Control System Design Guide

by Ellis, George

• ISBN13: 9780122374654
• ISBN10: 0122374657
• Format: Hardcover
• Copyright: 2000-05-01
• Publisher: Academic Pr

Summary

Control System Design Guide, 2E will allow engineers and hobbyists to apply control theory to practical systems using your PC. This book provides an intuitive approach to controls, avoiding unnecessary math and emphasizing key concepts with more than a dozen control system models. Control System Design Guide is written for engineers and technicians that want to improve their machines and processes. Whether you are just starting to use controllers or have years of experience, Control System Design Guide will walk you through control system theory with a well-founded, clear approach that is focused on making your system work better. * Teaches control from an intuitive approach; avoids unnecessary mathematics * Based on virtual laboratory--key topics are demonstrated with over a dozen models of control systems * The models are written in ModelQ, and can be run on software available free of charge via the Internet to every reader with a PC * Goes beyond proportional-integral-differential (PID) control * Provides detailed comparison of seven different controllers * Explains how to model machines and processes including how to measure working equipment; describes many non-linear behaviors seen in industrial control systems * Provides discussion of electronic motion control including details on how motors and motor feedback devices work, causes and cures mechanical resonance, and shows how position loops work

Table of Contents

Foreword	xvii
Preface	xxi
Section I Applied Principles of Controls	1	(196)
Important Safety Guidelines for Readers	3	(2)
Introduction to Controls	5	(6)
ModelQ Simulation Environment	6	(1)
Installation of ModelQ	6	(1)
Errata	7	(1)
The Control System	7	(1)
The Controller	7	(1)
The Machine	8	(1)
The Controls Engineer	8	(3)
The Frequency Domain	11	(20)
The Laplace Transform	11	(1)
Transfer Functions	12	(2)
What is s?	13	(1)
Linearity, Time Invariance, and Transfer Functions	13	(1)
Examples of Transfer Functions	14	(5)
Transfer Functions of Controller Elements	14	(2)
Transfer Functions of Power Conversion	16	(1)
Transfer Functions of Physical Elements	16	(3)
Transfer Functions of Feedback	19	(1)
Block Diagrams	19	(2)
Combining Blocks	20	(1)
Phase and Gain	21	(3)
Phase and Gain from Transfer Functions	23	(1)
Bode Plots: Phase and Gain versus Frequency	23	(1)
Measuring Performance	24	(7)
Command Response	25	(2)
Stability	27	(1)
Time Domain versus Frequency Domain	28	(1)
Experiment 2-1: PI+ Controller	29	(2)
Tuning a Control System	31	(26)
Closing Loops	32	(2)
The Source of Instability	32	(2)
A Detailed Review of the Model	34	(5)
Integrator	35	(1)
Power Converter	36	(1)
PI Control Law	37	(2)
Feedback Filter	39	(1)
The Open-Loop Method	39	(2)
Margins of Stability	41	(4)
Quantifying GM and PM	42	(1)
Experiment 3-1: Understanding the Open-Loop Method	42	(1)
Open Loop, Closed Loop, and the Step Response	43	(2)
A Zone-Based Tuning Procedure	45	(4)
Zone One: Proportional	47	(1)
Zone Two: Integral	48	(1)
Variation in Plant Gain	49	(2)
Accommodating Changing Gain	50	(1)
Multiple (Cascaded) Loops	51	(1)
Saturation and Synchronization	52	(5)
Avoid Saturation when Tuning	55	(2)
Delay in Digital Controllers	57	(12)
How Sampling Works	58	(1)
Sources of Delay in Digital Systems	59	(3)
Sample-and-Hold Delay	59	(1)
Calculation Delay	60	(1)
Velocity Estimation	61	(1)
The Sum of the Delays	61	(1)
Experiment 4-1: Understanding Delay in Digital Control	62	(3)
Tuning the Controller	63	(2)
Selecting the Sample Time	65	(4)
Aggressive Assumptions for General Systems	65	(1)
Aggressive Assumptions for Position-Based Motion Systems	66	(1)
Moderate and Conservative Assumptions	67	(2)
The z-Domain	69	(30)
Introduction to the z-Domain	69	(3)
Definition of z	69	(1)
z-Domain Transfer Functions	70	(1)
Bilinear Transform	70	(2)
z Phasors	72	(1)
Aliasing	73	(2)
Experiment 5-1: Aliasing	75	(3)
Bode Plots and Block Diagrams in z	77	(1)
DC Gain	77	(1)
From Transfer Function to Algorithm	78	(2)
Functions for Digital Systems	80	(10)
Digital Integrals and Derivatives	80	(3)
Digital Derivatives	83	(4)
Sample-and-Hold	87	(2)
DAC/ADC: Converting to and from Analog	89	(1)
Reducing the Calculation Delay	90	(1)
Selecting a Processor	91	(3)
Fixed- and Floating-Point Math	91	(2)
Overrunning the Sample Time	93	(1)
Other Algorithms	93	(1)
Ease of Programming	93	(1)
The Processor's Future	93	(1)
Making the Selection	94	(1)
Quantization	94	(5)
Limit Cycles and Dither	95	(2)
Offset and Limit Cycles	97	(2)
Six Types of Controllers	99	(34)
Tuning in This Chapter	100	(1)
Using the Proportional Gain	101	(4)
P Control	101	(4)
Using the Integral Gain	105	(9)
PI Control	105	(5)
PI+ Control	110	(4)
Using the Differential Gain	114	(9)
PID Control	115	(8)
PID+ Control	123	(3)
How to Tune a PID+ Controller	124	(2)
PD Control	126	(1)
How to Tune a PD Controller	127	(1)
Choosing the Controller	127	(2)
Experiment 6-1: PID Controller	129	(4)
Disturbance Response	133	(26)
Disturbances	134	(7)
Disturbance Response of a Power Supply	137	(4)
Disturbance Response of a Velocity Controller	141	(6)
Time Domain	143	(2)
Frequency Domain	145	(2)
Disturbance Decoupling	147	(12)
Applications for Disturbance Decoupling	149	(10)
Feed-Forward	159	(16)
Feed-Forward for the General System	160	(10)
Nonideal Power Conversion and Feedback	162	(4)
Increasing the Bandwidth versus Feed-Forward Compensation	166	(1)
Imperfect Knowledge of the Plant	167	(2)
Overshoot to Nonsquare Waves	169	(1)
Feed-Forward for the Double-Integrating Plant	170	(2)
Experiment 8-1: Feed-Forward	172	(3)
Filters in Control Systems	175	(22)
Filters in Control Systems	176	(4)
Filters in the Controller	176	(3)
Filters in the Power Converter	179	(1)
Filters in the Feedback	179	(1)
Filter Passband	180	(9)
Low-Pass Filters	180	(6)
Notch	186	(3)
Implementation of Filters	189	(8)
Passive Analog Filters	189	(1)
Active Analog Filters	190	(1)
Switched Capacitor Filters	190	(1)
IIR Digital Filters	190	(4)
FIR Digital Filters	194	(3)
Section II Modeling	197	(62)
Introduction to Modeling	199	(22)
What Is a Model?	200	(1)
Frequency-Domain Modeling	200	(2)
How the Frequency Domain Works	200	(2)
Time-Domain Modeling	202	(19)
State Variables	202	(3)
The Modeling Environment	205	(3)
The Model	208	(11)
Frequency Information from Time-Domain Models	219	(2)
Nonlinear Behavior and Time Variation	221	(28)
LTI versus Non-LTI	221	(1)
Non-LTI Behavior	222	(2)
Slow Variation	222	(1)
Fast Variation	223	(1)
Dealing with Nonlinear Behavior	224	(3)
Modify the Plant	224	(1)
Tuning for Worst Case	225	(1)
Compensate in the Controller (``Gain Scheduling'')	226	(1)
Ten Examples of Nonlinear Behavior	227	(22)
Plant Saturation	227	(3)
Deadband	230	(2)
Reversal Shift	232	(1)
Variation of Apparent Inertia	233	(1)
Friction	234	(5)
Quantization	239	(1)
Deterministic Feedback Error	239	(2)
Power Converter Saturation	241	(2)
Pulse Modulation	243	(3)
Hysteresis Controllers	246	(3)
Seven Steps to Developing a Model	249	(10)
Determine the Purpose of the Model	250	(2)
Training	250	(1)
Troubleshooting	250	(1)
Testing	251	(1)
Predicting	251	(1)
Model in SI Units	252	(1)
Identify the System	252	(4)
Identifying the Plant	253	(1)
Identifying the Power Converter	254	(1)
Identifying the Feedback	255	(1)
Identifying the Controller	256	(1)
Build the Block Diagram	256	(1)
Select Frequency or Time Domain	257	(1)
Write the Model Equations	257	(1)
Verify the Model	257	(2)
Section III Motion Control	259	(116)
Encoders and Resolvers	261	(28)
Accuracy, Resolution, and Response	263	(1)
Encoders	264	(1)
Resolvers	265	(4)
Software Resolver-to-Digital Converter	266	(1)
Resolver Error and Multispeed Resolvers	267	(2)
Impact of Resolution on Velocity Estimation	269	(4)
Higher Gain Generates More Noise	270	(1)
Filtering the Noise	271	(2)
Experiment 13-1: Resolution Noise	273	(1)
Alternatives for Increasing Resolution	273	(3)
The 1/T Interpolation or Clock Pulse Counting Method	273	(2)
Sine Encoders	275	(1)
Cyclic Error and Torque Ripple	276	(5)
Experiment 13-1 (Continued): Cyclic Errors and Torque Ripple	281	(4)
Relationship between Error Magnitude and Ripple	282	(1)
Relationship between Velocity and Ripple	283	(1)
Relationship between Bandwidth and Ripple	283	(1)
Relationship between Inertia and Ripple	283	(1)
Effect of Filters	284	(1)
Effect of Changing the Error Harmonic	284	(1)
Effect of Raising Resolver Speed	284	(1)
Choosing a Feedback Device	285	(4)
Suppliers	286	(3)
Basics of the Electric Servomotor and Drive	289	(42)
Definition of a Drive	290	(1)
Definition of a Servo System	291	(1)
Basic Magnetics	292	(5)
Electromagnetism	295	(1)
The Right-Hand Rule	295	(1)
Completing the Magnetic Path	296	(1)
Electric Servomotors	297	(4)
Torque Ratings	298	(1)
Rotary and Linear Motion	299	(1)
Linear Motors	299	(2)
Permanent-Magnet (PM) Brush Motors	301	(10)
Creating the Winding Flux	302	(1)
Commutation	302	(1)
Torque Production	302	(1)
Electrical Angle versus Mechanical Angle	303	(2)
KT, the Motor Torque Constant	305	(1)
Back EMF	306	(1)
Control of PM Brush Motors	307	(3)
Brush Motor Strengths and Weaknesses	310	(1)
Brushless PM Motors	311	(15)
Windings of Brushless PM Motors	312	(1)
Sinusoidal Commutation	312	(2)
Phase Control of Brushless PM Motors	314	(7)
DQ Control of Brushless PM Motors	321	(3)
Comparing DQ and Phase Control	324	(2)
Six-Step Control of Brushless PM Motor	326	(4)
Sensing Position for Commutation	327	(3)
Comparison of Brush and Brushless Motors	330	(1)
Induction and Reluctance Motors	330	(1)
Compliance and Resonance	331	(20)
Equations of Resonance	333	(3)
Resonance with Load Feedback	335	(1)
High-Frequency and Low-Frequency Resonance	336	(2)
Curing Resonance	338	(13)
Stiffen the Transmission	339	(1)
Add Damping	340	(1)
Increase Motor Inertia	341	(3)
Filters	344	(7)
Position Loops	351	(24)
Cascaded Position/Velocity Loops	351	(7)
Feed-Forward in Cascaded Controllers	352	(3)
Tuning a Cascaded Controller	355	(3)
PID Position Loops	358	(3)
Tuning a PID Position Controller	359	(2)
Comparing Position Loops	361	(3)
Comparing Feed-Forward	362	(1)
Velocity versus Current Drive	363	(1)
Dual-Loop Control	364	(1)
Frequency-Domain Measurements	365	(10)
Using a DSA on a Digital System	366	(1)
Measuring PI Velocity Controllers	366	(1)
Factor in Velocity Sample Delay	367	(1)
Measuring PI+ Velocity Controllers	368	(2)
Measuring Cascaded Position Loops	370	(1)
Measuring PID Position Loops	371	(4)
Appendix A Active Analog Implementation of Controller Elements	375	(8)
Integrator	375	(1)
Differentiator	376	(1)
Lag Compensator	377	(1)
Lead Compensator	378	(1)
Lead-Lag Compensator	379	(1)
Sallen-and-Key Low-Pass Filter	380	(1)
Adjustable Notch Filter	381	(2)
Appendix B European Symbols for Block Diagrams	383	(4)
Part I. Linear Functions	383	(1)
Part II. Nonlinear Functions	384	(3)
Appendix C The Runge-Kutta Method	387	(6)
The Runge-Kutta Algorithm	387	(1)
Basic Version of the Runge-Kutta Algorithm	388	(2)
C Programming Language Version of the Runge-Kutta Algorithm	390	(3)
Appendix D Development of the Bilinear Transformation	393	(4)
Bilinear Transformation	393	(1)
Prewarping	394	(1)
Factoring Polynomials	395	(1)
Phase Advancing	395	(2)
Appendix E Mason's Signal Flow Graph Rule	397	(4)
Signal Flow Graphs	397	(1)
Step-by-Step Procedure	398	(3)
Appendix F The Parallel Form of Digital Algorithms	401	(4)
Appendix G Basic Matrix Math	405	(2)
Matrix Summation	405	(1)
Matrix Multiplication	405	(1)
Matrix Scaling	406	(1)
Matrix Inversion	406	(1)
Appendix H Using ModelQ to Produce Figures	407	(12)
Appendix I Variables and Constants Used in Simulations	419	(18)
Experiment 2-1	419	(1)
Experiment 3-1	420	(1)
Experiment 4-1	421	(1)
Experiment 5-1	422	(1)
Experiment 5-2	422	(1)
Experiment 6-1	423	(2)
Experiment 7-1	425	(1)
Experiment 8-1	426	(1)
Experiment 9-1	427	(1)
Experiment 9-2	428	(1)
Experiment 13-1	429	(1)
Experiment 15-1	430	(2)
Experiment 16-1	432	(1)
Experiment 16-2	433	(4)
References	437	(4)
Index	441