John Chiasson - An Introduction to System Modeling and Control

An Introduction to System Modeling and Control

John Chiasson

Boise State University
Boise, Idaho
United States

This edition first published 2022
2022 John Wiley & Sons, Inc.

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Library of Congress CataloginginPublication Data

Names: Chiasson, John, author.
Title: An introduction to system modeling and control / John Chiasson.
Description: First edition. | Hoboken, NJ : John Wiley & Sons, Inc., 2022.
| Includes bibliographical references and index.
Identifiers: LCCN 2021030670 (print) | LCCN 2021030671 (ebook) | ISBN
9781119842897 (cloth) | ISBN 9781119842903 (adobe pdf) | ISBN
9781119842910 (epub)
Subjects: LCSH: Systems engineeringMathematics. | Mathematical models.
Classification: LCC TA168 .C55 2022 (print) | LCC TA168 (ebook) | DDC
620.001/171dc23
LC record available at https://lccn.loc.gov/2021030670
LC ebook record available at https://lccn.loc.gov/2021030671

Cover Design: Wiley
Cover Image: By Walter Barie

Preface

Quite honestly, I never thought I would write a book for a first controls course. So, what happened? Well, in my teaching career I have taught out of the textbooks by Ogata ). I realize that my emphasis on detailed modeling may be a bug to some (rather than a feature) as students find it difficult and it takes away from doing control stuff. However, as a colleague of mine put it, students develop important insight when they understand where the dynamic models come from and any linearization, approximation, or simplification used to obtain them.

It seemed to me early in my career that teaching the first controls course seemed to be more about its techniques, i.e., manipulating block diagrams, drawing root locus, Bode and Nyquist plots, doing the RouthHurwitz test, etc. Yet I think the course should be about making some physical system do what you want it to do such as having a robot arm rotate despite the weight of the object in its end effector, or ensure a magnetic bearing maintains an air gap despite various loads on it, keeping a pendulum rod pointing straight up, etc. I recall a colleague commenting on a lecture he gave in which he referred to the standard unity feedback controller block diagram (Figure ) and told the class that the controller was to be designed so that A student then simply asked why not just get rid of the blocks and set It seems that in teaching the first controls course we end up manipulating block diagrams so much and so easily that students get lost in the abstraction not understanding what they represent.

Control system in standard block diagram form.

Figures such as on the next page are included to help the students remember what a block diagrams represents.

Spending the time to do detailed derivations of a few models helps the student to understand and remember what the transfer function models represent. A similar confusion arises in the modeling of disturbances. When a disturbance is shown on the block diagram model, it is typically placed as input to the physical system. For example, one might have a load torque on a motor, but in the block diagram this disturbance is modeled coming into the motor input, which is a voltage (). I explain how this load torque is modeled as an equivalent voltage disturbance which has the same effect on the position/speed of the rotor as the actual load torque. This sort of understanding seems to be lost in the standard manipulations of converting a differential equation model into a block diagram model. Of course, some good laboratory work can really help to clarify these ideas as well.