First published 2018 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

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 and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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John Wiley & Sons, Inc.
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The rights of Jean Mbihi to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2018930828

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-78630-248-9

Table of Contents

Cover

Title

Preface

Introduction

I.1. Architectural and technological context
I.2. Scientific and teaching context
I.3. Purpose of the book
I.4. Organization of the book’s content

PART 1: Analog Feedback Control Systems

1 Models of Dynamic Processes
1. 1.1. Introduction to dynamic processes
2. 1.2. Transfer functions
3. 1.3. State models
4. 1.4. Linear state models with constant parameters
5. 1.5. Similarity transformation
6. 1.6. Exercises and solutions
2 Experimental Modeling Approach of Dynamic Processes
1. 2.1. Introduction to experimental modeling
2. 2.2. Step response-based modeling
3. 2.3. Frequency response-based modeling
4. 2.4. Modeling based on ARMA model
5. 2.5. Matlab-aided experimental modeling
6. 2.6. Exercises and solutions
3 Review of Analog Feedback Control Systems
1. 3.1. Open-loop analog control
2. 3.2. Analog control system
3. 3.3. Performances of an analog control system
4. 3.4. Simple analog controllers
5. 3.5. PID/PIDF controllers
6. 3.6. Controllers described in the state space
7. 3.7. Principle of equivalence between PID and LQR controllers
8. 3.8. Exercises and solutions

PART 2: Synthesis and Computer-aided Simulation of Digital Feedback Control Systems

4 Synthesis of Digital Feedback Control Systems in the Frequency Domain
1. 4.1. Synthesis methodology
2. 4.2. Transfer function G(z) of a dynamic process
3. 4.3. Transfer function D(z): discretization method
4. 4.4. Transfer function D(z): model method
5. 4.5. Discrete block diagram of digital control
6. 4.6. Exercises and solutions
5 Computer-aided Simulation of Digital Feedback Control Systems
1. 5.1. Approaches to computer-aided simulation
2. 5.2. Programming of joint recurrence equations
3. 5.3. Simulation using Matlab macro programming
4. 5.4. Graphic simulation
5. 5.5. Case study: simulation of servomechanisms
6. 5.6. Exercises and solutions
6 Discrete State Models of Dynamic Processes
1. 6.1. Discretization of the state model of a dynamic process
2. 6.2. Calculation of {A, B, C, D} parameters of a discrete state model
3. 6.3. Properties of a discrete state model {A, B, C, D}
4. 6.4. Exercises and solutions

Appendices

Appendix 1: Table of Z-transforms
Appendix 2: Matlab® Elements Used in This Book

Bibliography

Index

End User License Agreement

List of Tables

2 Experimental Modeling Approach of Dynamic Processes

Table 2.1. Table of the first 30 lines of the Strejc table
Table 2.2. Table for the comparison of modeling methods
Table 2.3. Comparison of modeling methods

3 Review of Analog Feedback Control Systems

Table 3.1. Determination of PID parameters by Ziegler–Nichols methods
Table 3.2. Table for the calculation of the parameters of an optimal PID controller according to IAE, ITAE and ISE optimization criteria
Table 3.3. Electronic diagrams and transfer functions of simple analog controllers

4 Synthesis of Digital Feedback Control Systems in the Frequency Domain

Table 4.1. Padé approximant of e^X with x = – τ₀p
Table 4.2. Results of the numerical calculation of [4.29]
Table 4.3. D(z) for phase-lead/lag controller
Table 4.4. D(z) for PID controller
Table 4.5. D(z) for PIDF controller
Table 4.6. Table of the first 12 samples

5 Computer-aided Simulation of Digital Feedback Control Systems

Table 5.1. D(z) for various discretization methods
Table 5.2. Table comparing simulation approaches
Table 5.3. Results of the comparison of simulation approaches
Table 5.4. Model of table summarizing the Matlab commands used
Table 5.5. Matlab commands used in the “SimEquaRec.m” program
Table 5.6. Matlab commands used in the “MacroSim.m” program
Table 5.7. Matlab commands used in the “MacroSim.m” program

Appendix 1: Table of Z-transforms

Table A1.1. Table of z-transforms (T: sampling period)

Appendix 2: Matlab® Elements Used in This Book

Table A2.1. Matlab elements used in this book

List of Illustrations

1 Models of Dynamic Processes

Figure 1.1. Controllable dynamic process
Figure 1.2. Step response to simple dynamic models. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 1.3. Bode diagrams of simple dynamic models. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 1.4. Variables of a dynamic process in the state space
Figure 1.5. Operational calculus scheme for a dynamic model
Figure 1.6. Block diagram of a linear state model with constant parameters
Figure 1.7. Response of a dynamic system with input δ(t)
Figure 1.8. Profile of y(t)
Figure 1.9. Operational calculus scheme
Figure 1.10. Schematic representation of a simple pendulum
Figure 1.11. Schematic representation of a robotic axis
Figure 1.12. Operational calculus scheme of the robot
Figure 1.13. Bode diagrams of G_c(s)

2 Experimental Modeling Approach of Dynamic Processes

Figure 2.1. Experimental modeling methodology
Figure 2.2. Virtual instrumentation system
Figure 2.3. Remote virtual instrumentation system
Figure 2.4. Identification of parameters of a model of order 1 based on the response to a step u(t – τ₀) of magnitude E₀
Figure 2.5. Graphic profile of the step response of a model of order 2 (with ξ < 1)
Figure 2.6. Strejc method for experimental modeling
Figure 2.7. Bode diagram of a process of order 1. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 2.8. Bode diagram of a damped process of order 2. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 2.9. Bode diagram of an under-damped process of order 2. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 2.10. Identification data. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 2.11. Experimental response and response of the estimated model
Figure 2.12. Graph of response y(t)
Figure 2.13. Graph of the response to the open-loop step. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 2.14. Boost chopper controlled by DCM circuit. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 2.15. Virtual response
Figure 2.16. Graph of the response to step E₀ = 4V
Figure 2.17. Graph of the response to step E₀ = 2V
Figure 2.18. Measurements D and T_m
Figure 2.19. Bode diagram of a dynamic process of order 2
Figure 2.20. Measurements on Bode diagram. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 2.21. Graph of the response y(t) to a step E₀ = 2
Figure 2.22. Measurements of T_u and T_a

3 Review of Analog Feedback Control Systems

Figure 3.1. Open-loop control of a dynamic process
Figure 3.2. Control principle of a dynamic process
Figure 3.3. Generic block diagram of analog control systems
Figure 3.4. Roles of parameters of a PIDF controller
Figure 3.5. Open-loop response of the test to step E₀. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 3.6. Results of the application of ITAE criterion of Table 3.2
Figure 3.7. Structure of a linear state feedback law
Figure 3.8. State feedback control system with integral action
Figure 3.9. State feedback control system with integral action and observer
Figure 3.10. Control system with dynamic state feedback
Figure 3.11. PID control loop of a second-order process
Figure 3.12. Buck chopper with duty-cycle modulation control
Figure 3.13. PID control loop of a second-order process
Figure 3.14. Results of optimal control by optimal PID controller
Figure 3.15. Step response
Figure 3.16. Closed-loop step response
Figure 3.17. Closed-loop step response
Figure 3.18. Graphs of step responses of G(s) and G_e(s). For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 3.19. Graphs of step responses of G(s) and G_e(s). For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 3.20. Test results. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 3.21. Block diagram of integral feedback control
Figure 3.22. Graph of the response obtained
Figure 3.23. Optimal state trajectories. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 3.24. Graphic results. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 3.25. Resulting trajectories
Figure 3.26. Graph of signals obtained

4 Synthesis of Digital Feedback Control Systems in the Frequency Domain

Figure 4.1. Synthesis of a sampled dynamic model. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 4.2. Comparison of step responses of G_c(s) and G(z). For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 4.3. Software nature of a digital controller law
Figure 4.4. Synthesis principle of discrete block diagram
Figure 4.5. Result of the execution of the proposed program
Figure 4.6. Graph resulted from the execution of the proposed program
Figure 4.7. Graph of the step response
Figure 4.8. Result of the comparison
Figure 4.9. Graphs of the step response and of the digital control

5 Computer-aided Simulation of Digital Feedback Control Systems

Figure 5.1. Analog control loop
Figure 5.2. Result of the step response simulation using Matlab programming
Figure 5.3. Step responses obtained in continuous and discrete time
Figure 5.4. Variable structure block diagram of the digital control loop
Figure 5.5. Step responses for T = 0.1 s. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 5.6. Closed-loop step responses for T = 0.3 s. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip
Figure 5.7. Graphic simulation in the Simulink environment
Figure 5.8. Graph and table of values of the function T(m) = τ₀ / m
Figure 5.9. Open-loop step responses
Figure 5.10. Block diagram of a digital feedback control system of a servomechanism
Figure 5.11. Open-loop and closed-loop responses of a speed servomechanism
Figure 5.12. Open-loop step response of the position servomechanism
Figure 5.13. Open-loop and closed-loop responses of a position servomechanism
Figure 5.14. New graphs obtained. For a color version of this figure, see www.iste.co.uk/mbihi/automation.zip

6 Discrete State Models of Dynamic Processes

Figure 6.1. Block diagram of a dynamic process sampled in the state space
Figure 6.2. Block diagram of the discrete state model of a dynamic process
Figure 6.3. System of m new state variables allowing the encapsulation of the pure input delay

Preface

Analog automation is a multidisciplinary science that studies techniques, tools and technologies for the design and implementation of analog controllers for dynamic processes, the controller being a device for automatic correction of possible errors between the set point quantity and the corresponding response.

Therefore, in an uncertain operating environment that is subjected to unknown disturbances or unpredictable noise, a dynamic process equipped with an appropriate controller can provide good dynamic performances (stability, overshoot, rapidity) and static performances (precision, robustness).

According to the history of automation, the first mechanical controller, known as the “water clock”, was invented in Greece by Ktesibios around 270 BC [STU 96]. After 23 centuries, in 1956, analog electronic controllers were developed [FRI 82, THO 07]. The first computer-aided digital feedback control processes were then implemented in major industries in the United States starting from 1950 [BAK 12]. Moreover, starting from the 1970s, the digital automation techniques assisted by microprocessor and PLC (programmable logic controller) have progressively occupied the wide SMI (small and medium-sized industries) sector, which had been beyond the reach of these computers until that time. They were, indeed, bulky, expensive and difficult to program. Furthermore, they had high maintenance costs and were sensitive to industrial environments.

Nevertheless, after the emergence of the first PC (personal computer) generations in the 1980s, followed by the development of microcomputer models featuring increasingly high performances at low costs (industrial PC, multimedia PC, PC/pad and PC/panel), the range of application of computer-aided digital control technology has rapidly extended to SMIs in various fields: manufacturing, textile, foodprocessing industry, chemical industry, energy, robotics, telescopic devices, avionics, bio-mechatronics, home automation, etc.

Given the lack of reference manuals intended to serve as a learning bridge between analog and digital control systems, this book will allow the readers to easily master analog automation skills and then to rapidly become introduced to the techniques for design and simulation of modern PC-aided digital control systems. The book is mainly addressed to students and teachers of engineering schools, to teachers’ training schools for technical education and to vocational training centers for applied sciences.

Indeed, readers will discover in this book the following relevant main elements:

– the stakes of computer-aided control in the set of control technologies for dynamic processes;
– a summary of the theory of analog control systems;
– a clear presentation of the experimental modeling of dynamic processes, with or without input delay;
– modern tools for the rapid design of optimal PID controllers;
– techniques for computer-aided synthesis and simulation of digital control loops, with a detailed case study of speed and position servomechanisms;
– methods for the discretization of dynamic process state models;
– Matlab® programs for teaching purposes, allowing the convenient introduction, if needed, of the digital and graphic results presented;
– a variety of corrected exercises at the end of each chapter.

The analog and digital control systems presented in this book are the result of the continuously enhanced teaching of the “Computer-aided automation of feedback control systems” course, which the author has taught since 2000 in the “Electrical Engineering” department of ENSET (École Normale Supérieure d’Enseignement Technique), a technical higher education school of the University of Douala, and in the “Computer Science Engineering” department of ESSET (Écoles Supérieures des Sciences et Techniques), scientific and technical higher education schools of Douala and Nkongsamba.

The author acknowledges the favorable effects of the scientific research grant offered by MINESUP (Ministry of Higher Education) of Cameroon. It has facilitated the access to support and scientific and technical research resources needed for editing activities involved in this book project.

Moreover, the author sincerely thanks his close collaborators in the scientific field of industrial automation and computing who have offered their constructive suggestions concerning both technical and teaching aspects, as follows:

– Prof. Womonou Robert, director and promoter of ESSET at Douala and Nkongsamba;
– Prof. Nneme Nneme Léandre, director of ENSET at the University of Douala;
– Pauné Félix, PhD, lecturer in the “Computer Science” department of ENSET at the University of Douala;
– Moffo Lonla Bertrand, PhD, lecturer at ENSET at the University of Buea.

The author also wishes to thank:

– The students of the second cycle of the “Electrical Engineering” department, ENSET, at the University of Douala and of ESSET at Douala and Nkongsamba, who have followed his “Computer-aided automation of feedback control systems” course with great interest. Thanks to their many relevant questions, which have allowed him to identify certain obscure didactic aspects of basic automation that have been clarified in this book.
– His wife, Mrs. Mbihi born Tsafack Pélagie Marthe, and her entire family, who have all offered him continuous and comforting support, as well as unforgettable close assistance.
– Mr. Ajoumissi Jean’s and Nkongli Teuhguia’s families, who motivated him to initiate and complete this book project.
– The ISTE editorial team, who provided him with the tools and means that facilitated this book’s content restructuring and improvement.

January 2018