Motion Control Systems E-Book

Asif Sabanovic

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 542

Veröffentlichungsjahr: 2011

Beschreibung

Motion Control Systems is concerned with design methods that support the never-ending requirements for faster and more accurate control of mechanical motion. The book presents material that is fundamental, yet at the same time discusses the solution of complex problems in motion control systems. Methods presented in the book are based on the authors' original research results. Mathematical complexities are kept to a required minimum so that practicing engineers as well as students with a limited background in control may use the book. It is unique in presenting know-how accumulated through work on very diverse problems into a comprehensive unified approach suitable for application in high demanding, high-tech products. Major issues covered include motion control ranging from simple trajectory tracking and force control, to topics related to haptics, bilateral control with and without delay in measurement and control channels, as well as control of nonredundant and redundant multibody systems. * Provides a consistent unified theoretical framework for motion control design * Offers graduated increase in complexity and reinforcement throughout the book * Gives detailed explanation of underlying similarities and specifics in motion control * Unified treatment of single degree-of-freedom and multibody systems * Explains the fundamentals through implementation examples * Based on classroom-tested materials and the authors' original research work * Written by the leading researchers in sliding mode control (SMC) and disturbance observer (DOB) * Accompanying lecture notes for instructors * Simulink and MATLAB® codes available for readers to download Motion Control Systemsis an ideal textbook for a course on motion control or as a reference for post-graduates and researchers in robotics and mechatronics. Researchers and practicing engineers will also find the techniques helpful in designing mechanical motion systems.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface

About the Authors

Part One: Basics of Dynamics and Control

Chapter 1: Dynamics of Electromechanical Systems

1.1 Basic Quantities

1.2 Fundamental Concepts of Mechanical Systems

1.3 Electric and Electromechanical Systems

References

Further Reading

Chapter 2: Control System Design

2.1 Basic Concepts

2.2 State Space Representation

2.3 Dynamic Systems with Finite Time Convergence

References

Further Reading

Part Two: Issues in Motion Control

Chapter 3: Acceleration Control

3.1 Plant

3.2 Acceleration Control

3.3 Enforcing Convergence and Stability

3.4 Trajectory Tracking

References

Further Reading

Chapter 4: Disturbance Observers

4.1 Disturbance Model Based Observers

4.2 Closed Loop Disturbance Observers

4.3 Observer for Plant with Actuator

4.4 Estimation of Equivalent Force and Equivalent Acceleration

4.5 Functional Observers

4.6 Dynamics of Plant with Disturbance Observer

4.7 Properties of Measurement Noise Rejection

4.8 Control of Compensated Plant

References

Further Reading

Chapter 5: Interactions and Constraints

5.1 Interaction Force Control

5.2 Constrained Motion Control

5.3 Interactions in Functionally Related Systems

References

Further Reading

Chapter 6: Bilateral Control Systems

6.1 Bilateral Control without Scaling

6.2 Bilateral Control Systems in Acceleration Dimension

6.3 Bilateral Systems with Communication Delay

References

Further Reading

Part Three: Multibody Systems

Chapter 7: Configuration Space Control

7.1 Independent Joint Control

7.2 Vector Control in Configuration Space

7.3 Constraints in Configuration Space

7.4 Hard Constraints in Configuration Space

References

Further Reading

Chapter 8: Operational Space Dynamics and Control

8.1 Operational Space Dynamics

8.2 Operational Space Control

References

Further Reading

Chapter 9: Interactions in Operational Space

9.1 Task–Constraint Relationship

9.2 Force Control

9.3 Impedance Control

9.4 Hierarchy of Tasks

References

Further Reading

Index

This edition first published 2011

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Library of Congress Cataloging-in-Publication Data

Šabanovi, Asif.

Motion control systems / Asif Šabanovi.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-82573-0 (hardback)

1. Motion control devices. I. Title.

TJ214.5.S33 2011

621.4–dc22

2010041054

Print ISBN: 978-0-470-82573-0

ePDF ISBN: 978-0-470-82574-7

oBook ISBN: 978-0-470-82575-4

ePub ISBN: 978-0-470-82829-8

Preface

This book is concerned with the development of an understanding of the design issues in controlling motion within mechanical systems. There seems to be a never-ending discussion on what motion control is – a new field or an extension or a combination of existing fields. Despite this, both industry and academia have been involved in fulfilling real-world needs in developing efficient design methods that will support never-ending requirements for faster and accurate control of mechanical motion. High-precision manufacturing tools, product miniaturization, the assembly of micro- and nanoparts, a need for high accuracy and fidelity of motion in robot-assisted surgery – in one way or another all these employ motion control.

Looking back at its brief history, the concept of motion control was not well established in the 1970s and 1980s. Many people still believed that controlling the torque needed for a load should be achieved through velocity control. However, we found that torque and velocity could be separately controlled. This was very effective for dexterous motion in robotics. We were very excited and naturally wanted to announce this interesting finding and create a new field. Meetings and discussions with other researchers and students encouraged us to create a new workshop covering the problems of motion control. In March 1990, the first workshop dedicated only to motion control (the IEEE International Workshop on Advanced Motion Control – later known as AMC Workshops) was held at Keio University. To our surprise, there were more than 100 papers presented at the workshop. Since then, many ideas, concepts and results have come out. Subsequently, motion control gained visibility and attracted many researchers. Time flows very fast and now it is time to summarize the results, particularly for the new students coming into this field. We hope readers enjoy this book.

The intention of this book is to present material that is both elementary and fundamental, but at the same time to discuss the solution of complex problems in motion control systems. We recognize that the motion control system as an entity, separable from the rest of the universe (the environment of the systems) by a conceptual or physical boundary, is composed of interacting parts. This allows treatment of simple single degree of freedom systems as well as complex multibody systems in a very similar if not identical way. By considering complex motion control systems as physically or conceptually interconnected entities, design ideas applied to single degree of freedom systems can also be applied with small changes to complex multibody systems. Material in this book is treated in such a way that the complexity of a system is gradually increased, starting from fundamentals shown in the framework of single degree of freedom systems and ending with a treatment for the control of complex multibody systems. Mathematical complexities are kept to a required minimum so that practicing engineers as well as students with a limited background in control may use the book.

This book has nine chapters, divided into three parts. The first part serves as an overview of dynamics and control. It is intended for those who would like to refresh ideas related to mathematical modeling of electromechanical systems and control. The first chapter is related to the dynamics of mechanical and electromechanical systems. It presents basic ideas for deriving equations of motion in mechanical and electromechanical systems. The second chapter gives fundamental concepts in the analysis and design of control systems. Design is discussed for systems with continuous and discontinuous control.

In the second part we discuss fundamentals of acceleration control framework for motion control systems and give essential methods which are used in the third part of the book. Chapter 3 deals with single degree of freedom motion control system with asymptotic or finite time convergence to the equilibrium. The design is based on the assumption that any disturbance due to a change in parameters and interaction with environment should be rejected. In the fourth chapter the design of a disturbance observer and the dynamics of a system with a disturbance observer is discussed. Chapter 5 discusses the behavior of single degree of freedom motion systems in interaction with the environment. While rejections of the interaction forces is a basic requirement in Chapter 3, Chapter 5 considers modification of motion due to interaction. Such a modification introduces a more natural behavior of the motion control system. The interaction control is extended to controlling systems that need to maintain some functional relationship, thus introducing a conceptual functional relationship between physically separated systems. This serves as a background for a discussion of specific relationships – bilateral control – discussed in chapter six for systems without and with a delay in the communication channels.

The third part extends the results obtained in part two to controlling fully actuated multibody mechanical systems. Chapter 7 discusses the control of constrained systems in configuration space and the enforcement of constraints by a selected group of degrees of freedom. In Chapter 8 control design in operational space is carried out for nonredundant and redundant tasks. The relationship between task and constraint is discussed and the similarities and differences between the two are investigated. Chapter 9 discusses problems related to the concurrent realization of multiple redundant tasks for constrained or unconstrained systems. Problems in the hierarchy of the execution of multiple tasks are described.

The idea of writing this book stems from a long-term collaboration between the authors. It began in early 1980s when we met at a conference in Italy and developed during Asif's stay at Keio. The book is the result of our discussions and common understanding of problems and control methods applicable in the field of motion control. Obviously we do not pretend that it is a final world; rather it is just a beginning, maybe a first step in establishing motion control as a stand alone academic discipline. Results produced by many other authors are included in the book in one way or another. Many authors, and especially our students, influenced our way of treating certain material.

We would like to thank our numerous students, from whom we have learned a lot, and we hope that they have learned something from us. We would like to express our sincerest thanks to our families for their support during many years of research and especially during the preparation of the manuscript.

Asif Šabanovi

Kouhei Ohnishi

About the Authors

Asif Šabanovi is Professor of Mechatronics at Sabancı University, Istanbul, Turkey. He received undergraduate and graduate education in Bosnia and Herzegovina, at the Faculty of Electrical Engineering, University of Sarajevo. From 1970, for 20 years he was with ENERGOINVEST-IRCA, Sarajevo, where he was head of research in sliding mode control applications in power electronics and electric drives. He was Visiting Professor at Caltech, USA, at Keio University, Japan, and at Yamaguchi University, Japan. He was Head of the CAD/CAM and Robotics Department at Tubitak – MAM, Turkey. He has received Best Paper Awards from the IEEE. His fields of interest include motion control, mechatronics, power electronics and sliding mode control.

Kouhei Ohnishi is Professor of the Department of System Design Engineering at Keio University, Yokohama, Japan. After receiving a PhD in electrical engineering from the University of Tokyo in 1980, he joined Keio University and has been teaching, conducting research and educating students for more than 30 years. His research interests include motion control, haptics and power electronics. He received Best Paper Awards and a Distinguished Achievement Award from the Institute of Electrical Engineers of Japan. He received the Dr.-Ing. Eugene Mittelmann Achievement Award from the IEEE Industrial Electronics Society (IES). He is an IEEE Fellow and served as President of the IEEE IES in 2008 and 2009. He enjoys playing clarinet on holidays.

Part One

Basics of Dynamics and Control

No mathematical representation can precisely model a real physical system. One cannot predict exactly what the output of a real physical system will be even if the input is known, thus one is uncertain about the system. Uncertainty arises from unknown or unpredictable inputs (disturbance, noise, etc.), unpredictable dynamics and unknown or disregarded dynamics and change of parameters. Yet, to design control systems one need a mathematical description of the physical systems – plants – that will allow the application of mathematical tools to predict the output response for a defined input, so that it can be used to design a controller. The models should allow a design which leads to a control that will work on the real physical system. This limits the details needed to describe the system and the scope of the details we will be including in the mathematical models of physical systems.

Generally speaking the objective in a control system is to make some output behave in a desired way by manipulating some inputs. The output of design is a mathematical model of a controller that must be implemented. Motion control involves assisting in the choice and configuration of the overall system or, in short, taking a system view of the overall performance. For this reason it is important that an applied control framework not only leads to good and consistent designs but also indicates when the performance objectives cannot be met. In order to make sense of the issues involved in the design of a motion control system, a short overview of the control methods for analysis and design are presented in Chapter 2. In addition to classical frequency and state space methods, systems with finite-time convergence are treated.

Chapter 1

Dynamics of Electromechanical Systems

In this chapter we will discuss methods of deriving equations of motion for mechanical and electromechanical systems. We use the term equations of motion to understand the relation between accelerations, velocities and the coordinates of mechanical systems [1]. For electromechanical systems the equations of motion, in addition to mechanical coordinates, also establish the relationship between electrical system coordinates and their rate of change.

Traditionally, introductory mechanics begins with Newton's laws of motion which relate force, momentum and acceleration vectors. Analytical mechanics in the form of Lagrange equations provides an alternative and very powerful tool for obtaining the equations of motion. The Lagrange equations employ a single scalar function, and there are no annoying vector components or associated trigonometric manipulations. Moreover, analytical approaches using Lagrange equations provide other capabilities that allow the analysis of a wide range of systems.

The advantage of using Lagrange equations is that they are applicable to an extensive field of particle and rigid body problems, including electromechanical systems, by reducing derivation to a single procedure while repeating the same basic steps. The procedure is based on scalar quantities such as energy, work and power, rather than on vector quantities.

In this chapter only basic ideas will be discussed, without detailed and long derivations. Our goal is to show ways of deriving the equations of motion as a first step for the later design of control systems. The scope is to show basic procedures and their application to different plants (mechanical, electrical, electromechanical) often used in motion control.

1.1 Basic Quantities

1.1.1 Elements and Basic Quantities in Mechanical Systems

Mechanics is based on the notion that the measure of mechanical interactions between systems is force and/or torque (the turning effect of forces):

Force is related to deformation by material properties (elasticity, viscosity, etc.) and to motion by the laws of mechanics.Every action has an equal and opposite reaction.The net force on a system causes a net linear acceleration and the net turning effect of forces on a system causes it to rotationally accelerate.The change of energy of a system is due to energy flowing into the system.

In mechanics, a body receives work from a force or a torque that acts on it if the body undergoes a displacement in the direction of the force or torque, respectively, during the action. It is the force or torque, not the body, which does the work. Basic quantities and their relations will be given here for a rigid body with pure translational motion (with position and velocity ) or pure rotational motion (with angular position and angular speed ).

The work done by a force on a rigid body moving from position along a translational path to position is defined by . Here is the differential displacement of the body moving along the path .

The work done by a torque on a body during its finite rotation, parallel to , from angular position to angular position is given by , where is the angular differential displacement.

The motion of a mass at the position is governed by Newton's second law

(1.1)

Here is the force, is the linear momentum.

The kinetic energy of nonrotating rigid body with mass and velocity is given by

(1.2)

The change in kinetic energy with time is . The work done by changing position from to can be expressed as

For a conservative force (depending only on positions and not on velocities, thus the work done is independent on the path taken) the closed path work is zero. This force can appear as a result of a potential and can be expressed as . This property implies the law of conservation of energy expressed as

(1.3)

The number of degrees of freedom of a system is the number of coordinates that can be independently varied, that is, the number of ‘directions’ a system can move in small displacements from any initial configuration. A configuration of rigid multibody system with degrees of freedom (n-dof) is described by a vector completely specifying the position of each point of multibody system. The set of all admissible configurations is called the configuration space. If the number of degrees of freedom of a system of particles is less than we say that the system is constrained. A system of free particles constrained to move in two dimensions has -dof. The number of degrees of freedom is equal to the number of independent generalized coordinates.

1.1.2 Elements and Basic Quantities in Electric Systems

In this section, electric energy storage and flow will be shown and the fundamental relations related to the electric energy storage in the form of magnetic field or electric field energy will be derived. Basic quantities and relations are shown for systems with concentrated parameters which allow the space changes of the quantities to be neglected thus dynamics can be represented by ordinary differential equations instead of partial differential equations.

1.1.2.1 Inductance and Magnetic Field Energy

The concept of inductance is associated with physical objects consisting of one or more loops of conducting material. An ideal inductor is associated with three variables: current , flux and voltage . The constitutive relationship between the flux-linkage and the current is given as either or , respectively. There also exists a dynamic relationship between the flux-linkage and voltage (Faraday's law) described by .

The work done in establishing a flux-linkage in an inductor is the stored magnetic energy. It is a function of the flux-linkage and the current and can be expressed by . Here the subscript ‘e’ is used to distinguish electromagnetic energy functions from the mechanical systems energy functions. The current can be determined from . If the constitutive relation is linear, then , where is defined as the inductance of the inductor, and the stored magnetic energy becomes

(1.4)

It is interesting to note the role of the energy and the coenergy variables. Let the constituent relation describing flux linkage and its inverse be known. Then product for any given point on the curve can be expressed as the sum of the integral and its dual integral representing the so-called magnetic coenergy