Table of Contents

Cover

Title

Preface

List of Acronyms and Notations

1 Introduction – Models and Dynamic Systems

1.1. Overview
1.2. Industrial process modeling
1.3. Model classes

2 Linear Identification of Closed-Loop Systems

2.1. Overview of system identification
2.2. Framework
2.3. Preliminary identification of a CL process
2.4. CLOE class of identification methods
2.5. Application: identification of active suspension

3 Digital Control Design Using Pole Placement

3.1. Digital proportional-integral-derivative algorithm control
3.2. Digital polynomial RST control
3.3. RST control by pole placement
3.4. Predictive RST control

4 Adaptive Control and Robust Control

4.1. Adaptive polynomial control systems
4.2. Robust polynomial control systems

5 Multimodel Control

5.1. Construction of multimodels
5.2. Stabilization and control of multimodels
5.3. Design of multimodel command: fuzzy approach
5.4. Trajectory tracking

6 Ill-Defined and/or Uncertain Systems

6.1. Study of the stability of nonlinear systems from vector norms
6.2. Adaptation of control
6.3. Overvaluation of the maximum error for various applications
6.4. Fuzzy secondary loop control

7 Modeling and Control of an Elementary Industrial Process

7.1. Modeling and control of fluid transfer processes
7.2. Modeling and controlling liquid storage processes
7.3. Modeling and controlling the storage process of a pneumatic capacitor
7.4. Modeling and controlling heat transfer processes
7.5. Modeling and control of component transfer processes

8 Industrial Applications – Case Studies

8.1. Digital control for an installation of air heating in a steel plant
8.2. Control and optimization of an ethylene installation
8.3. Digital control of a thermoenergy plant
8.4. Extremal control of a photovoltaic installation

Appendix A: Matrix Transformation from Any Representation to the Companion Form or Arrow Form

A1.1. Transition from a companion matrix to an arrow form matrix
A1.2. Direct transition of a matrix of any form to an arrow form

Appendix B: Determination of the Maximum Error for Pole Placement for a Nonlinear Third-Order Process

Appendix C: Determining the Attractor in a Nonlinear Process Controlled by Linear Decoupling

Appendix D: Overvaluation of the Maximum Error in a Tracking Problem for a Lur’e Postnikov Type Process

Blibliography

Index

End User License Agreement

List of Illustrations

1 Introduction – Models and Dynamic Systems

Figure 1.1. Digital system in a closed-loop system

2 Linear Identification of Closed-Loop Systems

Figure 2.1. Closed-loop process block diagram based on an RST-type regulator
Figure 2.2. Implementation block diagram based on the RST-type regulator
Figure 2.3. Principle of CLOE identification methods
Figure 2.4. Attenuation of resonant spectral lines for a process by varying the weights in W-CLOE method
Figure 2.5. Experimental active suspension system hosted by the GIPSA Laboratory in Grenoble, France
Figure 2.6. Operating diagram of the experimental active suspension system hosted by the GIPSA Laboratory in Grenoble, France
Figure 2.7. Spectrum of the active suspension subsystem estimated in OL
Figure 2.8. Automatic control configuration with an RST-YK regulator
Figure 2.9. Performance levels of the best identification methods for the active suspension subsystem
Figure 2.10. Performance levels of the best solutions of RST and RST-YK control for the complete suspension system

3 Digital Control Design Using Pole Placement

Figure 3.1. PID-type control system in polynomial form
Figure 3.2. RST control system
Figure 3.3. RST structure with independent objectives in tracking and regulation
Figure 3.4. Principle of predictive regulation with a unitary horizon
Figure 3.5. Diagram of predictive dead-beat control
Figure 3.6. Improved diagram for predictive dead-beat control
Figure 3.7. Diagram of incremental predictive control

4 Adaptive Control and Robust Control

Figure 4.1. Robustness margin of the system on the Nyquist plot
Figure 4.2. Diagram of RST robust control
Figure 4.3. Margin | ∆M (jω) | and the sensitivity function
Figure 4.4. General structure of the system (Δ ,M)
Figure 4.5. Equivalent structure of the real system (C,P)
Figure 4.6. Closed-loop structure of the real system (C,P)
Figure 4.7. Structure of the nonlinear system
Figure 4.8. Popov circle and tolerance limits of the nonlinearity
Figure 4.9. Template tube specified for the sensitivity

5 Multimodel Control

Figure 5.1. Division into classes
Figure 5.2. Structure of fuzzy control
Figure 5.3. Data classes
Figure 5.4. Establishment of rules
Figure 5.5. Table of rules defining Δμ
Figure 5.6. Defuzzification

6 Ill-Defined and/or Uncertain Systems

Figure 6.1. Block diagram of input–output linearization by state feedback
Figure 6.2. Decoupled subsystem in a chain of integrators
Figure 6.3. Lur’e Postnikov type process
Figure 6.4. Nonlinearity of the studied system
Figure 6.5. Solutions near θ = [2,0]
Figure 6.6. Evolution of the best solutions
Figure 6.7. Evolution of the state vector
Figure 6.8. Evolution of the state vector toward an attractor
Figure 6.9. Secondary regulation loop of fuzzy nature

7 Modeling and Control of an Elementary Industrial Process

Figure 7.1. Fluid flow pipe
Figure 7.2. Representation of a storage process
Figure 7.3. Representation of a pneumatic process
Figure 7.4. Representation of a heat transfer process
Figure 7.5. Representation of a process without reaction
Figure 7.6. Transfer process of components with chemical reaction

8 Industrial Applications – Case Studies

Figure 8.1. Response of gasoline and steam flow control systems
Figure 8.2. Response of the (TRC-3) temperature control system. For a color version of this figure, see http://www.iste.co.uk/popescu/controldesign.zip
Figure 8.3. Response of the pressure control system. For a color version of this figure, see http://www.iste.co.uk/popescu/controldesign.zip
Figure 8.4. Sensitivity function of the nominal temperature control system. For a color version of this figure, see http://www.iste.co.uk/popescu/controldesign.zip
Figure 8.5. Sensitivity function of the robust temperature control system. For a color version of this figure, see http://www.iste.co.uk/popescu/controldesign.zip
Figure 8.6. Response of the robust temperature control system. For a color version of this figure, see http://www.iste.co.uk/popescu/controldesign.zip
Figure 8.7. Response of the closed-loop (TRC-1) system
Figure 8.8. Response of the closed-loop (TRC-2) system
Figure 8.9. Response of the closed-loop system, DPRC-3
Figure 8.10. Diagram of a photovoltaic platform
Figure 8.11. Ideal model of a PV cell
Figure 8.12. Model of a PV cell with one diode
Figure 8.13. A two-diode model of a PV cell
Figure 8.14. Characteristic I(V) of a photovoltaic cell
Figure 8.15. Characteristic P(V) of a photovoltaic cell
Figure 8.16. Calculated characteristic, I(V)
Figure 8.17. Calculated characteristics, P(V)
Figure 8.18. Characteristics calculated at different temperature values with constant illumination. For a color version of this figure, see http://www.iste.co.uk/popescu/controldesign.zip
Figure 8.19. Characteristics calculated at different values of illumination at constant temperature. For a color version of this figure, see http://www.iste.co.uk/popescu/controldesign.zip
Figure 8.20. Digital system for maximum power control
Figure 8.21. Electromechanical diagram of a DC motor
Figure 8.22. General diagram of the extremal system
Figure 8.23. Response of a closed-loop extremal system implemented on a microcontroller. For a color version of this figure, see http://www.iste.co.uk/popescu/controldesign.zip

Appendix B: Determination of the Maximum Error for Pole Placement for a Nonlinear Third-Order Process

Figure B.1. Evolution of the system toward the attraction zone

Appendix C: Determining the Attractor in a Nonlinear Process Controlled by Linear Decoupling

Figure C.1. Evolution of system variables to the attractor

Appendix D: Overvaluation of the Maximum Error in a Tracking Problem for a Lur’e Postnikov Type Process

Figure D.1. Evolution of the state of the initial system in autonomous mode toward its attractor

First published 2017 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:

ISTE Ltd

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www.iste.co.uk

John Wiley & Sons, Inc.

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USA

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The rights of Dumitru Popescu, Amira Gharbi, Dan Stefanoiu and Pierre Borne to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2017930552

British Library Cataloguing-in-Publication Data

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

ISBN 978-1-78630-014-0

Preface

The purpose of this book is to present the various aspects and the different approaches most commonly employed in the control of industrial processes.

Considering that process control design is carried out using a model based approach, the modeling and identification of the systems are presented with the main objective of producing dynamic control models.

Using the chosen model, the control system is determined so as to ensure that the process satisfies the required level of performance. In the case of linear models, the main methods used in control design are based on the notion of pole placement.

In order to account for the fact that the chosen model is only a simplified and often imperfect description of the process’ behavior, more elaborate controls can be suggested: adaptive control, predictive control, internal model control, etc.

When the behavior of the process is strongly nonlinear, the use of a multimodel control can become necessary. The determination, choice and consideration of the various models that can describe the evolution of the process at various operating points depend on the validity of each of these models at the chosen operating points.

We propose a method for estimating the error induced by the models’ own estimation difficulties, and by the presence of uncertainties, noise and bounded perturbations.

After presenting the physical laws that govern the evolution of continuous variation processes, we go on to to explore in detail several real optimized control solutions, carried out in an industrial setting, providing the reader with a better understanding of the approaches developed.

Dumitru POPESCU, Amira GHARBI,

Dan STEFANOIU and Pierre BORNE

February 2017

List of Notations and Acronyms

	Dynamic control model
	Dynamic tracking model
AF-CLOE	Adaptively Filtered Closed Loop Output Error (identification method)
A,B,C,D	State-space representation of the continuous MIMO system
A_d,B_d,C_d,D_d	State-space representation of the discrete MIMO system
A,b,c,d	State-space representation of the continuous SISO system
A_d,b_d,c_d,d_d	State-space representation of the discrete SISO system
ARMAX	Model or class of identification models expressed by 3 terms: autoregressive (AR), moving average (MA) and exogenous control (X)
ARX	Identification model of autoregressive type (AR), with exogenous control (X)
(C,M)	Closed loop nominal system
(C,P)	Closed loop real system
DPRC	Differential Pressure Control System
FRC	Flow Control System
LRC	Level Control System
LS	Least Squares identification technique
RLS	Recursive Least Squares identification technique
PID	Proportional-integral-derivative algorithm
PRC	Pressure Control System
SM	State Model
TRC	Temperature Control System
BJ	Identification model of Box-Jenkins type
CL	Closed Loop (system, identification method etc.)
CLOE	Closed Loop Output Error (idenfication methods)
CLSI	Closed Loop System Identification
dB	decibel(s) – measuring unit for the signals/systems spectra
E-LSM	Extended Least Squares Method
F-CLOE	Filtered Closed Loop Output Error (identification method)
FIR	Finite Impulse Response (filter, system)
FT	Fourier Transform
G-CLOE	Generalized Closed Loop Output Error (identification method that replaces ARX model by BJ model)
G-LS	Generalized Least Squares (PEMM for the BJ model)
G(s)	Continuous system transfer function
G(z)	Discrete system transfer function
G_R(z^-1), G_S(z^-1)	Pre-specified polynomials for robust control
I-CLOE	Integral Closed Loop Output Error (identification method)I/O Input-Output (type of identification model, transformation, operator, etc.)
IIR	Infinite Impulse Response (filter, system)
I=f(V)	Photovoltaic Current-Voltage characteristic
L	Estimator matrix
LSM	Least Squares Method
M	Sylvester matrix
MIMO	Multi-Input Multi-Output (type of fully multi-variable model or system or process)
MISO	Multi-Input Single-Output (type of multi-variable model or system or process with several inputs and on single output)
MV-LSM	Multi-Variable Least Squares Method
OL	Open Loop (system, identification etc.)
OLOE	Open Loop Output Error (identification method)
OLSI	Open Loop System Identification
PEMM	Prediction Error Minimization Method (identification method)
P(z^-1)	Characteristic polynomial of the system
P=f(I,V)	Photovoltaic Power-Current, Voltage characterstic
PRS	Pseudo-Random signal
PV	Photovoltaic pannel
Q	Observability matrix
R	Controlability matrix
R-ELS	Recursive Extended Least Squares (identification method)
RST	Automatic regulator with 3 polynomials: R (regulation), S (sensitivity) and T (tracking)
RST-YK	RST regulator expressed in Youla-Kucera parametric form
SI	System identification
SISO	Single-Input Single-Output (type of model or system or process with one input and one output)
SNR	Signal-to-Noise Ratio
S_vy(jω)	Disturbance-output sensitivity function
W-CLOE	Weighted Closed Loop Output Error (identification method)
X-CLOE	Extended Closed Loop Output Error (identification method that replaces ARX model with ARMAX model)
X-OLOE	Extended Open Loop Output Error (identification method employed in case of ARMAX model instead of ARX model)
YK	Youla-Kucera (parametric expressions of a regulator)
\|∆M (jω)\|	Modulus margin of the system robustness