Predictive Control

By Daniel Lequesne

Predictive Control is aimed at students wishing to learn predictive control, as well as teachers, engineers and technicians of the profession. The book proposes a simple predictive controller where the control laws are given in clear text that requires no calculations. Adjustment, reduced to one or two parameters, is particularly easy, by means of charts, thus allowing the operator to choose the horizon according to the desired performances. Implementation is discussed in detail in two forms: RS or RST controller in z-1, and pseudo-code realization algorithms for a complete program (model and controller).

The book is simple and practical, with the aim of the industrial implementation of many processes: Broïda models, Strejc, integrators, dual integrators, with delay, or with inverse response. All settings are abundantly illustrated with response curves.

• Present a practical guide to predictive control
• Offers a simple predictive controller for a wide range of industrial applications
• Summarizes, in tables, all the calculations that have been carried out to allow immediate implementation

• Language: English
• Publisher: Elsevier Science
• Release date: Jun 26, 2017
• ISBN: 9780081023884

Daniel Lequesne

Daniel Lequesne began his work in speed variation as a business engineer for Alstom. He continued in instrumentation and process control with Emerson Process Management, before devoting himself to the vocational training of adults in automatic and industrial computer science.

Book preview

Predictive Control

Daniel Lequesne

Series Editor

Jean-Paul Bourrières

Table of Contents

Cover

Title page

Copyright

Preface

1: Principle

Abstract

1.1 Trajectory

1.2 Models

1.3 Prediction

2: Control Law

Abstract

2.1 Principle of predictive control

2.2 Stable system with delay

2.3 Integrating systems

2.4 Double integrating systems

3: Process Models

Abstract

3.1 Decomposition of a model into systems of first order

3.2 Sampling transfer function of systems

3.3 Transfer functions execution algorithms

4: Implementation

Abstract

4.1 System of first order

4.2 Stable systems

4.3 Integrating systems

4.4 Double integrating systems

5: Setting of Stable Systems

Abstract

5.1 Setting parameters

5.2 Setting of stable systems

5.3 Strejc models

5.4 Strejc models with inverse response

5.5 Damped oscillating systems

6: Setting of Integrating Systems

Abstract

6.1 Setting elements

6.2 Integrating models and time constants

6.3 Integrating models and time constants with inverse response

6.4 Double integrating systems

7: Performances and Setting

Abstract

7.1 Sampling period

7.2 Model conformity

7.3 Command constraints

7.4 Linearization

7.5 Passage to automatic mode

7.6 Examples of settings

Conclusion

Default setting

Delay, tracking and control

Architecture

Summary

Appendix

A.1 Systems of first order: trajectory

A.2 Decomposition of a damped oscillating system

A.3 Common structure: control law

A.4 System with disturbance

A.5 Specific algorithms

Bibliography

Index

Copyright

First published 2017 in Great Britain and the United States by ISTE Press Ltd and Elsevier Ltd

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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Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

For information on all our publications visit our website at http://store.elsevier.com/

© ISTE Press Ltd 2017

The rights of Daniel Lequesne to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing-in-Publication Data

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

Library of Congress Cataloging in Publication Data

A catalog record for this book is available from the Library of Congress

ISBN 978-1-78548-262-5

Printed and bound in the UK and US

Preface

Daniel Lequesne April 2017

Predictive control is a general technique that can take on many aspects, as it can be adapted to the whole spectrum of automatic control (single or multivariable control, space state control, consideration of constraints, nonlinear systems, robotics, etc.) not to mention the variety of processes that can be controlled.

This work is part of a narrower industrial context, as it relates to single-variable processes (SISO: single input single output) and proposes all the practical ingredients required for an easy implementation that leads to simple control.

Chapter 1 recalls the specificity of predictive control and sets the context: the need to have a process model in order to predict future evolution.

Chapter 2 focuses on the study of control laws, from the principles to obtaining the relations characterizing the controller: U = f(C,M) (U = command, C = set-point, M = measure). The study relates to stable systems, and simple and double integrating systems.

Chapter 3 presents the main process models that can be employed: they are given in terms of sampling transfer function as well as in the form of implementation algorithms (pseudo-code).

Chapter 4 relates to implementation, which involves obtaining a controller in two forms:

– RS or RST type of controller in z−1;

– overall controller algorithm (in pseudo-code) for industrial implementation.

Chapters 5 and 6 relate to the setting of stable systems and integrating systems.

Chapter 7 approaches the practical reality of control, taking into account the constraints: limitations, nonlinearities and influence of the model.

Finally, in the Conclusion, the conclusion on loop control using summary synthesis tables that show the homogeneity of settings over a wide range of processes is presented.

This is above all a practical guide, which proposes a simple predictive controller that can be employed in many industrial applications.

It is addressed to students who wish to learn the basics of predictive control as well as to teachers, engineers and technicians active in this field.

1

Principle

Abstract

Predictive control is a general technique that relies essentially on the capacity to predict how processes behave in order to better correct them.

Keywords

Models; Prediction; Ramp prediction; Simulation; Stable systems; Trajectory

Predictive control is a general technique that relies essentially on the capacity to predict how processes behave in order to better correct them.

The correction is provided by a controller: this is the case for a classical control loop, in which the controller receives a setpoint value C and measure M of the quantity to be controlled; it provides a command U that controls the process. The loop is represented in Figure 1.1 where the input X symbolizes the eventual external disturbances.

Figure 1.1 Control loop

The specificity of predictive control resides in the calculation of what will be measured in the future and its consideration in order to determine the command for obtaining the given desired trajectory corresponding to a setpoint value. This results in the following points:

– it is not possible to know a future measurement unless a representation model of the process is available;

– a future moment implies a present moment: the controller is numerical, with a sampling period Te; at each Te, the command U is recalculated;

– the trajectory is defined by the user and it is a way of representing the performances to be obtained.

1.1 Trajectory

The trajectory is defined relative to the (desired) setpoint and the measure on the process as shown in Figure 1.2. Instant k is the present instant; the trajectory represents the desired evolution of the measure starting from its current value M(k) to a final value that is equal to the setpoint. The represented setpoint corresponds to the current instant, C(k), and it is supposed constant during the future period, since it is the aimed value.

Figure 1.2 Desired future trajectory at instant k

If the setpoint varies, it will have a new value at the next instant, and this value will be the new aim, being supposed constant during the prediction.

At each Te, there is a desired trajectory of amplitude C(k) – M(k), therefore variable.

If the measure is stabilized at the setpoint and a setpoint step ΔC is applied, the trajectory of amplitude ΔC represents the desired process response in tracking mode. It is characterized by its form and its response time.

In practice, a first-order exponential response is often chosen due to its simple and well-known form:

or the sampling form:

T is the desired time constant which allows us to obtain a response time (at 95%): tr = 3T.

Figure 1.3 Exponential trajectory

Chapter 5 (Setting of Stable Systems) provides other elements on the choice and role of trajectories.

1.2 Models

Most control methods use a process model. Even the Proportional Integral Derivative (PID) controllers use a process model to calculate their actions. Compared to predictive control, there is a structural difference.

When using classical methods, the model is on paper; it results from identifying the process that allows its characterization and the calculations on paper that yield the control formulas. In the best-case scenario, these calculations can be computerized and lead to an automated control of the controller.

In predictive control, the model is embedded in the controller and it operates in real time: the model measure (which is equal to the process measure if the model is perfect) at each sampling period is known and its future evolution can be calculated in order to better correct the action of the controller.

It leads to the block diagram is shown in Figure 1.4.

Figure 1.4 Predictive controller

There are two types of models: realigned or independent, as shown in Figure 1.5.

Figure 1.5 Realigned model (on the left) and independent model (on the right)

In the realigned model, the output is permanently reset on the process.

1.2.1 Stable systems

Counterintuitively, the independent model yields better results and it will be used to simulate stable processes.

In this book, the study of stable processes is limited to Strejc models, with an eventual inverse response, with and without delay.

1.2.2 Unstable systems

This direct approach to modeling is not adequate for unstable processes. In a closed loop, the implementation is reflected by compensation of an unstable pole by an unstable zero, which does not work in practice [BOR 93].

The remedy is to decompose the unstable model Mi into two stable models M1 and M2 as shown in Figure 1.6. It is worth noting that the sign + of the M2 feedback is rather recommended as an indicator of the unstable aspect of the model.

Figure 1.6 Decomposition of an unstable model into two stable models

The equivalence is expressed by the relation:

This relation offers several choices, the most simple of which is to choose a first-order M2, and then deduce M1 from the equivalence relation. The method involves replacing the input of M2 (which is the model output) with the measure M of the process as shown in Figure 1.7. This is a type of realigned model.

Figure 1.7 Unstable process modeling

This approach presents the advantage that it can be extended to more complex models of the type:

where I(p) is an unstable model and Ms(p) is a stable transfer function.

Let us consider the example of an integrating system with Strejc model and inverse response:

The integrating part I(p) will be modeled according to the method shown in Figure 1.6, by choosing a first-order M2:

A time constant Ta can be chosen (see Chapter 6). The stable part Ms(p) will be added in series on the command U. The result is presented in Figure 1.8.

Figure 1.8 Modeling an integrating system with Strejc model and inverse response

1.2.2.1 Case of a system with two unstable modes

This is notably the case of two integrators in