Modern Practice in Servo Design

Contents

Preface

Authors

Chapter 1. Basic Servomechanism Theory


1.1. Introduction


1.2. The Laplace Transform and Complex Frequencies


1.3. Transfer Functions


1.4. The Complex Frequency Plane


1.5. Block Diagrams


1.6. Closed Loop Transfer Functions


1.7. Absolute Stability


1.8. Frequency Response Design Methods


1.8.1. NyquistPlot


1.8.2. Bode Plot


1.8.3. Nichols Charts


1.8.4. The Root Locus Method


1.8.5. Servo Design Using the Root Locus Method


1.8.6. Routh's Stability Criterion


1.9. Servo Components


1.9.1. Error Detectors


1.9.2. Potentiometer Detectors


1.9.3. Synchro Error Detectors


1.9.4. Block Diagram of the Error Detector


1.10. Servo Compensation


1.11. Power Amplification


1.12. The d.c. Servo Motor


1.13. Gearing and Mechanical Load Resonance


1.14. Conclusion

References

Chapter 2. Preliminary Design of a Large Servomechanism


2.1. Introduction


2.2. Performance Specification


2.3. Steady State and Transient Performance


2.3.1. Servomechanism Errors


2.3.2. Steady-state Error Coefficients


2.4. Selection of Motor and Gear Ratio


2.4.1. d.c. Servo Motors


2.4.2. Gear Ratio Selection


2.4.3. Motor Rating


2.5. Effects of Disturbances


2.5.1. Evaluation of Errors from Spectral Density Functions


2.6. Example: Ward-Leonard Speed Regulator


2.6.1. Series Compensation


2.6.2. Feedback Compensation

References

Chapter 3. Development of the Servo Design


3.1. Introduction


3.2. Mechanics


3.3. The Motors


3.4. The Power Stage


3.4.1. General Requirements


3.4.2. The Rotary Power Drive


3.5. The Exciter and Servo Amplifiers


3.6. The Completed Control Loop and Its Stability


3.7. Saturation Levels and Designed Non-linearities


3.7.1. Effects of Saturation on Stability


3.7.2. The Error Channels


3.7.3. Saturation Levels


3.7.4. Coarse Braking


3.8. Mechanical Resonance


3.8.1. Resonance Inside the Feedback Loop


3.8.2. Resonance


3.8.3. Anti-resonance


3.8.4. Locked Rotor Resonant Frequency


3.8.5. The Anti-resonant Rotor Frequency


3.8.6. The Free Rotor and Load Resonance


3.8.7. Resonance Outside the Servo Loop


3.8.8. Cascaded Resonances and Compensation


3.8.9. Example


3.9. Additional Factors


3.10. Summary


3.11. Appendix

References

Chapter 4. Digital Servo Techniques


4.1. Introduction


4.2. Speed Control


4.3. Digital Codes


4.3.1. Binary Code


4.3.2. BCD Code


4.3.3. Gray Code


4.4. Digital Circuitry


4.4.1. Logic Functions


4.4.2. Boolean Algebra


4.4.3. Bi-stable Memory Unit


4.4.4. Binary Counters


4.4.5. 8421 BCD Counter


4.4.6. 2421 BCD Counter


4.4.7. Bi-directional Counters


4.4.8. Digital Subtractors


4.5. Digital Encoders


4.5.1. Brush Contact Encodes


4.5.2. Optical Encoders


4.5.3. Magnetic Encoders


4.5.4. Inductive Encoders


4.5.5. Capacitive Encoders


4.5.6. Encoder Ambiguity


4.6. Digital to Analog Convertors


4.7. Stepper Motors


4.8. Digital Position Control of a Large Antenna


4.9. Conclusions

References

Chapter 5. Design of Large Antennae for Radio Telescope and Satellite Trackers


5.1. Introduction


5.2. Servo System Performance


5.2.1. Radio Telescopes


5.2.2. Satellite Trackers


5.3. Servo Control Input Equipment


5.3.1. Radio Telescopes


5.3.2. Other Methods of Polar Coordinate to Alt./Az. Coordinate Conversion


5.3.3. Input Equipment for Satellite Trackers


5.4. Choice of Servo Configuration


5.4.1. Basic Servo Design Philosophy


5.5. Dynamic Performance


5.5.1. Zenith Angle Velocity


5.5.2. Azimuth Velocity


5.5.3. Accelerations


5.6. Tracking Accuracy Requirements


5.6.1. Error Distribution


5.6.2. Acceleration Error


5.6.3. Error Due to Tracking Receiver Noise


5.6.4. Tracking Null Shift Error


5.6.5. Wind Gusts: Mechanical Deflections


5.6.6. Servo Bandwidth


5.6.7. Aerial Inertia


5.6.8. Motor Rating


5.6.9. Mechanical Natural Frequency


5.7. Closed Loop Performance


5.7.1. Wind Gusts: Servo Errors


5.7.2. Running into Alignment


5.8. Commissioning and Testing


5.8.1. Maximum Acceleration and Velocity Checks


5.8.2. Response Tests


5.9. Conclusion

References

Chapter 6. The Practical Control System


6.1. Introduction


6.2. Practical Servos


6.2.1. Interference


6.2.2. Environment


6.2.3. User Requirements


6.2.4.Saturations


6.2.5. Backlash


6.2.6. Friction


6.3. On-site Adjustments


6.3.1. Zero Alignment


6.3.2. Servo Adjustments


6.3.3. Performance


6.3.4. Optimization


6.4. Measuring Devices and Error Detection


6.4.1. Potentiometers


6.4.2. Synchros


6.4.3. Inductosyn


6.4.4. Optical Measuring Device


6.4.5. Digital Error Detectors


6.4.6. Mechanical Shaft Encoder


6.4.7. Optical Encoders


6.4.8. Magnetic Encoder


6.5. Programming the Input Command to a Servomechanism


6.5.1. Analog Inputs


6.5.2. Digital Inputs


6.5.3. Digital/Analog Convertors


6.5.4. On-line programming


6.5.5. Satellite-tracking aerial

References

Chapter 7. Application of the Analog Computer to the Design of a Servomechanism


7.1. Introduction


7.2. Definition of Analog Computer Functions


7.2.1. High Gain d.c. Amplifier


7.2.2. Virtual Earth Concept


7.2.3. Integration


7.2.4. Differentiation


7.2.5. Addition


7.2.6. Application of the Potentiometer


7.2.7. Summary of the Basic Analog Computer Operations


7.2.8. Read-out Facilities


7.2.9. Programming a Simple Example


7.3. Preparation of the Problem for the Computer


7.3.1. Problem Description


7.3.2. Problem Definition


7.3.3. Scaling Factors


7.3.4. Preparing the Computer Diagrams


7.3.5. Static Check Procedure


7.4. Simulation of a Position Servomechanism


7.4.1. System Equations


7.4.2. Scaled Equations


7.4.3. Time Scaling


7.4.4. Problem Check Procedure


7.5. Design of a Compensating Network


7.5.1. Simulation of the Compensating Network


7.6. Non-linear Analog Methods


7.6.1. Introduction


7.6.2. Synthesis of Non-linearities


7.6.3. Limiter


7.6.4. Coulomb Friction


7.6.5. Dead Zone


7.6.6. Hard Limiter


7.6.7. Half-wave Rectifier


7.6.8. Hysteresis


7.7.Non-linear Computer Faculties


7.7.1. Arbitrary Function Generators


7.7.2. Generation of Functions of Two Variables


7.7.3. Particular Function Generators


7.7.4. Multipliers


7.7.5. Division


7.7.6. Relay Comparators

References and Bibliography

Chapter 8. Hybrid Computers in Servo Design


8.1. Introduction


8.2. The Parallel Hybrid Computer


8.2.1. Parallel Hybrid Computer Elements


8.2.2. Analog Section Elements


8.2.3. Logic Section Elements


8.2.4. Linkage Elements


8.3. Applications of the Parallel Hybrid Computer


8.3.1. Computing the Transient Response of a System for Increasing Values of Disturbance, e.g. Increasing Values of Step Input


8.3.2. Computing Transient Responses for Increasing Values of Initial Conditions


8.3.3. Computing Transient Responses for Increasing Values of Parameters


8.3.4. Boundary Value Problems


8.3.5. Simulation of Systems which Contain Decision-making Elements


8.4. Optimization of a Position Servomechanism


8.4.1. Method of Solution


8.4.2. Solution on a Parallel Hybrid Computer

References and Bibliography

Chapter 9. Servo Amplifier Design


9.1. Introduction


9.2. Amplifiers for Large Position Servos


9.2.1. d.c. Transistor Amplifiers


9.3. Low Power a.c. Servo Amplifiers


9.4. Low Power d.c. Servo Amplifiers


9.5. Power Output Stages


9.6. Low Level Amplifiers


9.7. Modern Techniques and Construction


9.7.1. Silicon Integrated Circuits


9.7.2. Thin Film Circuits


9.7.3. Thick Film Circuits


9.7.4. Micro-welding Techniques


9.7.5. Potting and Encapsulation


9.7.6. Multi-layer Printed Circuit Boards and Plated-through Techniques


9.7.7. Semiconductor Cooling Devices and Vapour-phase Cooling Systems


9.8. Summary and Future Trends


9.9 Examples

References

Chapter 10. Thyristor Applications


10.1. Introduction


10.2. Thyristors, Firing Circuits and Ratings


10.2.1. Construction and Operation of the Thyristor


10.2.2. Trigger Requirements


10.2.3. A Typical Firing Circuit with Phase Control


10.2.4. Thyristor Ratings


10.3. Thyristor Power Amplifiers


10.4. Design of a Thyristor Power Amplifier for a 50 h.p. d.c. Motor Velocity Servo


10.4.1. System Specification


10.4.2. Selection of Amplifier Configuration


10.4.3. Voltage Rating of Thyristors and Protection


10.4.4. Thyristor Current Ratings and Protection


10.4.5. Amplifier Design Fuse Protection Calculations


10.4.6. Steady-state System Design


10.4.7. Regenerative Braking and Reversing


10.4.8. Ripple Instability


10.5. Variable Speed a.c. Motor Drives


10.5.1. Variable Frequency Control


10.5.2. Variable Voltage Control


10.5.3. Modified Kramer Drive

References

Chapter 11. Reliability


11.1. Introduction


11.2. The Fundamentals of Reliability Theory


11.2.1. The Exponential Reliability Model


11.3. Component and Equipment Testing Using Different Approaches


11.3.1. The Established Reliability Approach


11.3.2. AGREE Testing


11.3.3. The "Testing Extra" Approach to Equipment Reliability


11.4. The Designer's Approach to Equipment Reliability


11.4.1. Reliability Through Derating


11.4.2. Derating of Semiconductors


11.4.3. Derating of Capacitors


11.4.4. Derating of Resistors


11.5. The Achievement of Reliability Through Equipment Construction


11.5.1. Equipment Sealing


11.5.2. The Use of Plated-through Printed Circuit Boards


11.5.3. Printed Circuit Connectors to Interconnect Boards


11.5.4. Wire-wrapped Joints


11.5.5. Encapsulation of Components or Modules


11.5.6. Exotherm


11.5.7. Shrinkage Stress


11.5.8. The Use of Fillers


11.5.9. Ingress of Moisture


11.6. Equipment Reliability Through Component Selection and Examples


11.7. Equipment Reliability Through Redundancy Techniques


11.8. Reliability Through the Use of Micro-electronics Techniques


11.9. Summary of the Approach to Equipment Design

References

Appendix

Index

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