DC servos : application and design with MATLAB

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 ofnbsp;a wide range ofnbsp;engineering disciplines, makingnbsp;it difficult and time-consumingnbsp;to master it all--and even harder to find annbsp;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 21st century, Tobin guides the reader on a short journey through "servo school," imparting his lifelong passion for motion control along the way.

Author Notes

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 evermore complex machines of the 21st century, Tobin guides the reader on a short journey through "servo school", imparting his lifelong passion for motion control along the way.

Preface	p. xi
Acknowledgments	p. xv
About the Author	p. xvii
1 DC Servo Systems Defined	p. 1
1.1 Scope and Definition	p. 1
1.2 The Concept of Feedback Control	p. 1
1.3 Types of Control	p. 2
1.3.1 Open Loop vs. Closed Loop Control	p. 2
1.3.2 On/Off vs. Continuous Control	p. 2
1.4 Comments on Motion Control	p. 2
1.4.1 Continuous-Time vs. Discrete-Time Motion Control	p. 3
1.5 Introduction to a DC Motor Driving a Mechanical Load	p. 3
1.6 Realization of a Velocity Servo	p. 6
References	p. 9
2 Anatomy of a Continuous-Time DC Servo	p. 11
2.1 Description	p. 11
2.2 Intended Use	p. 11
2.3 The Prototype	p. 13
2.4 Electrical Design and Construction	p. 13
2.5 Mechanical Design and Construction	p. 15
2.6 Parts List	p. 16
2.7 The Prototype as a Control System	p. 16
2.8 Block Diagram Representations	p. 18
2.9 Electrical Schematic Walk-Through	p. 19
2.9.1 Reference Input Elements	p. 19
2.9.2 Summing Junction	p. 21
2.9.3 Control Elements	p. 21
2.9.4 Disturbance and Disturbance Input Elements	p. 22
2.9.5 Controlled System Elements	p. 23
2.9.6 Feedback Elements	p. 25
2.9.7 Power Supply Elements	p. 26
References	p. 26
3 DC Motors in Servo Systems	p. 27
3.1 Introduction	p. 27
3.2 Operational Principles	p. 27
3.3 Basic Classes of DC Motors	p. 30
3.3.1 Brushed vs. Brushless Motors	p. 30
3.3.2 Wound Field Motors	p. 31
3.3.3 Permanent Magnet Motors	p. 31
3.3.4 The Fractional Horsepower Brushed PMDC Motor	p. 33
3.4 Considerations in Motor Selection	p. 33
3.4.1 Motor Constants	p. 34
3.4.2 Steady-State Torque/Speed Curve	p. 34
3.4.3 Rotor Inertia	p. 35
3.4.4 Power Transmission to a Given Load	p. 36
3.4.4.1 Gear Train Drive	p. 37
3.4.4.2 Belt-Pulley Drive	p. 41
3.4.4.3 Lead Screw Drive	p. 42
3.4.5 Mechanical Friction and Damping	p. 42
3.4.5.1 Sliding Friction	p. 43
3.4.5.2 Viscous Friction	p. 44
3.5 Procedure for Meeting a Design Goal	p. 44
3.5.1 Inertia Matching	p. 47
3.6 Mathematical Modeling of DC Motors and Transmissions	p. 47
3.7 Direct-Drive Model	p. 49
3.7.1 Direct Drive-Transfer Function Representation	p. 49
3.7.2 The State-Variable Approach to Dynamic Systems Modeling	p. 52
3.7.3 Direct Drive-State-Variable Representation	p. 52
3.8 Motor and Gear Train Model	p. 54
3.8.1 Gear Train Drive-Transfer Function Representation	p. 54
3.8.2 Gear Reduction Drive-State-Variable Representation	p. 56
References	p. 57
4 Feedback Control Systems	p. 59
4.1 Introduction	p. 59
4.2 Mathematical Notation	p. 59
4.3 Linear, Time-Invariant Systems	p. 60
4.4 Oscillations, Rotating Vectors, and the Complex Plane	p. 60
4.5 From Fourier Series to Laplace Transform	p. 63
4.6 Elementary Laplace Transforms	p. 66
4.7 System Analysis Using Laplace Transforms	p. 67
4.7.1 Final and Initial Value Theorems	p. 70
4.8 Philosophy of Feedback Control	p. 70
4.8.1 Terminology of Loop Closing	p. 71
4.9 Accuracy of Feedback Systems	p. 72
4.10 Stability of Feedback Systems	p. 73
4.11 Stability Assessment-The Root-Locus Method	p. 74
References	p. 77
5 Proportional Control of a Second-Order DC Servo	p. 79
5.1 Introduction	p. 79
5.2 Proportional Control	p. 79
5.3 Second-Order Approximation	p. 80
5.4 Basic Approach	p. 80
5.5 Transfer Function Development	p. 81
5.6 Response to a Step-Input Command	p. 82
5.6.1 Steady-State Error Analysis for a Step Command	p. 86
5.7 Response to a Ramp-Input Command	p. 89
5.7.1 Steady-State Error Analysis for a Ramp Command	p. 91
5.8 Response to a Sinusoidal-Input Command	p. 92
References	p. 95
6 Compensation of a Continuous-Time DC Servo	p. 97
6.1 Introduction	p. 97
6.2 Compensation Using Derivative Control	p. 98
6.3 Compensation Using Integral Control	p. 100
6.4 Compensation Using Derivative and Integral Controls	p. 101
6.5 Tools for Predicting Performance	p. 101
6.5.1 Root Locus	p. 101
6.5.2 Bode Plot	p. 102
6.5.3 Transient Response	p. 102
6.6 Overall Compensation Strategy	p. 102
6.7 Op-Amps and Control Systems	p. 103
6.7.1 A Control System within a Control System	p. 106
6.7.2 Going around the Servo Loop	p. 108
6.8 Compensation by Theoretical Prediction	p. 111
6.8.1 Synthesizing a P-D Controller	p. 113
6.8.2 Schematic Changes	p. 117
References	p. 121
7 DC Servo Amplifiers and Shaft Encoders	p. 123
7.1 Introduction	p. 123
7.1.1 Scope of Discussion	p. 123
7.2 DC Servo Amplifiers	p. 124
7.2.1 The Nature of PWM	p. 124
7.3 PWM Switch-Mode Amplifiers	p. 125
7.3.1 H-Bridge Topology	p. 125
7.3.2 Waveform Analysis	p. 127
7.3.3 Other Switching Schemes	p. 132
7.4 Sign/Magnitude Control with the LMD18200	p. 133
7.4.1 Notes on Implementation	p. 134
7.5 Voltage Source versus Current Source	p. 137
7.5.1 Voltage and Current Source Stability Assessment	p. 139
7.6 Shaft Encoders	p. 143
7.6.1 The Optical Rotary Incremental Encoder	p. 145
7.6.2 Principle of Operation	p. 147
7.6.3 Signal Transfer through Cables	p. 150
References	p. 151
8 Control of a Position Servo Using a PIC Microcontroller	p. 153
8.1 Introduction	p. 153
8.1.1 On-the-Fly versus Preprogrammed Moves	p. 153
8.1.2 Scope of Discussion	p. 156
8.1.3 DC Servos versus Step Motors	p. 158
8.2 Initial Motor Selection	p. 159
8.3 Setting the Move Requirements	p. 160
8.3.1 The PIC18F4331 Quadrature Encoder Interface	p. 160
8.3.2 Velocity and Position Profiling	p. 161
8.3.3 Setting the Servo Sampling Rate	p. 162
8.3.4 Calculating the Position Profile	p. 165
8.3.5 Other Encoder Resolutions	p. 165
8.4 Hardware and Software Development	p. 168
8.4.1 Software Development	p. 168
8.4.2 Notes on Implementation	p. 169
References	p. 174
Appendix A: The R/C Hobby Servo	p. 177
Bibliography	p. 185
Index	p. 187

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