserting a dead zone (this results in a three-state controller ) or hysteresis
in order to cope with measurement noise and to limit the wear and tear of the
actuating device. The typical controller functions are shown in Figure 1.4.
Because of its remarkable simplicity (there are no parameters to adjust), the
On–Off controller is indeed suitable for adoption when no tight performance
is required, since it is very cost-effective in these cases. For this reason it is
generally available in commercial industrial controllers.
1.4 The Three Actions of PID Control
Applying a PID control law consists of applying properly the sum of three
types of control actions: a proportional action, an integral action and a deriva-
tive one. These actions are described singularly hereafter.
1.4.1 Proportional Action
The proportional control action is proportional to the current control error,
according to the expression
u(t) = Kpe(t) = Kp(r(t) − y(t)), (1.2)
where Kp is the proportional gain. Its meaning is straightforward, since it
implements the typical operation of increasing the control variable when the

0 5 10 15 20 25 30 35 40 45 50
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
time
Fig. 1.3. Example of an On–Off control application. Solid line: process variable;
dashed line: control variable.
e
u u u
e e
u
u
min
max umax
umin
max
u
umin
c)
b)
a)
Fig. 1.4. Typical On–Off controller characteristics. a) ideal; b) modified with a
dead zone; c) modified with hysteresis.
control error is large (with appropriate sign). The transfer function of a pro-
portional controller can be derived trivially as
C(s) = Kp. (1.3)
With respect to the On–Off controller, a proportional controller has the ad-
vantage of providing a small control variable when the control error is small
and therefore to avoid excessive control efforts. The main drawback of using a
pure proportional controller is that it produces a steady-state error. It is worth
noting that this occurs even if the process presents an integrating dynamics
(i.e., its transfer function has a pole at the origin of the complex plane), in
case a constant load disturbance occurs. This motivates the addition of a bias

1.4 The Three Actions of PID Control 5
(or reset) term ub, namely,
u(t) = Kpe(t) + ub. (1.4)
The value of ub can be ﬁxed at a constant level (usually at (umax + umin)/2)
or can be adjusted manually until the steady-state error is reduced to zero.
It is worth noting that in commercial products the proportional gain is often
replaced by the proportional band PB, that is the range of error that causes
a full range change of the control variable, i.e.,
PB =
100
Kp
. (1.5)
1.4.2 Integral Action
The integral action is proportional to the integral of the control error, i.e., it
is
u(t) = Ki
t
0
e(τ)dτ, (1.6)
where Ki is the integral gain. It appears that the integral action is related to
the past values of the control error. The corresponding transfer function is:
C(s) =
Ki
s
. (1.7)
The presence of a pole at the origin of the complex plane allows the reduction
to zero of the steady-state error when a step reference signal is applied or a
step load disturbance occurs. In other words, the integral action is able to set
automatically the correct value of ub in (1.4) so that the steady-state error is
zero. This fact is better explained in Figure 1.5, where the resulting transfer
function is
C(s) = Kp

1 +
1
Tis

, (1.8)
i.e., a PI controller results. For this reason the integral action is also often
called automatic reset.
Thus, the use of a proportional action in conjunction to an integral action,
i.e., of a PI controller, solves the main problems of the oscillatory response
associated to an On–Oﬀ controller and of the steady-state error associated to
a pure proportional controller.
It has to be stressed that when integral action is present, the so-called inte-
grator windup phenomenon might occur in the presence of saturation of the
control variable. This aspect will be thoroughly analysed in Chapter 3.

u
e Kp
1
i s+1
T
Fig. 1.5. PI controller in automatic reset conﬁguration
1.4.3 Derivative Action
While the proportional action is based on the current value of the control
error and the integral action is based on the past values of the control error,
the derivative action is based on the predicted future values of the control
error. An ideal derivative control law can be expressed as:
u(t) = Kd
de(t)
dt
, (1.9)
where Kd is the derivative gain. The corresponding controller transfer function
is
C(s) = Kds. (1.10)
In order to understand better the meaning of the derivative action, it is worth
considering the ﬁrst two terms of the Taylor series expansion of the control
error at time Td ahead:
e(t + Td) e(t) + Td
de(t)
dt
. (1.11)
If a control law proportional to this expression is considered, i.e.,
u(t) = Kp

e(t) + Td
de(t)
dt

, (1.12)
this naturally results in a PD controller. The control variable at time t is
therefore based on the predicted value of the control error at time t + Td.
For this reason the derivative action is also called anticipatory control, or rate
action, or pre-act.
It appears that the derivative action has a great potentiality in improving the
control performance as it can anticipate an incorrect trend of the control error
and counteract for it. However, it has also some critical issues that makes it
not very frequently adopted in practical cases. They will be discussed in the
following sections.

1.5 Structures of PID Controllers 7
1.5 Structures of PID Controllers
The combination of the proportional, integral, and derivative actions can be
done in different ways. In the so-called ideal or non-interacting form, the PID
controller is described by the following transfer function:
Ci(s) = Kp

1 +
1
Tis
+ Tds

, (1.13)
where Kp is the proportional gain, Ti is the integral time constant, and Td
is the derivative time constant. An alternative representation is the series or
interacting form:
Cs(s) = K
p

1 +
1
T
i s

(T
ds + 1) = K
p

T
i s + 1
T
i s

(T
ds + 1) , (1.14)
where the fact that a modification of the value of the derivative time constant
T
d affects also the integral action justifies the nomenclature adopted.
It has to be noted that a PID controller in series form can be always repre-
sented in ideal form by applying the following formulae:
Kp = K
p
T
i + T
d
T
i
Ti = T
i + T
d
Td =
T
i T
d
T
i + T
d
(1.15)
Conversely, it is not always possible to convert a PID controller in series form
into a PID controller in ideal form. This can be done only if
Ti ≥ 4Td (1.16)
through the following formulae:
K
p =
Kp
2
⎛
⎝1 +

1 − 4
Td
Ti
⎞
⎠
T
i =
Ti
2
⎛
⎝1 +

1 − 4
Td
Ti
⎞
⎠
T
d =
Ti
2
⎛
⎝1 −

1 − 4
Td
Ti
⎞
⎠
(1.17)

It is worth noting that a PID controller has two zeros, a pole at the origin and
a gain (the fact that the transfer function is not proper will be discussed in
Section 1.6). When Ti = 4Td the resulting zeros of Ci(s) are coincident, while
when Ti 4Td they are complex conjugates. Thus, the ideal form is more
general than the series form since it allows the implementation of complex
conjugate zeros.
The reason for preferring the series form to the ideal form is that the series
form was the first to be implemented in the last century with pneumatic
technology. Then, many manufacturers chose to retain the know-how and to
avoid changing the form of the PID controller. Further, it is sometimes claimed
that a PID controller in series form is more easy to tune.
Another way to implement a PID controller is in parallel form 1
, i.e.,
Cp(s) = Kp +
Ki
s
+ Kds. (1.18)
In this case the three actions are completely separated. Actually, the parallel
form is the most general of the different forms, as it allows to exactly switch
off the integral action by fixing Ki = 0 (in the other cases the value of the
integral time constant should tend to infinity). The conversion between the
parameters of the parallel PID controller and those of the ideal one can be
done trivially by means of the following formulae:
Ki =
Kp
Ti
Kd = KpTd
(1.19)
1.6 Modifications of the Basic PID Control Law
The expressions (1.13), (1.14) and (1.18) of a PID controller given in the
previous section are actually not adopted in practical cases because of a few
problems that can be solved with suitable modifications of the basic control
law. These are analysed in this section.
1.6.1 Problems with Derivative Action
From Expressions (1.13), (1.14) and (1.18) it appears that the controller trans-
fer function is not proper and therefore it can not be implemented in practice.
1
Actually, the term parallel PID controller is often adopted also for expression
(1.13) (see for example (Tan et al., 1999; Seborg et al., 2004)). However, here
it is preferred to use the nomenclature of (Åström and Hägglund, 1995; Ang
et al., 2005) for the sake of clarity and in order to distinguish better the three
considered forms.

1.6 Modifications of the Basic PID Control Law 9
This problem is evidently caused by the derivative action. Indeed, the high-
frequency gain of the pure derivative action is responsible for the amplification
of the measurement noise in the manipulated variable. Consider for example
a sinusoidal signal
n(t) = A sin(ωt)
which represents measurement noise in the control scheme of Figure 1.2. If
the derivative action only is considered, the control variable term due to this
measurement noise is
u(t) = AKdω cos(ωt).
It can be easily seen that the amplification effect is more evident when the
frequency of the noise is high. In practical cases, a (very) noisy control variable
signal might cause a damage of the actuator. The problems outlined above can
be solved by filtering the derivative action with (at least) a first-order low-pass
filter. The filter time constant should be selected in order to filter suitably the
noise and to avoid to influence significantly the dominant dynamics of the
PID controller.
In this context, the PID control laws (1.13), (1.14) and (1.18) are usually
modified as follows. The ideal form becomes:
Ci1a(s) = Kp
⎛
⎜
⎜
⎝1 +
1
Tis
+
Tds
Td
N
s + 1
⎞
⎟
⎟
⎠ , (1.20)
or, alternatively (Gerry and Shinskey, 2005),
Ci1b(s) = Kp
⎛
⎜
⎜
⎜
⎜
⎜
⎝
1 +
1
Tis
+
Tds
1 +
Td
N
s + 0.5

Td
N
s
2
⎞
⎟
⎟
⎟
⎟
⎟
⎠
. (1.21)
The series form becomes:
Cs(s) = K
p

1 +
1
T
i s

⎛
⎜
⎜
⎝
T
ds + 1
T
d
N
s + 1
⎞
⎟
⎟
⎠ = K
p

T
i s + 1
T
i s

⎛
⎜
⎜
⎝
T
ds + 1
T
d
N
s + 1
⎞
⎟
⎟
⎠ , (1.22)
where N generally assumes a value between 1 and 33, although in the majority
of the practical cases its setting falls between 8 and 16 (Ang et al., 2005). The
expression of the parallel form can be straightforwardly derived as well. It is
worth noting that an alternative expression for the ideal form is to filter the
overall control variable, i.e., to use the following controller:

Ci2a(s) = Kp

1 +
1
Tis
+ Tds

1
Tf s + 1
, (1.23)
or, alternatively (Åström and Hägglund, 2004),
Ci2b(s) = Kp

1 +
1
Tis
+ Tds

1
(Tf s + 1)2
. (1.24)
The block diagrams of the most adopted controllers are shown in Figures
1.6–1.8. Note that if the PI part of a series controller is in the automatic
reset configuration, then the corresponding series PID controller is reported
in Figure 1.9.
While these modifications are those that can be usually found in the literature
(see for example (Luyben, 2001a)), it has to be stressed that the filter to be
adopted is a critical issue and therefore this design aspect will be thoroughly
analysed in Chapter 2.
Another issue related to the derivative action that has to be considered is
the so-called derivative kick. In fact, when an abrupt (stepwise) change of the
set-point signal occurs, the derivative action is very large and this results in
a spike in the control variable signal, which is undesirable. A simple solution
to avoid this problem is to apply the derivative term to the process output
only instead of the control error. In this case the ideal (not filtered) derivative
action becomes:
u(t) = −Kd
dy(t)
dt
. (1.25)
It is worth noting that when the set-point signal is constant, applying the
derivative term to the control error or to the process variable is equivalent.
Thus, the load disturbance rejection performance is the same in the two cases.
Kp
T
d s
u
s
i
s
d
T
T
1
N +1
e
Fig. 1.6. Block diagram of a PID controller in ideal form

1.6 Modifications of the Basic PID Control Law 11
1
s
Ti
p
K
1
Tf s+1
u
e
T
d s
Fig. 1.7. Alternative block diagram of a PID controller in ideal form
e
Kp
T
d s+1
N i
T
1
u
s
T
d s
Fig. 1.8. Block diagram of a PID controller in series form
u
e
Kp
1
Ti
T
d s+1
N s+1
T
d s
Fig. 1.9. Block diagram of a PID controller in series form with the PI part in
automatic reset configuration
1.6.2 Set-point Weighting
A typical problem with the design of a feedback controller is to achieve at the
same time a high performance both in the set-point following and in the load
disturbance rejection performance. Roughly speaking, a fast load disturbance
rejection is achieved with a high-gain controller, which gives an oscillatory
set-point step response on the other side. This problem can be approached by
designing a two-degree-of-freedom control architecture, namely, a combined
feedforward/feedback control law.
In the context of PID control this can be achieved by weighting the set-point
signal for the proportional action, that is, to define the proportional action as
follows:
u(t) = Kp(βr(t) − y(t)), (1.26)
where the value of β is between 0 and 1.
In this way, the control scheme represented in Figure 1.10 is actually imple-
mented, where

C(s) = Kp

1 +
1
Tis
+ Tds

(1.27)
and
Csp(s) = Kp

β +
1
Tis
+ Tds

(1.28)
(the ﬁlter of the derivative action has not been considered for the sake of sim-
plicity). It appears that the load disturbance rejection task is decoupled from
the set-point following one and obviously it does not depend on the weight β.
Thus, the PID parameters can be selected to achieve a high load disturbance
rejection performance and then the set-point following performance can be
recovered by suitably selecting the value of the parameter β. An equivalent
control scheme is shown in Figure 1.11, where
F(s) =
1 + βTis + TiTds2
1 + Tis + TiTds2
. (1.29)
Here it is more apparent that the function of the set-point weight is to smooth
the (step) set-point signal in order to damp the response to a set-point change.
Note also that if β = 0 the proportional kick is avoided. Indeed, many indus-
trial controllers implement this solution (Åström and Hägglund, 1995, page
110).
The use of the set-point weighting and of other feedforward control strategies
for the improvement of performances will be analysed thoroughly in Chapters
4 and 5.
r
sp
u
Ŧ1
y
C
C P
Fig. 1.10. Two-degree-of-freedom PID control scheme
r
F
e u
P
y
C
Fig. 1.11. Equivalent two-degree-of-freedom PID control scheme

1.7 Digital Implementation 13
1.6.3 General ISA–PID Control Law
If all the modifications of the basic control law previously addressed are con-
sidered, the following general PID control law can be derived:
u(t) = Kp

βr(t) − y(t) +
1
Ti
t
0
e(τ)dτ + Td

d(γr(t) − yf (t))
dt

Td
N
dyf (t)
dt
= y(t) − yf (t)
(1.30)
where, in general, it is 0 ≤ β ≤ 1 and 0 ≤ γ ≤ 1, although the value of
γ is usually either 0 (the derivative action is entirely applied to the process
output) or 1 (the derivative action is entirely applied to the control error), as
explained in Section 1.6.1.
The previous one is usually called a PID controller in ISA form or, alterna-
tively, a beta-gamma controller. Often, if β = 1 and γ = 0 the controller is
indicated as PI–D, while if β = 0 and γ = 0 it is indicated as I–PD. The block
diagram corresponding to an ISA–PID controller is the same as in Figure 1.11,
where in this case
C(s) = Ci1a(s) = Kp
⎛
⎜
⎜
⎝1 +
1
Tis
+
Tds
Td
N
s + 1
⎞
⎟
⎟
⎠ (1.31)
and
F(s) =
1 +

βTi +
Td
N

s + TiTd

γ +
β
N

s2
1 +

Ti +
Td
N

s + TiTd

1 +
1
N

s2
. (1.32)
1.7 Digital Implementation
If a digital implementation of the PID controller is adopted, then the previ-
ously considered control laws have to be discretised. This can be done with
any of the available discretisation method (Åström and Wittenmark, 1997).
For the sake of clarity and for future reference (see Chapter 8), an example is
shown hereafter. Consider the continuous time expression of a PID controller
in ideal form:
u(t) = Kp

e(t) +
1
Ti
t
0
e(τ)dτ + Td
de(t)
dt

, (1.33)
and define a sampling time ∆t. The integral term in (1.33) can be approxi-
mated by using backward finite differences as

tk
0
e(τ)dτ =
k
i=1
e(ti)∆t, (1.34)
where e(ti) is the error of the continuous time system at the ith sampling
instant. By applying the backward finite differences also to the derivative
term it results:
de(tk)
dt
=
e(tk) − e(tk−1)
∆t
. (1.35)
Then, the discrete time control law becomes:
u(tk) = Kp

e(tk) +
∆t
Ti
k
i=1
e(ti) +
Td
∆t
(e(tk) − e(tk−1))

. (1.36)
In this way, the value of the control variable is determined directly. Alterna-
tively, the control variable at time instant tk can be calculated based on its
value at the previous time instant u(tk−1). By subtracting the expression of
u(tk−1) from that of u(tk), we obtain:
u(tk) = u(tk−1)+
Kp

1 +
∆t
Ti
+
Td
∆t

e(tk) +

−1 −
2Td
∆t

e(tk−1) +
Td
∆t
e(tk−2)

.
(1.37)
For an obvious reason, the control algorithm (1.37) is called incremental algo-
rithm or velocity algorithm, while that expressed in (1.36) is called positional
algorithm.
Expression (1.37) can be rewritten more compactly as:
u(tk) − u(tk−1) = K1e(tk) + K2e(tk−1) + K3e(tk−2), (1.38)
where
K1 = Kp

1 +
∆t
Ti
+
Td
∆t

,
K2 = −Kp

1 +
2Td
∆t

,
K3 = Kp
Td
∆t
.
(1.39)
By defining q−1
as the backward shift operator, i.e.,
q−1
u(tk) = u(tk−1), (1.40)
the discretised PID controller in velocity form can be expressed as

1.8 Choice of the Controller Type 15
C(q−1
) =
K1 + K2q−1
+ K3q−2
1 − q−1
, (1.41)
where K1, K2 and K3 can be viewed as the tuning parameters.
1.8 Choice of the Controller Type
For a given control task, it is obviously not necessary to adopt all the three
actions. Thus, the choice of the controller type is an integral part of the over-
all controller design, taking into account that the final aim is to obtain the
best cost/benefit ratio and therefore the simplest controller capable to obtain
a satisfactory performance should be preferred.
In this context it is worth analysing briefly some guidelines on how the con-
troller type (P, PI, PD, PID) has to be selected. As already mentioned, a P
controller has the disadvantage, in general, of giving a non zero steady-state
error. However, in control tasks where this is not of concern, such as for exam-
ple in surge tank level control or in inner (secondary) loops of cascade control
architectures, where the zero steady-state error is ensured by the integral ac-
tion adopted in the outer (primary) controller (see Chapter 9), a P controller
can be the best choice, as it is simple to design (indeed, if the process has a
low-order dynamics the proportional gain can be set to a high value in order
to provide a fast response and a low steady-state error). Further, if an integral
component is present in the system to be controlled (such as in mechanical
servosystems or in surge vessels where the manipulated variable is the differ-
ence between inflow and outflow) and no load disturbances are likely to occur,
then there is no need of an integral action in the controller to provide a zero
steady-state control error. In this case the control performance can be usually
improved by adding a derivative action, i.e., by adopting a PD controller. In
fact, the derivative action provides a phase lead that allows to increase the
bandwidth of the system and therefore to speed up the response to a set-point
change.
If the zero steady-state error is an essential control requirement, then the sim-
plest choice is to use a PI controller. Actually, a PI controller is capable to
provide an acceptable performance for the vast majority of the process con-
trol tasks (especially if the dominant process dynamics is of first order) and
it is indeed the most adopted controller in the industrial context. This is also
due to the problems associated with the derivative actions, namely the need
of properly filtering the measurement noise and the difficulty in selecting an
appropriate value of the derivative time constant.
In any case, the use of the derivative action, that is, of a PID controller, pro-
vides very often the potentiality of significantly improve the performance.
For example, if the process has a second-order dominant dynamics, the
zero introduced in the controller by the derivative action can be adopted
to cancel the fastest pole of the process transfer function (see, for example,

(Skogestad, 2003)). However, it is also often claimed that if the process has a
significant (apparent) dead time, then the derivative action should be discon-
nected. Actually, the usefulness of the derivative action has been the subject
of some investigation (Åström and Hägglund, 2000b). Recent contributions to
the literature have shown that the performance improvement given by the use
of the derivative action decreases as the ratio between the apparent dead time
and the effective time constant increases but it can be very beneficial if this
ratio is not too high (about two) (Åström and Hägglund, 2004; Kristiansson
and Lennartson, 2006).
Finally, it is worth noting that for processes affected by a large dead time
(with respect to the dominant time constant) the use of a dead-time compen-
sator controller, such as a Smith predictor based scheme (Palmor, 1996) or
the so-called PID-deadtime controller (where the time-delay compensation is
added to the integral feedback loop of the PID controller in automatic reset
configuration) (Shinskey, 1994), can be essential in obtaining a satisfactory
control performance (Ingimundarson and Hägglund, 2002).
1.9 The Tuning Issue
The selection of the PID parameters, i.e., the tuning of the PID controllers,
is obviously the crucial issue in the overall controller design. This operation
should be performed in accordance to the control specifications. Usually, as
already mentioned, they are related either to the set-point following or to the
load disturbance rejection task, but in some cases both of them are of primary
importance. The control effort is also generally of main concern as it is related
to the final cost of the product and to the wear and life-span of the actuator.
It should be therefore kept at a minimum level. Further the robustness issue
has to be taken into account.
A major advantage of the PID controller is that its parameters have a clear
physical meaning. Indeed, increasing the proportional gain leads to an increas-
ing of the bandwidth of the system and therefore a faster but more oscillatory
response should be expected. Conversely, increasing the integral time constant
(i.e., decreasing the effect of the integral action) leads to a slower response
but to a more stable system. Finally, increasing the derivative time constant
gives a damping effect, although much care should be taken in avoiding to
increase it too much as an opposite effect occurs in this case and an unstable
system could eventually result.
The problem associated with tuning of the derivative action can be better
understood with the following analysis (Ang et al., 2005). Suppose that the
process to be controlled is described by a general FOPDT transfer function
P(s) =
K
Ts + 1
e−Ls
. (1.42)
Suppose also that an ideal PD controller is adopted, i.e.,

1.9 The Tuning Issue 17
C(s) = Kp (1 + Tds) . (1.43)
The gain of the open-loop transfer function is determined as
|C(jω)P(jω)| = KKp

1 + T 2
d ω2
1 + T 2ω2
≥ KKp min

1,
Td
T

, (1.44)
where the inequality is justified by the fact that

(1 + T 2
d ω2)/(1 + T 2ω2) is
monotonic with ω. It can be easily determined that if Td ≤ T and KKp ≥ 1 or
if Td ≥ T and Td ≥ T/(KKp), then the crossover frequency ωc is at infinity,
i.e., the magnitude of the open-loop transfer function is not less than 0 dB.
As a consequence, since the phase decreases when the frequency increases be-
cause of the time delay, the closed-loop system will be unstable.
To illustrate this fact, consider an example where the process (1.42) with
K = 2, T = 1 and L = 0.2 is controlled by a PID controller in series form
(1.14) with Kp = 1 and Ti = 1. Then, if it is selected Td = 0.01 the gain
margin results to be 12.3 dB and the phase margin results to be 68.2 deg.
Increasing the derivative time constant to Td = 0.05 yields an increase of the
gain margin and of the phase margin to 13.2 dB and 72.7 deg, respectively.
Thus, in this case, increasing the derivative action implies that a more slug-
gish response and a more robust system is obtained. However, if the derivative
time constant is raised to 0.5 the system stability is lost.
The aforementioned concepts allow the operator to manually tune the con-
troller in a relatively easy way, although the trial-and-error operation can be
very time consuming and the final result can be far from the optimum and
heavily depends on the operator’s skill.
In order to help the operator in tuning the controller correctly and with a
small effort, starting with the well-known Ziegler–Nichols formulae (Ziegler
and Nichols, 1942), a large number of tuning rules have been devised in the
last sixty years (Åström and Hägglund, 1995; O’Dwyer, 2006). They try to ad-
dress the possible different control requirements and they are generally based
on a simple model of the plant. They have been derived empirically or analyt-
ically. The operator has therefore to obtain a suitable model of the plant and
to select the most convenient tuning rule with respect to the given control
requirements. It has to be noted that the obtained PID parameters (that is,
the selected tuning rule) have to be appropriate for the adopted controller
structure (ideal, series, etc.), otherwise they have to be converted (see Ex-
pressions (1.15), (1.17) and (1.19)).
Finally, it is worth highlighting that many software packages have been devel-
oped and are available on the market which assist practitioners in designing
the overall controller, namely, to identify an accurate process model based on
available data, to tune the controller according to the given requirements, to
perform a what-if analysis and so on. A review of them can be found in (Ang
et al., 2005).

1.10 Automatic Tuning
The functionality of automatically identifying the process model and tuning
the controller based on that model is called automatic tuning (or, simply,
auto-tuning). In particular, an identification experiment is performed after
an explicit request of the operator and the values of the PID parameters are
updated at the end of it (for this reason the overall procedure is also called
one-shot automatic tuning or tuning-on-demand). The design of an automatic
tuning procedure involves many critical issues, such as the choice of the identi-
fication procedure (usually based on an open-loop step response or on a relay
feedback experiment (Yu, 1999)), of the a priori selected (parametric or non
parametric) process model and of the tuning rule. An excellent presentation
of this topic can be found in (Leva et al., 2001).
The one-shot automatic tuning functionality is available in practically all the
single-station controllers available on the market. Advanced (more expensive)
control units might provide a self-tuning functionality, where the identification
procedure is continuously performed during routine process operation in or-
der to track possible changes of the system dynamics and the PID parameters
values are modified adaptively. In this case all the issues related to adaptive
control have to be taken into account (Åström and Wittenmark, 1995).
1.11 Conclusions and References
In this chapter the fundamental concepts of PID controllers have been in-
troduced. The main practical problems connected with their use have been
outlined and the most adopted controller structures have been presented. In
the following chapters different aspects that have been considered will be fur-
ther developed.
Basic concepts of PID controllers can be found in almost every book of process
control (see for example (Shinskey, 1994; Ogunnaike and Ray, 1994; Luyben
and Luyben, 1997; Marlin, 2000; Corripio, 2001; Bequette, 2003; Seborg et
al., 2004; Corriou, 2004; Ellis, 2004; Altmann, 2005)). For a detailed treat-
ment, see (Åström and Hägglund, 1995) and (Åström and Hägglund, 2006)
where all the methodological as well as technological aspects are covered. An
excellent collection of tuning rules can be found in (O’Dwyer, 2006). Recent
advances are presented in (Tan et al., 1999).

2
Derivative Filter Design
2.1 Introduction
It is a matter of fact that the derivative action is seldom adopted in practical
cases (actually, 80% of the employed PID controllers have the derivative part
switched-off (Ang et al., 2005)), although it has been shown that it is pos-
sible to provide a significant improvement of the control performance (note
that this improvement becomes less important as the ratio between the ap-
parent time delay and the effective time constant increases (Kristiansson and
Lennartson, 2006; Åström and Hägglund, 2004)). This is due to a number of
reasons, one of them being certainly that it is the most difficult to tune, as
explained in Section 1.9. Indeed, the stability regions for PID controllers are
more complex than those for PI controllers and therefore the tuning of a PID
controller is more difficult (Åström and Hägglund, 2000b). Also, the inherent
amplification of the measurement noise represents a significant technological
problem, because, if not properly filtered, it might cause a damage to the
actuator.
In this chapter it is shown that part of the problem is due also to the structure
of the PID controller (see (1.20)–(1.24)), in particular if a PID controller in
ideal form with a fixed derivative filter parameter N is adopted.
2.2 The Significance of the Filter in PID Design
It is interesting to evaluate how the presence of a filter of the derivative action
changes the location of the zeros in the PID controller. It is trivial to derive
that if the PID controller is in series form (1.22) or in ideal form (1.23)–(1.24)
with the filter applied to the control variable, then the addition of the filter
does not alter the position of the zeros of the controller. Hence, the interesting
case to analyse is that related to the PID controller in ideal form (1.20) (or
(1.31)).

20 2 Derivative Filter Design
If the derivative filter is not applied, the zeros of the PID controller (1.13) are
the solution of the equation
TiTds2
+ Tis + 1 = 0. (2.1)
They can be easily derived as:
z1,2 =
1
2
− Ti ±

T 2
i − 4TiTd
TiTd
. (2.2)
If the derivative filter is applied, the zeros of the controller are the solution of
the equation
TiTd

1 +
1
N

s2
+

Ti +
Td
N

s + 1 = 0. (2.3)
It results:
z̄1,2 =
1
2
− TiN − Td ±

(TiN − Td)2 − 4TiTdN2
TiTd(1 + N)
. (2.4)
A sensitivity analysis can be performed in order to evaluate the influence
of the parameter N, i.e., of the filter, on the location of zeros (Leva and
Colombo, 2001). The relative perturbation of the ith zero can be calculated
as:
er,i :=
|z̄i − zi|
|zi|
. (2.5)
To evaluate it quantitatively with an example, Ti is fixed to be 100 and the
value of er,i has been determined by varying Td from 1 to 100, i.e., by varying
the ratio Td/Ti from 0.01 to 1. Results related to the case N = 5 and N = 20
are shown in Figures 2.1 and 2.2. It can be seen that the relative error can be
greater than 30% and a high value appears when Ti = 4Td (i.e., when the two
zeros are real and coincident), which is a very relevant case, as this relation
is adopted in many tuning rules such as the Ziegler–Nichols one .
This analysis is coherent with the results presented in (Kristiansson and
Lennartson, 2006), where the performance achieved by a PI(D) controller is
evaluated by considering both its capability in the load disturbance rejection
task and the corresponding control activity. It is shown that, in general, the
proper use of the derivative action allows to significantly increase the load dis-
turbance rejection performance with a modest increase of the control effort.
However, if Ti is fixed to be 4Td and N to be 10, then a (slight) increase of
the load disturbance rejection performance can be made only at the expense
of a much increased control effort (with respect to an optimal PI controller).
All these results confirm that the presence of the derivative filter in a PID
controller in ideal form cannot be neglected in general in the controller de-
sign phase (Leva and Colombo, 2001). Other practical issues concerning the
presence of the derivative filter are addressed in the following sections.

2.2 The Significance of the Filter in PID Design 21
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
5
10
15
20
25
30
Td/ Ti
relative
error
N=5
N=20
Fig. 2.1. Relative error of the controller zero z1 due to the presence of the derivative
filter in an ideal form PID controller
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
5
10
15
20
25
30
35
Td/ Ti
relative
error
N=5
N=20
Fig. 2.2. Relative error of the controller zero z2 due to the presence of the derivative
filter in an ideal form PID controller

2.3 Ideal vs. Series Form
From another point of view with respect to the approach made in Section
2.2, the PID controllers in the ideal and or in the series form are compared,
according to the analysis and the examples presented in (Isaksson and Graebe,
2002).
In particular, the role of the controller structure in the classical lead-lag design
or in the pole-placement design is outlined by means of the following examples.
Suppose that the control of a tank level with a ﬁrst-order actuator has to be
performed. The process is described by the following transfer function
P(s) =
Y (s)
U(s)
=
K
s(τs + 1)
, K = 0.1, τ = 2, (2.6)
where the input u(t) is the valve position set-point and the output y(t) is
the tank level. A classical controller design leads to the following controller
transfer function, in the context of the typical unitary-feedback control scheme
(see Figure 1.2 with F(s) = 1):
C(s) = 1.06
(3s + 1)(8s + 1)
3s(2s + 1)
. (2.7)
This assures a crossover frequency of 0.3 rad/s and a phase margin of slightly
more than 45 deg. The Bode diagram of the open-loop transfer function
C(s)P(s) is shown in Figure 2.3. The designed controller corresponds to a
PID controller in series form (1.22) where K
p = 1.06, T
i = 3, T
d = 8, and
N
= 4 or, equivalently, K
p = 2.83, T
i = 8, T
d = 3, and N
= 1.5. These con-
trollers can be converted in a PID controller in ideal form (1.20) by applying
the following formulae:
Ti = T
i +

1 −
1
N

Kp = K
p
Ti
T
i
Td = T
d

T
i
Ti
−
1
N

N =
TdN
T
d
(2.8)
In both cases, it follows that Kp = 3.18, Ti = 9, Td = 0.67 and N = 1/3. It
can be seen that N and N
are not within the typical range of 5÷20 and they
do have a signiﬁcant role in the overall controller design procedure. Indeed,
setting N = 1/3 in the ideal PID controller means that the additional pole

2.3 Ideal vs. Series Form 23
introduced by the derivative filter is still at a higher frequency than the two
controller zeros (the two zeros are at s = −0.121 and s = −1.026, while the
introduced pole is at s = −4.48). The fact that the derivative part provides a
phase lead is actually evident in the series controller, since N
is grater than
one.
Similar considerations apply if a pole-placement technique is adopted. Suppose
that an ideal PID controller (1.20) is applied to the tank level process (2.6).
The following characteristic equation results:
τ
Td
N
s4
+

τ +
Td
N

s3
+

1 + KpKTd

1 +
1
N

s2
+KKp

1 +
Td
NTi

s +
KKp
Ti
= 0
(2.9)
Assume now that the location of the desired closed-loop poles is such as there
are two complex poles at a distance λ from the origin and with the same
complex and real part (i.e., s = (−1 ± j)/(λ
√
2)) so that they have a corre-
sponding damping factor of
√
2/2. Then, the two remaining poles are placed
in the same position on the real axis at a distance of −1/λ from the origin.
In this way the desired characteristic equation is

s2
+
√
2
λ
s +
1
λ2

s +
1
λ
2
=
s4
+
2 +
√
2
λ
s3
+
2 + 2
√
2
λ2
s2
+
2 +
√
2
λ3
s +
1
λ4
= 0
(2.10)
Comparing the polynomial coefficients, the following PID parameters can be
determined by fixing λ = 3:
Kp = 3.36, Ti = 8.68, Td = 0.463, N = 0.296. (2.11)
It turns out that the value of N is significantly outside the typical range also
in this case, but this corresponds to a series controller with phase lead (i.e.,
with N
1). Actually, the parameters of the corresponding PID controller
in series form are:
K
p = 3.12, T
i = 8.08, T
d = 2.18, N
= 1.39. (2.12)
and the resulting zeros of the controller are s = −0.12 and s = −0.46 while
the poles are at s = 0 and s = −0.64. It is worth stressing that the choice of
λ = 3 results in a control system that has, as in the previous case, a crossover
frequency of about 0.3 rad/s and a phase margin of about 45 deg. The Bode
diagram of the open-loop system C(s)P(s) is presented in Figure 2.4. The
similarity with the previous one is evident. In order to verify the improve-

10
Ŧ3
10
Ŧ2
10
Ŧ1
10
0
10
1
Ŧ100
Ŧ50
0
50
100
magnitude
[dB]
frequency [rad/s]
10
Ŧ3
10
Ŧ2
10
Ŧ1
10
0
10
1
Ŧ180
Ŧ170
Ŧ160
Ŧ150
Ŧ140
Ŧ130
frequency [rad/s]
phase
[deg]
Fig. 2.3. Bode plot of the open-loop transfer function C(s)P(s) resulting from the
lead-lag design (Process (2.6))
10
Ŧ3
10
Ŧ2
10
Ŧ1
10
0
10
1
Ŧ100
Ŧ50
0
50
100
frequency [rad/s]
magnitude
[dB]
10
Ŧ3
10
Ŧ2
10
Ŧ1
10
0
10
1
Ŧ180
Ŧ170
Ŧ160
Ŧ150
Ŧ140
Ŧ130
frequency [rad/s]
phase
[deg]
Fig. 2.4. Bode plot of the open-loop transfer function C(s)P(s) resulting from the
pole-placement design (Process (2.6))

2.3 Ideal vs. Series Form 25
ment in the performance given by the derivative action, the pole-placement
approach is applied also with a PI controller (1.8). The characteristic equation
is in this case:
τs3
+ s2
+ KKps +
KKp
Ti
= 0. (2.13)
It has to be noted that there are three poles to be placed but only two design
parameters, while in the previous case there were four conditions for four
parameters, because of the presence of the derivative filter parameter N (N
).
Thus, a dominant pole design strategy is adopted, namely, only the location
of the two dominant poles is selected, while the location of the third pole is
checked at the end. In this context, the two dominant poles are chosen as
in the previous case at s = (−1 ± j)/(λ
√
2). Denoting as δ the third time
constant, the desired characteristic equation is:

s2
+
√
2
λ
s +
1
λ2

s +
1
δ

= s3
+
√
2
λ
+
1
δ

s2
+

1
λ2
+
√
2
λδ

s +
1
λ2δ
= 0.
(2.14)
By comparing the coefficients of Equations (2.13) and (2.14) it follows that:
√
2
λ
+
1
δ
=
1
τ
(2.15)
KKp
τ
=
1
λ2
+
√
2
δλ
(2.16)
KKp
τTi
=
1
λ2δ
(2.17)
From Equation (2.15) it turns out that the smaller λ is the higher δ is and
therefore the system cannot be made arbitrarily fast. Indeed, it is δ 0 (i.e.,
the system is asimptotically stable) if λ
√
2τ and therefore there is a clear
limitation in the nominal performance. The value of λ = 3.5 (that implies
δ = 10.4) is eventually selected in order to achieve the best performance
(Isaksson and Graebe, 2002). The resulting PI parameters are Kp = 2.41 and
Ti = 15.4.
Set-point step responses and load disturbance responses obtained by the two
designed PID controllers and the PI controller are shown in Figures 2.5 and
2.6. It appears that the two PID controllers give very similar responses and
they outperform the PI controller in the load disturbance rejection task. Thus,
the benefits of the derivative action appears in this case.
Summarising, from the examples presented, it can be deduced that, for a PID
controller in series form, it can be sensible to choose a fixed derivative factor

0 10 20 30 40 50 60
0
0.2
0.4
0.6
0.8
1
1.2
1.4
time
process
variable
0 10 20 30 40 50 60
Ŧ5
0
5
10
15
time
control
variable
Fig. 2.5. Set-point step response for the designed controllers (Process (2.6)). Solid
line: phase-lag PID; dashed line: pole-placement PID; dotted line: PI.
0 10 20 30 40 50 60
Ŧ0.1
0
0.1
0.2
0.3
0.4
time
process
variable
0 10 20 30 40 50 60
Ŧ1.4
Ŧ1.2
Ŧ1
Ŧ0.8
Ŧ0.6
Ŧ0.4
Ŧ0.2
0
time
control
variable
Fig. 2.6. Load disturbance step response for the designed controllers (Process (2.6)).
Solid line: phase-lag PID; dashed line: pole-placement PID; dotted line: PI.

2.4 Simulation Results 27
N
1, as a controller with a phase lead might result (note that the maximum
phase lead depends only on N
and it is achieved when N
= 10). Conversely,
for a PID controller in ideal form Ci1a(s) (1.20), the necessary phase lead
might be achieved with values of N also less than one and therefore fixing it
to a constant value greater than one (in the range from 8 to 16 as is done in
the vast majority of the industrial implementations (Ang et al., 2005)) can
represent an unnecessary limitation of the performance.
It is worth stressing that if the alternative output-filtered form of the ideal
controller Ci2a(s) (1.23) (or Ci2b(s) (1.24)) is adopted, the reasoning related
to the series form has to be applied, since the filter is in series with the overall
controller transfer function. Thus, if this structure is adopted, the choice of
the value of the filter time constant Tf is more intuitive.
In any case, it appears from this analysis that the tuning of a PID controller
should involve four parameters, since the derivative filter plays a major role
in the overall control system performance.
2.4 Simulation Results
In order to understand better the previously described problems associated
with the design of the derivative filter, some simulation results are given.
Consider the process
P(s) =
1
s + 1
e−0.2s
. (2.18)
Then, consider a PID controller whose parameters are selected according to
the Ziegler–Nichols rules based on the frequency response (note that the ulti-
mate gain Ku is equal to 8.5 and the ultimate period is Pu = 1.34). Both the
ideal form (1.20) and the series form (1.22) are evaluated. The controller pa-
rameters are reported in Table 2.1, where the conversion between the ideal and
series structure has been performed by means of formulae (1.17), i.e., without
taking into account the derivative filter. Note that Ti = 4Td, that is, the two
controller zeros are in the same position for the series controller and for the
ideal one if the derivative filter is not considered. The derivative filter time
Table 2.1. Parameters for the ideal and series PID controller for the examples of
Section 2.4
Ziegler–Nichols Kappa–Tau
Kp 5.00 5.74
Ti 0.672 0.66
Td 0.168 0.15
K
p 2.50 3.75
T
i 0.336 0.43
T
d 0.336 0.23

0 1 2 3 4 5 6 7 8 9 10
Ŧ0.05
0
0.05
0.1
0.15
0.2
time
process
variable
0 1 2 3 4 5 6 7 8 9 10
Ŧ2
Ŧ1.5
Ŧ1
Ŧ0.5
0
time
control
variable
Fig. 2.7. Load disturbance step response for the PID controllers with Ziegler–
Nichols parameters (Process (2.18)). Solid line: ideal form with derivative filter;
dashed line: series form with derivative filter.
constant has been selected as N = N
= 10. The control system responses
when a load disturbance unitary step is applied in both cases are plotted in
Figure 2.7. The significantly different behaviour of the control system ap-
pears. This is due to the fact that the actual zeros of the ideal controller are
in s = −2.77±j0.60, while they should be the same as those of the series con-
troller that are both in s = −2.98. Note that the phase margin of the resulting
ideal controller is 44.2 deg (the crossover frequency is ωc = 8.57 rad/s), while
that of the series one is 55.1 deg (the crossover frequency is ωc = 6.19 rad/s).
The same reasoning is applied by considering the Kappa–Tau tuning rules pro-
posed in (Åström and Hägglund, 1995). The parameters obtained are reported
in Table 2.1, while the load disturbance unitary step responses are plotted in
Figure 2.8. Also in this case the two responses are significantly different. The
series controller assures a phase margin of 41.7 deg (ωc = 7.83 rad/s), while
the ideal one, because of the presence of the derivative filter, provides a phase
margin of just 15.9 deg (ωc = 11.2 rad/s). These results confirm the issues
discussed in the previous sections that imply the fact that the design of the
derivative filter should be considered carefully. The filtering of the measure-
ment noise is also considered hereafter. Consider the same process (2.18) with
the following controllers:
• a PI controller with Kp = 4 and Ti = 1;
• a derivative-filtered PID controller in ideal form (1.20) with Kp = 4, Ti =
1, Td = 0.1 and N = 10;

• a derivative-filtered PID controller in ideal form (1.20), where the deriva-
tive filter is a second-order system, with again Kp = 4, Ti = 1, Td = 0.1
and N = 10;
• an output-filtered PID controller in ideal form (1.23) with Kp = 4, Ti = 1,
Td = 0.1 and Tf = 0.1;
• an output-filtered PID controller in ideal form (1.24), where the filter is a
second-order system with Kp = 4, Ti = 1, Td = 0.1 and Tf = 0.1;
• a derivative-filtered PID controller in series form with K
p = 3.55, T
i =
0.89, T
d = 0.11, N
= 10 (note that these parameters have been found by
converting the parameters of the controllers in ideal form).
In all the cases a measurement white noise whose amplitude is in the range [−5·
10−3
, 5·10−3
] is applied to the control system. The resulting process variables
and the control variables are plotted in Figures 2.9–2.14. It can be seen that
the control variable is less noisy for the output-filtered PID structures. This
is somewhat obvious, since the proportional action is also responsible for the
amplification of the measurement noise and therefore the filter applied to the
whole control variable is more effective than that applied to the derivative
action only. If a second-order filter is adopted, the reduction of the noise
effect is more evident. However, if the value of Tf in an output-filtered PID
controller in ideal form is such that the additional poles are not at a much
higher frequency with respect to the zeros (for a more effective filtering), then
the presence of the second-order filter might influence the control performance.
0 2 4 6 8 10 12 14 16 18 20
Ŧ0.1
Ŧ0.05
0
0.05
0.1
0.15
0.2
time
process
variable
0 2 4 6 8 10 12 14 16 18 20
Ŧ2
Ŧ1.5
Ŧ1
Ŧ0.5
0
time
control
variable
Fig. 2.8. Load disturbance step response for the PID controllers with Kappa–Tau
parameters (Process (2.18)). Solid line: ideal form with derivative filter; dashed line:
series form with derivative filter.

0 1 2 3 4 5 6 7 8 9 10
Ŧ0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
time
process
variable
0 1 2 3 4 5 6 7 8 9 10
Ŧ1.5
Ŧ1
Ŧ0.5
0
time
control
variable
Fig. 2.9. Load disturbance step response (with noise measurement) for the PI
controller
0 1 2 3 4 5 6 7 8 9 10
Ŧ0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
time
process
variable
0 1 2 3 4 5 6 7 8 9 10
Ŧ1.5
Ŧ1
Ŧ0.5
0
time
control
variable
Fig. 2.10. Load disturbance step response (with noise measurement) for the ideal
PID controller with a ﬁrst-order derivative ﬁlter

0 1 2 3 4 5 6 7 8 9 10
Ŧ0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
time
process
variable
0 1 2 3 4 5 6 7 8 9 10
Ŧ1.5
Ŧ1
Ŧ0.5
0
time
control
variable
PID controller with a second-order derivative filter
0 1 2 3 4 5 6 7 8 9 10
Ŧ0.05
0
0.05
0.1
0.15
0.2
0.25
time
process
variable
0 1 2 3 4 5 6 7 8 9 10
Ŧ1.5
Ŧ1
Ŧ0.5
0
time
control
variable
PID controller with a first-order output filter

0 1 2 3 4 5 6 7 8 9 10
0
0.1
0.2
0.3
0.4
time
process
variable
0 1 2 3 4 5 6 7 8 9 10
Ŧ1.5
Ŧ1
Ŧ0.5
0
time
control
variable
PID controller with a second-order output filter
0 1 2 3 4 5 6 7 8 9 10
Ŧ0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
time
process
variable
0 1 2 3 4 5 6 7 8 9 10
Ŧ1.5
Ŧ1
Ŧ0.5
0
time
control
variable
Fig. 2.14. Load disturbance step response (with noise measurement) for the series
PID controller with a first-order derivative filter

2.6 Conclusions 33
2.5 Four-parameters Tuning
In the previous sections it has been underlined that problems associated with
the derivative action that prevent a wide use of it are not just due to the noise.
Indeed, tuning rules for a PID controller should involve four parameters, as
also stressed in (Luyben, 2001a).
The most well-known design method that provides the values of all the four
parameters of an ideal output-filtered PID controller is surely that based on
the Internal Model Control (IMC) approach (Rivera et al., 1986; Morari and
Zafiriou, 1989). It can be remarked that a user-chosen parameter allows the
handling of the trade-off between aggressiveness and robustness. The effective-
ness of this tuning methodology has been shown in the literature; however, it
has to be borne in mind that, being based on a pole-zero cancellation, it is not
suitable for lag-dominant processes for which a very sluggish load disturbance
response occurs (Shinskey, 1994; Shinskey, 1996). In this context an effective
modification has been proposed in (Skogestad, 2003).
Recently, tuning rules that comprises also the derivative filter has been pro-
posed in (Åström and Hägglund, 2004). They are based on the maximisation
of the integral gain (so that the integrated error when a load disturbance oc-
curs is minimised), subject to a robustness constraint. It is also stressed that
the appropriate value of the ratio between the integral time constant and the
derivative time constant should vary depending on the process dynamics (in
particular, depending on the relative dead time of the process) and in most
cases is less than four.
Similar conclusions are drawn in (Kristiansson and Lennartson, 2006). There,
four-parameters tuning rules are proposed which take into account the trade-
off between load disturbance rejection performance (in terms of integrated
absolute error) and control effort, with a constraint on the generalised maxi-
mum sensitivity, which is a measure of the robustness of the control system.
It is shown that the benefits of the derivative action can be severely limited if
the ratio between the integral time constant and the derivative time constant
is fixed to four and if the derivative filter factor is fixed in a PID controller in
ideal form Ci1a(s) (1.20) (or Ci1b(s) (1.21)).
For this PID controller, it is suggested to set Ti/Td = 2.5. Further, it is shown
that considering the derivative filter time constant as a true tuning parameter
allows a significant improvement of the overall performance.
2.6 Conclusions
In this chapter the design of the derivative filter has been discussed. Although
the analysis provided and the examples presented are certainly not exhaustive,
they are sufficient to show that the choice of the controller structure and of
the derivative filter factor is indeed a critical issue and the PID controller
should be considered as a four-parameters controller. In fact, the derivative

action is a key factor in improving the control system performance and the
reason for being rarely adopted in practice is not only the amplification of the
measurement noise.
In particular, it has been shown that predefining the derivative filter factor in
an ideal form controller Ci1a(s) (1.20) (or Ci1b(s) (1.21)) might severely limit
the performance. If a series controller Cs(s) (1.22) is adopted, then the filter
does not influence the location of the controller zeros. However, in this case
the two zeros have to be real and this factor might limit the performance as
well. Thus, the most convenient choice appears to be the use of an output-
filtered ideal form PID controller Ci2a(s) (1.23) (or Ci2b(s) (1.24)) since this
is the most general expression and the drawbacks of the other two forms are
avoided. Further, effective tuning rules for the selection of the four parameters
Kp, Ti, Td, and Tf are available in this case.

3
Anti-windup Strategies
3.1 Introduction
One of the most well-known possible source of degradation of performance is
surely the so-called integrator windup phenomenon, which occurs when the
controller output saturates (thus, this problem is of particular concern at the
process start-up).
Strategies for limiting this effect are illustrated and compared in this chapter.
3.2 Integrator Windup
The integrator windup effect is explained in this section. When a set-point
change is applied, the control variable might attain the actuator limit during
the transient response. In this case the system operates as in the open-loop
case, since the actuator is at its maximum (or minimum) limit, independently
of the process output value. The control error decreases more slowly as in
the ideal case (where there is no saturation limits) and therefore the integral
term becomes large (it winds up). Thus, even when the value of the process
variable attains that of the reference signal, the controller still saturates due
to the integral term and this generally leads to large overshoots and settling
times.
The situation is illustrated in the following example. Consider the control
scheme depicted in Figure 3.1 which is similar to that of Figure 1.2 but in
this case the controller output u differs in general from the process input u
because of the presence of an actuator saturation with a upper limit umax and
an lower limit umin. In this context the process
P(s) =
1
10s + 1
e−4s
(3.1)
is controlled by an ideal PID controller (the derivative filter is not adopted for
simplicity) with Kp = 3, Ti = 8 and Td = 2 (note that these are the param-

36 3 Anti-windup Strategies
y
e C P
u
umax
umin
r u’
Fig. 3.1. General control scheme with saturation
eters obtained by employing the Ziegler–Nichols tuning rules). The actuator
saturation limits are umin = 0 and umax = 1.5. The set-point unitary step
response (starting from null initial conditions) is plotted in Figure 3.2. It can
be seen that at time t = 15 the process output attains the set-point value
but, despite this, the process input still remains (for quite a long time) at the
maximum level because of the high value of the integral term. This causes a
signiﬁcant overshoot which is recovered after a long time, that is, when the
integral term decrement is suﬃcient for the control variable to be lower than
the saturation limit.
From this example it is clear that the nonlinear dynamics of the actuator can
be detrimental for the performance and has therefore to be somehow taken
into account in the design of the PID controller.
0 5 10 15 20 25 30 35 40 45 50 55 60
60
0
0.5
1
1.5
2
2.5
3
3.5
time
Fig. 3.2. Set-point step response illustrative of the integrator windup phenomenon.
Solid line: process output; dashed line: process input; dotted line: integral term.

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form of a horseshoe. There are three stories of cells, and each cell
has a window opening upon the prison yard, while the doors of the
cell swing out toward a large court within the circle of the
horseshoe, and a covered veranda traverses the entire length of the
cellhouse. The cots are not near the floor, but about on a line with
the lower sash of the cell-window, some four or five feet from the
floor, insuring to bedding, cell and inmate the greatest possible
modicum of sunshine and air.
In the prison of the future each man will be paid a certain sum for
the performance of his work, whether his task be remunerative or
what is termed state work. From this wage he will pay for his food,
clothing and such other necessities or luxuries as he may obtain
from the inmates’ co-operative store. He will thus be accorded
greater latitude in the selection of the aforesaid raiment and food.
Hence even by these humble means, the prisoner’s power of
initiative will be somewhat retained against the day when he shall
again fare forth to take his place among the world’s free men.
In this prison of the coming day discipline will be largely maintained,
not by fear of force, but rather by the self-interest and personal
pride of the men confined. Punishment will more and more take the
form of deprivation of privileges, which latter will be greatly
increased because the better spirit and attitude of the men will be
such as to warrant the greatest possible privileges.
Wardens, under-officials and guards will be recruited from individuals
who have a positive social vision, and who will look upon their
position not as a “job,” but as an opportunity for service to humanity.
Already the day has dawned when men are being placed at the head
of these institutions, not because they are politicians with a “pull,”
but rather because they are capable business men and broad-
minded humanitarians with a heart. Men are to arise who will feel as
much “called” to labor among the prison “shut-ins” as do now those
who are set aside to serve as ministers of charity or uplift workers.
These changes, and even greater ones, will be strongly manifest in
the prison of the future, for the day will yet dawn when bastilles will

be no more in demand among the sons of men.

Are your neighbors very bad?
Pass a Law!
Do they smoke? Do they chew?
Are they always bothering you?
Don’t they do as you would do?
Pass a Law!
Are your wages awful low?
Pass a Law!
Are your prices much too high?
Do the wife and babies cry
’Cause the turkeys all roost high?
Pass a Law!
When M. D. finds new diseases,
Pass a Law!
Got the mumps or enfermisis?
Measles, croup or “expertesis?”
Lest we all fly to pieces
Pass a Law!
Are the lights a-burning red?
Pass a Law!
Paint ’em green, or paint ’em white!
Close up all them places tight!
My! Our town is such a sight!
Pass a Law!
No matter what the trouble,
Pass a Law!
Goodness sakes! But ain’t it awful?
My what are we going to do?
Almost anything ain’t lawful,
And the judges human, too!
Pass a Law!

W. L. Wells.
(From The Index, Wash. State Ref.)

BOOK REVIEWS.
By Philip Klein
Assistant Secretary Prison Association of New York.
The Walled City.—Edward Huntington Williams, M. D., New York,
1913, Frank Wagnalls Company. Pp. 263. Price $1.00.
The general public looks upon a convict with a certain amount of
fear. The word criminal is awe-inspiring. But the idea of the insane
criminal is more than that; it is replete with the vague terror of the
weird and unknown. People have in recent years come to consider
the criminal with a little better understanding; but the “insane
criminal” has retained its full quota of terror. Perhaps there was good
reason for that. The older ways of handling both the insane and the
criminal were very well calculated to bring forth the worst there was
in them. But no one could probably read the “Walled City,” without
experiencing a complete change of attitude towards the inmates of
institutions for the criminal insane. They are primarily men, these
unfortunates with hopes and plans, with differences in personality,
education, tastes, relations, in all things that make for the
differences among man and man in the normal outside life. And yet,
there is a “kink” in every man; an innocent kink generally, yet a
“kink” to be reckoned with. It makes things interesting, yet delicate
and difficult to handle. “Every man in his kink” we might paraphrase
Ben Jonson.
One gets from the book a feeling almost of old association. It is all
told in a pleasant, almost anecdotal form. The reader feels himself
introduced to citizen after citizen of the walled city and passes
through the book as if in a series of personal conversations with its
inmates. The author’s sympathy and understanding for his words
speaks from every line. And yet when we close the book, we are

surprised at how much we have learned. We have been given
scientific, correct, technical information without knowing it; the book
had done what it was evidently meant to do.
Hell in Nebraska.—Walter Wilson, Lincoln, Nebraska, 1913. The
Bankers Publishing Company. Pp. 372. Price $1.00.
If individuality in a man means the possession of decided and highly
developed qualities, both good and evil, and if books also may be
said to have individualities on the same basis, then the present book
has a valid claim to the distinction of possessing a goodly amount of
individuality. From the title,—and from the illustrations on both
covers,—one would be justified in expecting a horrible revelation of
fiendish cruelties practiced in the Nebraska Penitentiary. But it is
simply another indication of the “yellow journal” style that pervades
the whole book. In fact, were it not for the thorough knowledge of
conditions, evidenced throughout, one might very easily take the
volume for a reporter’s paraphrase of a few selected annual reports
of the penitentiary. It is full of inside personal information, of interest
to nobody but the friends, relatives and enemies of the persons
concerned. But there is a good deal of real good common sense and
practical penology, that comes from a sympathetic yet rational
observation, and from continued activity in the field. If the language
is too strong at spots, and the emotions unrestricted, it may well be
excused as being the result of righteous indignation, coupled with a
sense for journalism and strong feeling for friend and foe—and also
an invincible belief in one’s own righteousness. Incidentally, however,
the book gives really valuable information of the conditions in the
Nebraska Penitentiary.

Measures of Social Defence Against the Recidivist.—This was one of
the three questions discussed by the International Union of Criminal
Law at its congress in Copenhagen in August, 1913. A masterly
report on the subject was submitted by Prof. Nabokoff, and after a
spirited discussion by many of the leading authorities of Europe on
criminal law, the following resolutions were adopted by the
congress:
1. That system of procedure which combines the requirements of an
objective scale of proof of recidivism with subjective judgment of the
particular case in question and thereupon adjudges the said criminal
a habitual recidivist, dangerous to the social order, should be
recognized as the most rational.
2. The exclusion of the political criminal seeming inevitableness, they
made the acsures of social security, applicable to habitual recidivists,
are directed is a just and necessary proviso.
3. The minimum term to be pronounced against such recidivist at
the time of his trial shall be at least as great as the term to which he
would be sentenced if he were not adjudged a habitual recidivist;
but it may be greater by not more than two years.
A special commission shall, at the expiration of such minimum,
decide whether such prisoner shall be liberated or further detained.
In the latter case the prisoner shall have the right to have his case
reconsidered at intervals of two years. (It is understood that the
judge sentences such recidivist to an indefinite period of which he
fixes the minimum, but not the maximum).
4. The Congress is not agreed as to whether the period of preventive
detention pronounced against the recidivist shall follow the period of
punishment or take its place.
The IKV, Anniversary Number.—To celebrate the twenty-fifth
anniversary of the establishment of the “Internationale

Kriminalistische Vereinigung,” a special number was issued in
January of this year. It contains, in addition to the history of its
establishment, a symposium as to the effect that its activities have
had on the development of the problem of delinquency in its various
phases, and in the various countries. The contribution for the United
States is written by Prof. Charles R. Henderson of the Chicago
University. Most characteristic of the spirit of the IKV is perhaps the
paragraph in the introduction to the anniversary number, that reads
as follows: “This volume should be a milestone in this sense also,
that it shall define the program of the future activities of the Union.
In addition to such legal questions as the regulation of international
extradition, restitution instead of punishment, and the diminution of
the concept of the punishment by imprisonment as the ultima ratio
in the struggle against crime, the Union shall pay more attention to
the sociological aspect of crime.”
The Four Gunmen.—Under this title Winthrop D. Lane writes in the
Survey of April 4th about the social history of the four unfortunate
young fellows who were executed at Sing Sing on April 13th. Mr.
Lane found on careful investigation that all four came from “decent”
families; that their career of crime started apparently from street life
and its temptations; that each of the four had a previous correctional
institution record; that they each started their lawbreaking career
early; that the early years of each seem to have been normal and
straightforward, giving no hint of the direction later conduct was to
take. “One by one, through disease, going to school, or going to
work, they came into contact with the abnormal street life of a
crowded and heterogeneous community. Their youth demanded play
and excitement, and they sought these where they were easiest to
find. Gradually, but with seeming inevitableness, they made the
acquaintance of older boys and men who had mastered the trick of
turning an easy dollar.... Their own entrances into crime were
gradual, beginning in all but one case with petty attempts while they

were still in their teens to get spending money easily.... Whatever
help there may be in probation and suspended sentence was not
extended to them.”

EVENTS IN BRIEF.
[Under this heading will appear each month numerous paragraphs of
general interest, relating to the prison field and the treatment of the
delinquent.]
New Cell House at Iowa Penitentiary.—The new cell house, built by
convict labor at the Fort Madison penitentiary, will be completed in
May. The structure has been six years under construction, and its
value is said to be more than $200,000. It probably will be sixty days
before the board will have everything completed so that the new
prison house can be used. The structure is of stone and concrete,
and the cells are considerably larger than the rooms in the old cell
house. There will be room in each cell for a single iron bed, a
rocking chair, hot and cold water and toilet conveniences. The rooms
formerly provided for prisoners held but a cot.
The board of control has not yet decided what it will do with the old
cell house when the new one is occupied. It is probable that prison
labor will be used in the remodeling of the walls so that one fair-
sized cell may be made out of two cells.
There are 590 prisoners now in the Fort Madison penitentiary. The
new cell house will provide for 400 of them. The remainder will have
to remain in the old structure.
The board has received samples of hollow building blocks
manufactured at the State clay works at the hospital for inebriates at
Knoxville. This is the first of the output of the new industry and,
according to experts, the tile is as perfectly made as that of other
institutions. It is the intention to have the hollow building blocks
needed in the new building at Oakdale sanitarium made at Knoxville.
The State institution at Knoxville is also ready to turn out tile and
brick. Orders have been sent to all State institutions to order from

Knoxville whatever material of this kind is needed.
Training For Prison Warden.—Warden Clancy, of Sing Sing Prison,
recently resigned. Eugene Smith, president of the Prison Association
of New York, has written an open letter to the New York city papers,
as follows:
“The resignation of Mr. Clancy is an event that has, for several
reasons, unusual significance. Mr. Clancy has stated with great
candor the reasons that induced him to resign. The principal
reason, as alleged by him in an interview, was his lack of
experience and consequent ignorance of the work to be done.
He says, ‘The warden should be selected from among the
keepers or others who have had a large amount of experience.
There is nothing more ridiculous than the selection of a man
like myself who has no such experience.’
“These statements, so frankly made, do honor to Mr. Clancy
and they convey a valuable message to the public. A warm
heart and a large brain alone do not qualify a man to fill the
wardenship of a prison. The administration of a prison must be
governed, in this modern age, upon the principles established
by the science of penology. The proper treatment of prisoners
requires an acquaintance with those methods and agencies
which have been proved by scientific experiments to be most
effectual in reforming and rehabilitating the prisoners.
“No warden can administer a prison with success unless he has
a scientific knowledge of what has been developed and
accomplished through the studies and experience of the great
leaders in prison reform and such scientific knowledge can only
be acquired and practically applied by personal experience in
dealing with prisoners. There are to-day, in the prisons of this
State, men who have had long experience, as guards or in
other subordinate posts, who possess both the scientific

knowledge and executive ability qualifying them to fill with
success the office of warden of Sing Sing Prison. It is earnestly
hoped that the candidates for the vacancy may be selected
from some such competent source.
“But besides scientific knowledge, ability, and experience, there
is another condition, or sine qua non, absolutely essential to
success in administering Sing Sing or any other prison. As a
warden should be selected without the slightest regard to his
political affiliations, he should also have a free hand in
discharging his duties unhampered by political influence.
“Politics constitute the greatest obstacle encountered by every
movement for prison reform. So long as the appointment of
prison officials and their retention in office are dependent on
political favor or influence, it is hopeless to look for
improvement in prison systems or any measures of reform. The
infusion of politics into our prison can never be prevented
except by the force of a united public opinion, a consensus
strong enough to condemn and drive out of public service
every person who participates in the appointment or removal of
any prison officer for merely political ends in order to confer
favors or promote expedience.”
Progress in New York City’s Department of Correction.—
Commissioner of Correction Katharine Bement Davis, and her
deputy, Burdette G. Lewis, have already planned important
improvements in administration. The upper floor of the Tombs is to
be transformed into a hospital with nearly ninety beds; a visiting
building, with screens between visitors’ seats and prisoners’ seats,
will be built; food brought in from the outside is to be prohibited,
and improvement in the catering service in the Tombs is arranged
for; classification of prisoners in the various institutions is being
developed; the punishment cells in the Penitentiary are to be

abandoned in favor of a separate punishment building with
“reflection cells,” a detention house for women prisoners is to be
built; the Department has moved from an antique building on
Twentieth street into adequate quarters in the new Municipal
building; stripes are to be abolished in the Island institutions; several
“crews” of youngsters have been sent out to the tract of six hundred
acres in Orange county to be used for the new City Reformatory for
Misdemeanants; the clothing of women prisoners at the workhouse
and Penitentiary is to be considerably bettered; and so forth. The
fundamental plans for the re-organization of the Department’s
institutions are being carefully worked out.
The Power of Suggestion.—Some of the complacent ones who
maintain that you must leave to youngsters of either sex their own
governing, and hold them pretty completely responsible for crime
committed by them might pause for a moment to read the following
—except that no such complacent ones read The Delinquent. This is
from the monthly journal called the Training School, published at
Vineland, New Jersey:
Mamie S—— was a middle-grade imbecile girl about eighteen
years old, testing about six by the Binet. She was strong and
active, a cheerful and willing worker, subject to occasional fits
of temper, but usually quite easily controlled. Her work in the
laundry was helping Miss B. to feed the big steam mangle.
One day the superintendent was escorting a party of visitors
and explained to them the use of the shield over the reed rolls
of the mangle, saying that if it were out of place there would
be great danger of the workers’ fingers being caught between
the rolls and a serious accident occurring before the machinery
could be stopped. Mamie heard his remark and the visitors had
no sooner left the laundry than she turned to Miss B. and said:
“Say, Miss B., if I put my fingers in there, would it draw in my

arm and crush it?” Miss B. answered, “Of course it would, you
silly girl.” Mamie declared, “I am going to try it,” and at once
lifted the shield and would have put her fingers between the
rolls had not Miss B. grappled with her.
Mamie struggled desperately and would have overpowered Miss
B. but she called for help and it took three of the employees to
drag Mamie away to safety. It is needless to say that Mamie’s
work in the laundry ceased with that incident.
Farewell, and Don’t Come Back!—The editors of prison newspapers
sometimes “gets theirs” in very pleasant fashion. Here is one of the
most recent events of the kind, quoted from the Mirror, published at
the Minnesota State Prison:
“‘Chip’, the editor of Our View Point, the Walla Walla, Washington,
prison paper, has been paroled after serving several months
conscientiously and well as the guiding spirit of that publication.
Prior to his departure for the outside world, the inmates subscribed a
dime apiece and presented him with a watch as a testimonial of their
appreciation. The presentation speech was made by the warden in
the presence of the inmates in the chapel, the Sunday prior to his
departure.”
Hayward.—Here is a story to make a man “feel good”.
Harry S. Hayward, after seven years’ influential work with the
newspaper called the Cumberland, Md., News, disappeared recently
because politicians and evil interests he had opposed learned that he
had served in prison, and threatened to reveal his past. Hayward
had made very many friends. The proprietor of the newspaper
received a letter from Hayward, in which he reviewed the trials he

had endured in trying to live down the past, and in which he
declared that he was determined to lose himself in some distant part
of the country, and continue the struggle to live a decent life.
The proprietor, W. W. Brown, immediately tried to reach Hayward,
but in vain. He inserted then the following advertisement in papers
all over the country:
H. S. Hayward:—Have known two years. We are with
you to the end. Come back soon.
W. W. Brown.
Many prominent citizens joined in the effort to find Hayward. The
Governor of Maryland pardoned him and restored him to citizenship.
And, finally Hayward came back, in triumph.
The Latest Thing in Joy Rides.—Edward Smith, a lifer, and James
McGee, sentenced for seventeen years, escaped from the Joilet
Penitentiary recently, in Warden Allen’s automobile. After riding
around Chicago all night they decided to return to the prison. Guards
had been hunting the men in three States.
Smith was the Warden’s chauffeur and drove in and out of the prison
without attracting attention.
“We could have got away without much chance of being captured,”
he said, “but we got to thinking that our escape might interfere with
the good treatment given the other honor prisoners.
“Warden Allen treated us mighty well and we thought it best not to
violate the confidence he placed in us. We certainly had a fine time
while we were away. We rode all over Chicago and saw all the
sights.”

Advice in the Shadow of the Gallows.—Several years ago there was
executed at Trenton State Prison, New Jersey, a very intelligent man,
who had committed a fearful murder. A day before his execution he
was asked to leave some word for the young men of this country.
Here is what he wrote, in a firm hand, without tremor:
“I can add but little to what others have said. I would suggest
early religious training. It should begin with the lisping of the
child and be continuous and never end until death. The child
should be given to know the dangers of environment that is not
religious. His associations should be only those that reverence
God. The parental responsibility comes in here. The child looks
for examples. As the example set before it by its parents or
associates are good or evil, so it will in most cases grow.
“If the boy be disciplined in religion with environments good,
associations good, and with love as his teacher till he is come
of age, to the age of reason, the point of the early training will
be invariably a moral religious life. Not all of these came into
my early life but of those that did my one regret is that I did
not use them to my advantage, for the wages of sin is death,
and the gift of God is eternal life through Jesus Christ, our
Lord.”
Progress at Bellefonte.—According to the Pennsylvania Prison Society
(the 127th annual meeting of which was recently held), “about 75
prisoners from the old Western Penitentiary at Pittsburgh are at
Bellefonte, busily engaged in taking care of the farm and in various
preliminary operations. (Pennsylvania is to build a farm industrial
prison on 5,000 acres). They have been employed in the repairing of
the old buildings on the estate, in quarrying stone for roads, and for
other construction. There have been erected a number of new
buildings, among them a machine shop, blacksmith shop, power
house, large dining room and a dormitory. The work done on all the

buildings was almost entirely by the prisoners themselves,
superintended by an experienced outside foreman. It would be
difficult to get together on the outside an equal number of men who
worked as zealously or faithfully. There have been but three
attempted escapes since the men arrived in the summer of 1912.
The prisoners are allowed to go to all parts of the large farm in
gangs of from three to twenty, under the care of one guard or trusty.
The population is transitory, as almost weekly some are paroled,
while new ones take their places.”
An Honor Colony Hoped For.—The New Jersey Reformatory is a
congregate institution run by trustees and officers that believe in
individualization and classification. So, in the current annual report
the Board of Managers urges the establishment of an honor colony.
“This should be at some distance from the Institution, and should be
utilized for those inmates who are near parole, and who have
demonstrated that they are learning the lessons they have been sent
to the institution to learn.... It has been for some years the custom
to permit inmates to return to their homes when a death occurs in
the family, unaccompanied by anyone from the institution, relying
solely upon the promise of an inmate to return at a given time. In no
instance has an inmate broken the promise or failed to show an
appreciation of the trust reposed in him.”
The Limits of Reformatory Treatment.—Superintendent Frank Moore,
of the New Jersey State Reformatory, writes in his annual report:
“The Reformatory can take that which has worth, even though
it may be bent, twisted and corroded with sin, and making it
plastic, it may form it over again, reform it; but that which is
useless, which is only dross, it can do little with. The

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