Closed Loop Control and Management: Introduction to Feedback Control Theory with Data Stream Managers

396 Pages·2023·24.646 MB·English

by  Serge Zacher

Serge Zacher
Closed Loop
Control and
Management
Introduction to Feedback Control Theory
with Data Stream Managers
Closed Loop Control and Management
Serge Zacher
Closed Loop Control and
Management
Introduction to Feedback Control Theory
with Data Stream Managers
Serge Zacher
Stuttgart, Baden-Württemberg, Germany
ISBN 978-3-031-13482-1 ISBN 978-3-031-13483-8 (eBook)
https://doi.org/10.1007/978-3-031-13483-8
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
2022
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Preface
“The only important thing in a book is the meaning that it has for you.”
(Quote: William Somerset Maugham. Source https://www.goodreads.com/author/quotes/
4176632.W_Somerset_Maugham accessed April 24, 2022)
This book is very important to me because it summarizes concepts, methods, and appli-
cations that have been developed and published in various places over the years. I hope
that the book will also be important and useful for students, for my colleagues’ profes-
sors all over the world and their students, as well as for graduates who are already work-
ing in the industry. I am certainly sure that it will, because the conceptions are new, the
methods are practicable, and the applications allow to enormously simplify the engineer-
ing of closed loop control.
The questions I asked myself about 30 years ago were
• Is it possible to replace the established functional block diagram of a closed loop with
the elements of modern automation technology (bus, client/server, etc.) without losing
the mathematical basics of control theory?
• How can a closed loop be not only controlled but also managed like the technical
devices are managed through their whole life cycle?
• Is it possible to reduce the number of variables and the number of controllers which
are needed for multivariable control systems without converting their transfer func-
tions into the corresponding state space models?
The answers to these and more questions are given in the book, and I hope, in an under-
standable and exhaustive form. I was surprised myself by some of the results, e.g.,
that a controller could be adjusted based on a single point in the Bode diagram. Even
the Bode diagram can be determined using a single step response instead of as usual
a series of frequency responses. The set point behavior of a closed loop could be con-
trolled with one non-linear controller even if the parameters of the plant are far shifted
from its initial constant values. The disturbance behavior is not controlled with only one
v
vi Preface
conventional controller but supervised with a Data Stream Manager called “Terminator”
that destroyed at once as well all external as internal disturbances.
Altogether, the book describes almost 20 Data Stream Managers (DSM), most of
which are designed as visually human-like silhouettes as in the case of software-agents.
The DSM symbolized with these silhouettes are control elements, which include the
open loop control (e.g., switches and logical operations) and/or closed loop control (i.e.,
sensors, actuators, and controllers). Some of the DSMs are developed on the principles
of neuro-networks and fuzzy logic, and another on the new approaches like bus-approach
or Antisystem Approach (ASA).
As mentioned above, almost all the topics covered in this book have already been
published in many books, articles, and papers in German. When translating formulas and
indices, I took the liberty of sticking to their original designations and hope for your
understanding. Some transfer functions are left the same as in the original publications,
e.g., a controller is G , oriented on the word “Regler” (controller). The “S” by the trans-
R
fer function Gs indicates “Strecke” (plant). The settling time is T and not T , as is
aus set
expected in English literature. Turning over such an enormous number of formulas and
figures is practically impossible for me alone.
The book is aimed at students at technical universities and colleges as well as at tech-
nology engineers of automation. More documents on the topics of the book can be found
on my author’s website https://www.zacher-automation.de or directly asked via mail:
[email protected].
u All numerical data, test results, curves, etc. available in book are not real but ficti-
tious data. The further development or use of the publication without reference to
the author is not permitted. The scripts and Simulink models created with MAT-
LAB® are subject to the copyright reserved by the author and the publisher. The
author and the publisher accept no liability for use in practical cases or for any
damage that may result from incomplete or incorrect information during imple-
mentation.
Finally, I would like to always thank the employees at Springer Vieweg Verlag for their
friendly atmosphere and constructive cooperation, namely the chief editor for electrical
engineering/IT/computer science, Mr. Reinhard Dapper, and the editorial assistant, Ms.
Andrea Brossler. My thanks go to the entire team at Springer-Nature Verlag’s German
Books Production, especially the project coordinator, Ms. Anupriya Harikrishnan.
Stuttgart, Germany Serge Zacher
May 2022
Contents
1 Closed Loop Control and Management ............................. 1
1.1 Introduction ............................................... 1
1.1.1 The aim of this book ................................. 1
1.1.2 Content of this book .................................. 3
1.2 From Single Controller to Automation System .................... 3
1.2.1 Historical Overview .................................. 3
1.2.2 Automation Levels ................................... 7
1.2.3 Automation Subsystems and Functions ................... 11
1.3 Control ................................................... 12
1.3.1 Closed Loop Control (CLC) ........................... 12
1.3.2 Open Loop Control .................................. 14
1.3.3 Examples of open and closed loop control ................ 16
1.3.4 Bus ............................................... 23
1.4 Management ............................................... 24
1.4.1 Management of Automation System ..................... 24
1.4.2 Management of CLC ................................. 25
1.4.3 Example of a CLC Life Cycle .......................... 26
1.5 Conceptions and Approaches, used in this book ................... 33
1.5.1 Classical Control Theory .............................. 33
1.5.2 System-Approach .................................... 33
1.5.3 Bus-Approach ...................................... 34
1.5.4 Symmetry and Antisymmetry .......................... 35
1.5.5 CLIMB & HOLD-modes .............................. 36
1.6 Summary: Data Stream Management ........................... 37
References ...................................................... 39
2 Basics of System Dynamics and Control Theory ...................... 43
2.1 Three Levels of Mathematical Descriptions ...................... 44
2.1.1 Introduction ........................................ 44
2.1.2 Time Domain ....................................... 44
vii
viii Contents
2.1.3 Laplace-Domain ..................................... 48
2.1.4 Frequency Domain ................................... 54
2.1.5 Summary .......................................... 58
2.2 Plants .................................................... 60
2.2.1 Proportional P-plants ................................. 60
2.2.2 Integral or I-plants ................................... 62
2.2.3 Derivative D-plants .................................. 62
2.3 Controllers ................................................ 63
2.4 CLC Behavior ............................................. 68
2.4.1 Example: Level Control ............................... 68
2.4.2 Stabilty ............................................ 69
2.4.3 Retained Error ...................................... 71
2.5 Simulation of CLC with MATLAB® ............................ 73
2.5.1 Scripts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.5.2 Simulink-Model ..................................... 76
References ...................................................... 80
3 Controller Tuning ............................................... 81
3.1 Controller Tuning in Time Domain ............................. 81
3.1.1 Performance Criteria of Control ........................ 81
3.1.2 Settability of PTn Plants .............................. 83
3.1.3 Empirical Tuning Methods ............................. 85
3.1.4 Tuning of Controller Minimizing Integral Criterion ......... 89
3.1.5 ITAE Criterion ...................................... 92
3.2 Controller Tuning in Laplace Domain ........................... 97
3.2.1 Standard Controller .................................. 97
3.2.2 Open and Closed Loop ................................ 100
3.2.3 Model Based Compensating Controller ................... 102
3.2.4 Tuning of Typical Simple Loops ........................ 103
3.2.5 Optimum Magnitude ................................. 108
3.2.6 Symmetrical Optimum ................................ 110
3.2.7 Pole Placing ........................................ 112
3.2.8 Algebraic Stability Criterion of Hurwitz .................. 114
3.3 Controller Tuning in Frequency Domain ......................... 116
3.3.1 Nyquist Stability Criterion ............................. 116
3.3.2 Controller Tuning with Bode-Plot ....................... 119
References ...................................................... 123
4 Bus-Approach .................................................. 125
4.1 Definition of Virtual Bus ..................................... 125
4.1.1 Curse of Dimensionality .............................. 125
4.1.2 Course of Dimensionality ............................. 128
Contents ix
4.2 Basics of Bus-Approach ..................................... 131
4.2.1 Construction of Virtual Bus ............................ 131
4.2.2 Bus-Creator and Bus-Selector .......................... 134
4.2.3 Applications of Virtual Buses for SISO- and MIMO CLC .... 135
4.3 Bus-Approach for MIMO Control .............................. 142
4.3.1 Kinds of MIMO Plants ................................ 142
4.3.2 Kinds of Coupled MIMO Plants ........................ 143
4.3.3 Stability of Coupled MIMO Plants ...................... 147
4.3.4 Kinds of MIMO Control .............................. 148
4.3.5 Interaction Transfer Function and Coupling Gain ........... 150
4.4 Stability of MIMO Control ................................... 151
4.4.1 Stability of MIMO Single-Loops Control ................. 151
4.4.2 Stability of Separated MIMO Control .................... 152
4.4.3 Stability Check with MATLAB®-Script .................. 158
4.5 Summary ................................................. 159
References ...................................................... 161
5 ASA: Antisystem Approach ....................................... 163
5.1 What is ASA? .............................................. 163
5.1.1 Definition of ASA ................................... 163
5.1.2 The Long Way to ASA ................................ 165
5.1.3 Examples of ASA Implementations ...................... 175
5.2 Basics of ASA ............................................. 177
5.2.1 Introduction: ASA is Everywhere ....................... 178
5.2.2 Balance of Functions and Numbers ...................... 180
5.2.3 Balance of Algebraic Equations ......................... 182
5.3 ASA Application for Control .................................. 184
5.3.1 Balance Control ..................................... 184
5.3.2 Compression and Extraction of Variables ................. 185
5.3.3 MIMO Control ...................................... 186
5.3.4 Multi-Stage MIMO Plants ............................. 188
5.3.5 ASA Control ....................................... 190
References ...................................................... 191
6 BAD: Bode Aided Design ......................................... 193
6.1 Introduction ............................................... 193
6.1.1 Stability ........................................... 193
6.1.2 Hurwitz Stability Criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.2 Overview of Stability Criteria in Frequency Domain ............... 196
6.2.1 Nyquist Stability Criterion ............................. 196
6.2.2 Mikhailov stability criterion ............................ 202
6.2.3 Leonhard Stability Criterion ........................... 203
x Contents
6.3 Three Bode Plots ........................................... 207
6.3.1 Conception ......................................... 207
6.3.2 Two Bode Plots Method ............................... 208
6.3.3 Symmetry Operations With Controllers ................... 211
6.3.4 Decomposition of mirrored controllers ................... 213
6.3.5 3BP Method ........................................ 215
6.3.6 Implementation of 3BP Method for Unstable Plants ......... 218
6.4 BAD ..................................................... 220
6.4.1 Bode Plots of Mirrored Controllers ...................... 221
6.4.2 BAD of P controller .................................. 223
6.4.3 BAD of I controller .................................. 225
6.4.4 BAD of PID controller ................................ 226
6.5 Implementation of BAD ...................................... 230
6.5.1 BAD upon one single frequency response ................. 230
6.5.2 Bode plot upon single step response ..................... 231
References ...................................................... 234
7 Management of Identification ..................................... 237
7.1 Introduction ............................................... 237
7.1.1 Data Stream Management ............................. 237
7.1.2 DSM of this Chapter ................................. 239
7.2 DSM Ident ................................................ 241
7.2.1 Structure ........................................... 241
7.2.2 DSM Ident-1 ....................................... 242
7.2.3 DSM Ident 3 ........................................ 244
7.2.4 MATLAB® Script of DSM Ident 3 ...................... 247
7.3 DSM Tuner ................................................ 249
7.4 AFIC .................................................... 255
7.4.1 Conception of Adaptive Filter for Identification
and Control ......................................... 255
7.4.2 Adaptive Filter: Theoretical Backgrounds ................. 256
7.4.3 Identification of Plant ................................. 256
7.4.4 App DSM AFIC with MATLAB® ....................... 261
References ...................................................... 264
8 Management of Setpoint Behavior ................................. 267
8.1 Control and Management ..................................... 267
8.1.1 Setpoint behavior and disturbance behavior ............... 267
8.1.2 CLIMB and HOLD .................................. 270
8.1.3 Overview of DSM of this chapter ....................... 270
8.2 Dual control with reference model ............................. 272
8.2.1 SPFC ............................................. 272
8.2.2 SFC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275