DC Servos: Application and Design with MATLAB / Edition 1

by Stephen M. Tobin

Overview

Fundamental to the control of mechatronic devices, the servomechanism applies feedback from the device in question to regulate its position, velocity, or some other physical attribute. Successful mastery of servo control requires an understanding of a wide range of engineering disciplines, making it difficult and time-consuming to master it all-and even harder to find an all-encompassing guide that shows you how.

DC Servos: Application and Design with MATLAB® is designed and written with this problem in mind. It breaks down the practical knowledge required from the various branches of applied science-electrical and mechanical engineering, analog electronics, mechanics, control theory, digital electronics, embedded computing, and firmware design-into a cohesive and usable framework. Today, DC servos are working around the world in countless applications-CD players, ink-jet printers, robots, machining centers, vending machines, eyeglass manufacturing machines, home appliances, and automotive seat positioners, just to name a few.

This book balances coverage of theoretical and practical aspects of application and design of DC servomechanisms. It also provides detailed coverage of feedback transducers, particularly the application of optical encoders to real systems. It covers how to use the MATLAB^® Control System Toolbox specifically for servo design, to make the design process faster and more interactive. It also presents two complete, bench-tested reference designs that can be duplicated using readily available parts, so you can build your own servo and see it in action.

Author Stephen M. Tobin is an expert in motion control and electro-optical instrumentation and a respected consultant in the medical device and manufacturing automation communities. In order to instill confidence in the engineers, scientists, students, and hobbyists designing the ever more complex machines of the 21^st century, Tobin guides the reader on a short journey through "servo school," imparting his lifelong passion for motion control along the way.

Product Details

ISBN-13:	9781420080032
Publisher:	Taylor & Francis
Publication date:	10/13/2010
Pages:	220
Product dimensions:	6.10(w) x 9.20(h) x 0.70(d)

About the Author

Stephen M. Tobin is the founder and president of Optical Tools Corporation. He received his B.S. degree in Mechanical Engineering from the University of New Hampshire in 1983. He spent the first five years of his career in the motion control field, working in step motor and optical encoder design engineering with divisions of Allied-Signal and Dresser Industries. He then turned his attention to the development of electro-optical instrumentation. He joined General Eastern Instruments (now a division of General Electric) in 1988, working on closed-loop optical humidity measurement systems. While employed at General Eastern, he earned his M.S. degree in electrical engineering with a concentration in electro-optics from Tufts University in 1994. He later spent six years developing medical devices at Arthur D. Little, a world-renowned consulting firm based in Cambridge, Massachusetts. Motion control continues to be a lifelong passion for Mr. Tobin, who founded Optical Tools Corporation in 2004 and continues to consult for the medical device and manufacturing automation communities. He holds four U.S. patents and is a member of the Tau Beta Pi National Engineering Honor Society.

Table of Contents

Preface xi

Acknowledgments xv

About the Author xvii

1 DC Servo Systems Defined 1

1.1 Scope and Definition 1

1.2 The Concept of Feedback Control 1

1.3 Types of Control 2

1.3.1 Open Loop vs. Closed Loop Control 2

1.3.2 On/Off vs. Continuous Control 2

1.4 Comments on Motion Control 2

1.4.1 Continuous-Time vs. Discrete-Time Motion Control 3

1.5 Introduction to a DC Motor Driving a Mechanical Load 3

1.6 Realization of a Velocity Servo 6

References 9

2 Anatomy of a Continuous-Time DC Servo 11

2.1 Description 11

2.2 Intended Use 11

2.3 The Prototype 13

2.4 Electrical Design and Construction 13

2.5 Mechanical Design and Construction 15

2.6 Parts List 16

2.7 The Prototype as a Control System 16

2.8 Block Diagram Representations 18

2.9 Electrical Schematic Walk-Through 19

2.9.1 Reference Input Elements 19

2.9.2 Summing Junction 21

2.9.3 Control Elements 21

2.9.4 Disturbance and Disturbance Input Elements 22

2.9.5 Controlled System Elements 23

2.9.6 Feedback Elements 25

2.9.7 Power Supply Elements 26

References 26

3 DC Motors in Servo Systems 27

3.1 Introduction 27

3.2 Operational Principles 27

3.3 Basic Classes of DC Motors 30

3.3.1 Brushed vs. Brushless Motors 30

3.3.2 Wound Field Motors 31

3.3.3 Permanent Magnet Motors 31

3.3.4 The Fractional Horsepower Brushed PMDC Motor 33

3.4 Considerations in Motor Selection 33

3.4.1 Motor Constants 34

3.4.2 Steady-State Torque/Speed Curve 34

3.4.3 Rotor Inertia 35

3.4.4 Power Transmission to a Given Load 36

3.4.4.1 Gear Train Drive 37

3.4.4.2 Belt-Pulley Drive 41

3.4.4.3 Lead Screw Drive 42

3.4.5 Mechanical Friction and Damping 42

3.4.5.1 Sliding Friction 43

3.4.5.2 Viscous Friction 44

3.5 Procedure for Meeting a Design Goal 44

3.5.1 Inertia Matching 47

3.6 Mathematical Modeling of DC Motors and Transmissions 47

3.7 Direct-Drive Model 49

3.7.1 Direct Drive-Transfer Function Representation 49

3.7.2 The State-Variable Approach to Dynamic Systems Modeling 52

3.7.3 Direct Drive-State-Variable Representation 52

3.8 Motor and Gear Train Model 54

3.8.1 Gear Train Drive-Transfer Function Representation 54

3.8.2 Gear Reduction Drive-State-Variable Representation 56

References 57

4 Feedback Control Systems 59

4.1 Introduction 59

4.2 Mathematical Notation 59

4.3 Linear, Time-Invariant Systems 60

4.4 Oscillations, Rotating Vectors, and the Complex Plane 60

4.5 From Fourier Series to Laplace Transform 63

4.6 Elementary Laplace Transforms 66

4.7 System Analysis Using Laplace Transforms 67

4.7.1 Final and Initial Value Theorems 70

4.8 Philosophy of Feedback Control 70

4.8.1 Terminology of Loop Closing 71

4.9 Accuracy of Feedback Systems 72

4.10 Stability of Feedback Systems 73

4.11 Stability Assessment-The Root-Locus Method 74

References 77

5 Proportional Control of a Second-Order DC Servo 79

5.1 Introduction 79

5.2 Proportional Control 79

5.3 Second-Order Approximation 80

5.4 Basic Approach 80

5.5 Transfer Function Development 81

5.6 Response to a Step-Input Command 82

5.6.1 Steady-State Error Analysis for a Step Command 86

5.7 Response to a Ramp-Input Command 89

5.7.1 Steady-State Error Analysis for a Ramp Command 91

5.8 Response to a Sinusoidal-Input Command 92

References 95

6 Compensation of a Continuous-Time DC Servo 97

6.1 Introduction 97

6.2 Compensation Using Derivative Control 98

6.3 Compensation Using Integral Control 100

6.4 Compensation Using Derivative and Integral Controls 101

6.5 Tools for Predicting Performance 101

6.5.1 Root Locus 101

6.5.2 Bode Plot 102

6.5.3 Transient Response 102

6.6 Overall Compensation Strategy 102

6.7 Op-Amps and Control Systems 103

6.7.1 A Control System within a Control System 106

6.7.2 Going around the Servo Loop 108

6.8 Compensation by Theoretical Prediction 111

6.8.1 Synthesizing a P-D Controller 113

6.8.2 Schematic Changes 117

References 121

7 DC Servo Amplifiers and Shaft Encoders 123

7.1 Introduction 123

7.1.1 Scope of Discussion 123

7.2 DC Servo Amplifiers 124

7.2.1 The Nature of PWM 124

7.3 PWM Switch-Mode Amplifiers 125

7.3.1 H-Bridge Topology 125

7.3.2 Waveform Analysis 127

7.3.3 Other Switching Schemes 132

7.4 Sign/Magnitude Control with the LMD18200 133

7.4.1 Notes on Implementation 134

7.5 Voltage Source versus Current Source 137

7.5.1 Voltage and Current Source Stability Assessment 139

7.6 Shaft Encoders 143

7.6.1 The Optical Rotary Incremental Encoder 145

7.6.2 Principle of Operation 147

7.6.3 Signal Transfer through Cables 150

References 151

8 Control of a Position Servo Using a PIC Microcontroller 153

8.1 Introduction 153

8.1.1 On-the-Fly versus Preprogrammed Moves 153

8.1.2 Scope of Discussion 156

8.1.3 DC Servos versus Step Motors 158

8.2 Initial Motor Selection 159

8.3 Setting the Move Requirements 160

8.3.1 The PIC18F4331 Quadrature Encoder Interface 160

8.3.2 Velocity and Position Profiling 161

8.3.3 Setting the Servo Sampling Rate 162

8.3.4 Calculating the Position Profile 165

8.3.5 Other Encoder Resolutions 165

8.4 Hardware and Software Development 168

8.4.1 Software Development 168

8.4.2 Notes on Implementation 169

References 174

Appendix A: The R/C Hobby Servo 177

Bibliography 185

Index 187