Design of Control Systems for DC Drives

This book is intended to introduce the reader to the practical calculation of feedback control circuits by examples of application. Only an understanding of basic mathematics and of basic electricity is prerequisite. The book can be used for independent study, to serve the specialist as a reference book, and to offer the drive-system engineer a comprehensive presentation of the standard problems and solutions of drive-systems engineering.

1. Normalization.- 2. Signal Flow Diagram.- 3. Open-Loop Control.- 3.1 Basic Concepts.- 3.2 Example of a Calculation.- 3.2.1 Controller.- 3.2.2 Controlled System.- 3.2.3 Signal-flow Diagram.- 3.2.4 Conclusion.- 4. Basic Concepts and Definitions of Feedback Control.- 4.1 Basic Principle of a Feedback Control.- 4.2 The Feedback Control System.- 4.3 Control Requirements.- 4.3.1 Accuracy and Steady-state-stability (Constancy).- 4.3.2 Response to Command and Disturbance.- 5. Calculation of Feedback Control in the Steady-State.- 5.1 Amplification.- 5.2 Steady-State Closed-Loop Amplification.- 5.3 Additive and Multiplicative Disturbances.- 5.4 Basis of Calculation.- 5.4.1 Additive Disturbances.- 5.4.2 Multiplicative Disturbances.- 5.5 Controllable and Noncontrollable Errors.- 5.6 Example.- 5.6.1 Control Element and Controlled System.- 5.6.2 Controller.- 5.6.3 Output Transducer.- 5.6.4 Signal-Flow Diagram.- 5.6.5 Conclusion.- 6. Basic Mathematics of Dynamic Control.- 6.1 Differential Equations (DE’s).- 6.2 Equations of Irrational Elements.- 6.2.1 Dead-Time Elements (DT-Element).- 6.2.2 Characteristic-Curve Elements (CC-Element).- 6.2.3 Multiplier (M-Element).- 6.3 Example.- 6.3.1 Control Amplifier.- 6.3.2 Half-Controlled Single-Phase Bridge Circuit.- 6.3.3 Armature Circuit.- 6.3.4 Developed Torque.- 6.3.5 Accelerating Torque.- 6.3.6 Motor Speed.- 6.3.7 Motor EMF.- 6.3.8 Response.- 7. Unit Step Response.- 7.1 Definition.- 7.2 Unit Step Response of Common Control-Circuit Elements.- 7.2.1 P-Element (Proportional Element).- 7.2.2 I-Element (Integrator).- 7.2.3 PI-Element.- 7.2.4 D-Element (Differentiator).- 7.2.5 PD-Element.- 7.2.6 TD1-Element (First-Order Time-Delay Element).- 7.2.7 TD2-Element (Second-Order Time-Delay Element).- 7.2.8 DD-Element (Time-Delay and Differentiation Element).- 7.2.9 DT-Element (Dead-Time Element).- 7.2.10 Nonlinear Elements.- 7.3 Significance of the unit Step Response.- 8. Sinusoidal Transfer Function.- 8.1 Transformation of DE’s into Transfer-Function Equations.- 8.2 Sinusoidal and Laplace Transfer Functions.- 8.3 Transfer Function and Complex AC Analysis.- 8.4 Transfer Functions of Common Control-Circuit Elements.- 8.5 Example.- 9. System Diagram.- 9.1 Symbolic Representation of Control-System Elements.- 9.1.1 Rational System Elements.- 9.1.2 Irrational System Elements.- 9.2 Example.- 10. Conversion of System Diagrams and Transfer Functions.- 10.1 Conversion Rules for Rational Elements.- 10.2 Conversion Rules for Irrational Elements.- 10.3 Negative and Positive Feedback.- 10.3.1 Negative Feedback.- 10.3.2 Positive Feedback.- 10.3.3 Examples.- 10.4 Resolution of Control-System Elements into P- and I-Elements.- 10.5 Conversion of a TD2-Element.- 10.5.1 Negative Feedback of a TD1- and an I-Element.- 10.5.2 Replacement of a TD2-Element by two Series-Connected TD1-Elements.- 10.5.3 Example: Armature Circuit of DC Drives.- 11. Stability.- 11.1 Definition.- 11.2 Stability Analysis of Positive Feedback.- 11.3 Stability Criteria.- 11.4 The Nyquist Criterion.- 12. Use of Bode Diagrams.- 12.1 Bode Diagrams.- 12.2 Bode Diagrams of Common Control-System Elements.- 12.2.1 P-Element.- 12.2.2 I-Element.- 12.2.3 PI-Element.- 12.2.4 D-Element.- 12.2.5 PD-Element.- 12.2.6 TD1-Element.- 12.2.7 TD2-Element.- 12.2.8 DD-Element.- 12.2.9 Dead-Time Element.- 12.3 Rules for Calculation.- 12.3.1 Multiplication of Transfer-Functions.- 12.3.2 Inversion.- 12.4 Curve-Drawing Instrument.- 12.4.1 Determination of the Phase Angle.- 12.4.2 Conversion $$\left| G \right|$$ of into $${\left| G \right|_{dB}}$$.- 12.4.3 Drawing the Gain Characteristic.- 12.5 Stability Analysis by Bode Diagram.- 13. Stabilization of Control Systems without an I-Element in the Controlled System.- 13.1 P-Controller.- 13.2 I-Controller.- 13.3 PI-Controller.- 13.4 PD-Controller.- 13.5 PID-Controller.- 14. Stabilization of Control Systems with an I-Element in the Controlled System.- 14.1 P- and PD-Controllers.- 14.2 I-Controller.- 14.3 PI-Controller.- 14.4 PID-Controller.- 15. Closed Control Loops.- 15.1 Calculation.- 15.2 Approximation Procedure.- 15.3 Nichols Chart.- 16. Normalized Bode Diagrams and Step Responses.- 16.1 Sum of Small Time Constants.- 16.2 Systems with an I-Element in the Controlled System.- 16.2.1 Optimal Stabilization.- 16.2.2 Response to a Unit Step of Command or Disturbance.- 16.2.3 Smoothing of the Command Variable.- 16.3 System without an I-Element in the Controlled System.- 16.3.1 System with Compensation of the Large Time Constant.- 16.3.2 Controller Setting by the Symmetrical Optimum.- 16.3.3 Criteria for Optimum Response to Disturbance.- 16.3.4 Controller Design with $${\phi _x} = - 143^\circ$$ and Symmetrical Stabilization.- 16.4 Summary.- 17. Improvement of Dynamic Behaviour by Internal Loops.- 18. Programming Control Systems on the Analog Computer.- 18.1 Computer Elements.- 18.2 Basis of Programming.- 18.3 Example.- 19. Programming Control Systems on the Digital Computer.- 19.1 Basic Principle.- 20. Hints on Calculating Bode Diagrams with the Digital Computer.- 20.1 Determination of Amplitude and Phase Angle.- 20.2 Amplitude and Phase Angle of the Most Important Control System Elements.- 21. Connection of Control Amplifiers.- 21.1 Negative Feedback.- 21.2 Basic Connections.- 21.3 Controller Connections.- 21.4 Special Connections.- 21.4.1 Smoothing.- 21.4.2 D-Limiting.- 21.4.3 PI-Controller with Adjustable P-Amplification.- 21.4.4 PI-Controller with Adjustable Time Constant.- 21.4.5 PD-Controller with TD1-Element in the Feedback Loop.- 21.4.6 Limiting.- 21.4.7 Inhibition of Control.- 21.4.8 Slope of Characteristic.- 21.5 Control Amplifier Errors.- 21.5.1 Static Errors.- 21.5.2 Dynamic Errors.- 22. Static and Dynamic Characteristics of Line-Commutated Rectifiers.- 22.1 Static Characteristic.- 22.2 Internal Resistance.- 22.3 Dynamic Behaviour.- 22.4 Representation in the System Diagram.- 23. System Diagram of the dc Drive.- 23.1 System Diagram for Variable Field Excitation.- 23.2 System Diagram for Constant Field Excitation.- 24. Speed Control of a Converter Drive with Current Feedback.- 24.1 Connection Diagram.- 24.2 System Diagram.- 24.3 Current Control.- 24.4 Speed Control.- 24.5 Making Allowance for the EMF-Loop.- 25. Voltage Control of Converter Drives.- 25.1 Simple Voltage Control.- 25.2 Voltage Control with Current Feedback.- 25.3 Comments on the System Diagram.- 26. Control of Ward-Leonard Drives.- 26.1 Speed Control with Current Feedback.- 26.2 Speed Control with Current Feedback and Exciter-Current Control.- 27. Speed Control by Field Weakening.- 28. Control with an Oscillatory Mechanical System.- 28.1 System Diagram of an Undamped Two-Mass System.- 28.2 System Diagram of a Damped Two-Mass System.- 28.3 Bode Diagram and Dynamic Behaviour.- 28.4 Determination of Characteristic Values.- 28.5 Measures to Improve Dynamic Behaviour.- 29. Superimposed Control Systems.- 29.1 Control of Tension.- 29.2 Control of a Loop.- 29.3 Control by Level Gauge.- 29.4 Positional Control.- 30. Adaptive Controllers in Drive Systems.- 30.1 Speed Control by Motor Field Weakening.- 30.2 Control of Converter Drives with Discontinuous and Continuous Armature Current.- 30.2.1 System Diagram of the Control for Discontinuous Armature Current.- 30.2.2 Requirements of an Adaptive Armature-Current Controller.- 30.3 Adaptive Speed Controller with Variation of the Run-Up Time Constant.- 31. Digital Control.- 31.1 Digital Feedback Control.- 31.2 The z-Transform.- 31.3 The z-Transform Function of a P-, PI- and PID-Controller.- 31.4 Example of a Digital Control.- 31.4.1 Micro-Controller.- 31.4.2 Current Controller Design.- 31.4.3 Speed Controller Design.- 31.4.4 Controller Algorithm.- References.- Fig. 4 Nichols Chart.- Table 4 The most Important Controller Connections.- Table 5 The most Important Control-System Elements.