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Tables of Contents for Digital Control Systems
Chapter/Section Title
Page #
Page Count
Preface
xix
Introduction
1
18
Introduction
1
1
Digital Control-System Modeling
2
9
Sampling Process
2
2
System Terminology
4
1
General Sampled-Data System Variables
5
2
Systems Modeling
7
4
Why Use Digital Control?
11
1
Control-System Analysis and Synthesis
12
1
The Interdisciplinary Field of Digital Control
13
1
Digital Control Development
14
2
Nature of the Engineering Control Problem
16
1
Text Outline
17
1
Summary
18
1
Continuous-Time Control-System Response Characteristics
19
44
Introduction
19
1
Background
20
3
Simple Second-Order System Tracking-Response Characteristics
23
4
Higher-Order System Tracking-Response Characteristics
27
10
Time-Response Characteristics of a Third-Order All-Pole Plant
28
1
Time-Response Characteristics of a Third-Order, One-Zero Plant
28
3
Time-Response Characteristics of a Sixth-Order Plant
31
1
Correlation between Frequency and Time Domains
32
2
Correlation of the Control Ratio with Frequency and Time Responses
34
3
Nichol's Chart (NC) Analysis
37
2
Cascade-Compensator Design Procedures
39
4
Synthesizing a Desired Tracking Control Ratio with a Unit-Step Input
43
6
Feedback Compensation
49
2
Disturbance Rejection
51
11
Second-order Disturbance-Rejection Model
51
4
Single-Input Single-Output (SISO) Design Principles for Disturbance Rejection
55
1
Examples
56
6
Summary
62
1
Linear Systems and the Sampling Process
63
36
Introduction
63
1
Linear Time-Invariant (LTI) System
63
5
Solution of Linear Difference Equations
68
5
Sampling Process (Frequency Domain Analysis)
73
4
Ideal Sampler
77
6
Shannon's Sampling Theorem
83
1
Sampling-Time Selection
84
2
Single-Rate Sampling
85
1
Multirate Sampling
85
1
Weighting Sequence
86
8
Data Conversion Introduction
94
4
Zero-Order Hold (ZOH)
94
4
Summary
98
1
Discrete Systems Modeling
99
52
Introduction
99
1
Definition and Determination of the z-Plane Transform Z
100
11
Mapping between s and z Domains
111
7
Mapping of the Primary Strip
112
2
Mapping of the Constant Frequency Loci
114
1
Mapping of the Constant Damping-Coefficient Loci
114
1
Mapping of the Constant Damping-Ratio Loci
115
3
Z-Transform Theorems
118
5
The Inverse Z-Transform, Z--1
123
7
Partial-Fraction Method
124
4
Power-Series Method (Direct Division Method)
128
2
Limitations
130
1
Z Transform of System Equations
131
14
Open-Loop Hybrid Sampled-Data Control System
131
5
Open-Loop Discrete-Input-Data Control System
136
1
Closed-Loop Sampled-Data Control System
137
3
Signal Flow Graphs for Hybrid Systems (HSFG)
140
5
Digital-Computer Transfer Function
145
4
Summary
149
2
Discrete Control Analysis
151
47
Introduction
151
1
System Stability
152
8
z-Plane Stability
153
2
z-Domain Nyquist Stability
155
1
Polar Plot Analysis
156
1
Extended z-Domain Stability Analysis: Jury's Stability Test
157
3
Steady-State Error Analysis for Stable Systems
160
6
Steady-State Error-Coefficient Formulation
162
1
Evaluation of Steady-State Error Coefficients
163
1
Use of Steady-State Error Coefficients
164
2
Root-Locus Analysis
166
10
Procedure Outline
167
1
Root-Locus Construction Rules for Negative Feedback
168
2
Examples
170
6
Bilinear Transformations
176
7
s-Plane and w-Plane Relationship
177
3
Routh Stability Criterion in w-Plane
180
3
Time-Response Correlation between Planes (s, z, and w)
183
5
Frequency Response
188
6
Summary
194
4
Discrete Transform Analysis (Approximations)
198
22
Introduction
198
2
Folding or Aliasing
200
1
Transformation Methods between Planes (s, z, and w)
201
5
Mapping Approximations of Z-Transform (Or Numerical Solution of Differential Equations)
206
7
First-Backward Difference
206
3
Tustin Transformation
209
4
Pseudo-Continuous-Time (PCT) Control System
213
2
Analysis of a Basic (Uncompensated) System
215
4
PCT Control System Model
215
1
Sampled-Data Control System
216
3
Summary
219
1
Principles of Signal Conversion and Measurement
220
47
Introduction
220
1
Timing Considerations
220
2
Binary Coding of Information
222
2
Conversion Systems
224
1
Digital-to-Analog (D/A) Conversion Structures
225
4
General Analog-to-Digital (A/D) Conversion Structures
229
5
Specific Analog to Digital Conversion Systems
234
9
Measures of Converter Performance
243
2
Sample-and-Hold Operation
245
2
Multiplexing
247
1
Integrated A/D and D/A Interfaces
248
2
Measurement in Digital Control Systems
250
10
Temperature Measurements
250
3
Pressure and Related Measurements
253
3
Motion Measurement
256
2
Position Measurement
258
2
Transducer Signal Conditioning
260
1
Saturation Analysis
260
1
Programming Input and Output (I/O)
260
5
I/O Hardware Structure
261
1
Programmed I/O Mode
261
2
Interrupt I/O Devices
263
2
Summary
265
2
Digital-Control-System Implementation
267
44
Introduction
267
1
Control Logic
268
3
Computer Architecture for Control
271
3
Software for Control
274
4
Algorithms
274
3
Language Hierarchy
277
1
Software Engineering in Digital Control Systems
278
3
Requirements---Data Flow Diagrams (DFDs)
281
4
Real-Time Design for Digital Control
285
4
Software Design in Control Systems
289
3
Direct Design Method
292
1
Structured Programming and Implementation
293
1
Software Testing
293
2
Real-Time Scheduling
295
4
Real-Time Operating Systems for Digital Control
299
5
Real-Time Operating Systems Requirements
301
1
Simple Real-Time Operating System
302
2
Watchdog Timers
304
1
Sampling-Time Selection
305
3
Single-Rate Sampling
306
1
Multirate Sampling
307
1
User Interfaces to Real-Time Operating Systems
308
1
Summary
309
2
Random Processes in Digital Control Systems
311
19
Introduction
311
1
Digital Control of Random Inputs
312
1
Random Processes (Stochastic Processes)
313
4
Random Process Time Averages
317
2
Linear System Response to Random Signals
319
7
Convolution Model
319
3
Difference Equation Model
322
2
Spectral Density of Linear Discrete Systems
324
2
Vector-Matrix Representation of Random Processes
326
3
Summary
329
1
Finite Word Length and Compensator Structure
330
40
Introduction
330
1
Quantization Errors
331
10
Compensator Structure and Arithmetic Errors
341
7
Compensator Coefficient Representation
348
4
Sensitivity of Coefficients
352
4
Scaling
356
2
Limit-Cycle Phenomenon Due to Quantization
358
9
Simulation and Tuning
367
1
Detailed Design/Implementation Process
368
1
Summary
369
1
Cascade Compensation---Digitization (DIG) Technique
370
24
Introduction
370
2
Digitization (DIG) Design Technique
372
2
Guillemin--Truxal (GT) Compensation Method
374
5
Lead Cascade Compensation
379
6
s-Plane DIG Design
379
2
w-Plane DIG Design
381
3
s-Plane to w-Plane Correlation
384
1
Lag Compensation
385
1
Lag-Lead Compensation
385
2
Extensive Cascade DIG Example
387
5
Analysis of the Basic System
387
1
Guillemin--Truxal Approach
388
1
Pseudo-Continuous Time (PCT) Approach
389
2
w-Domain DIG Design
391
1
Summary
392
2
Cascade Compensation---Direct (DIR) Technique
394
19
Introduction
394
1
Direct (DIR) Design Technique
394
2
Lead Compensation (DIR)
396
1
Lag Compensation (DIR)
397
3
Lag-Lead Compensation---DIR
400
1
Frequency-Response Characteristics
400
4
Proportional Integral Derivative (PID) Controller
404
2
Set-Point PID Controllers
406
2
Extensive Cascade Example (DIR)
408
3
Lead Compensation
408
1
Lag Compensation
409
1
Controller Implementation
410
1
Deadbeat Response
411
1
Summary
412
1
Feedback Compensation
413
23
Introduction
413
1
General Analysis
414
3
DIR Technique for Feedback Control
417
4
Guillemin--Truxal Approach
417
3
Root-Locus Approach
420
1
DIG Technique for Feedback Control
421
3
Controlling Unwanted Disturbances
424
4
DIG Technique
425
3
DIR Technique
428
1
Extensive Digital Feedback Compensator Example
428
3
DIG Example
429
1
DIR Example
430
1
Software for Digital Controllers
431
4
Summary
435
1
Discrete State-Variable Model
436
41
Introduction
436
1
State-Variable Representation
437
6
Time-Domain State and Output Equations for Sampled-Data Control Systems
443
5
State-Variable Representation of a Discrete-Time SISO System
448
16
Phase-Variable Method
448
5
Canonical-Variable Method
453
6
Physical-Variable Method
459
3
State Transition Equation
462
2
State-Variable Representation Summary
464
1
State-Variable Representation in the z Domain
464
7
System Stability
471
3
Time Response between Sampling Instants
474
2
Summary
476
1
State-Space Design Methods
477
31
Introduction
477
1
State-Feedback Pole Placement
477
2
State-Variable Feedback: Parameter Insensitivity
479
1
State Feedback Using Digitization
479
4
State-Feedback H-Equivalent Digital Control System
483
3
Design Procedure
486
4
Frequency-Domain Compensation Design Using Mean-Square Error Minimization
490
3
Digital Filters
493
6
Direct s-Plane to w-Plane Transformation
499
7
Scalar Case Relationship
500
2
Vector-Matrix Formulation
502
1
Accuracy Considerations of the w Transformation
503
2
Model Relationship as T → Zero
505
1
Normal Form
506
1
Summary
506
2
Discrete Quantitative Feedback Technique
508
38
Introduction
508
1
Continuous MISO and MIMO QFT Approach
509
4
Non-Minimum-Phase Analog Plant
513
4
Analog QFT Design Procedure for an nmp Plant
514
3
Discrete MISO Model with Plant Uncertainty
517
1
QFT w-Domain DIG Design
518
17
Closed-Loop System Specifications
520
3
Plant Templates
523
1
Bounds B(jv) on Lo(jv)
524
1
Nonminimum-Phase Lo(w)
524
3
Synthesizing Lmo(w)
527
1
ws = 120 Is Too Small
528
4
Error in the Design
532
3
Design of the Prefilter F(w)
535
1
Simulation
535
3
Basic Design Procedure for a MISO Sampled-Data Control System
538
4
Applicability of Design Techniques to Other Plants
542
1
MIMO Plants
542
1
Nonlinear Plants
543
1
QFT Technique Applied to the PCT System
543
1
Summary
543
3
Minimum-Phase, Nonminimum Phase and Unstable P(s)
543
1
Disturbance Attenuation
544
1
Conclusions
544
2
Modern Discrete Control Theory
546
19
Introduction
546
1
Basic System Structure
547
1
Discrete Controllability
548
4
State-Space Pole Placement
552
1
Discrete Observability
553
4
State Observers
557
6
Full-State Observers
557
4
Reduced-Order and Current Observers
561
2
State-Space Stability
563
1
Summary
563
2
Discrete Optimal Control
565
18
Introduction
565
1
Optimal Control Concepts
566
1
Maximum Principle
567
1
Discrete Linear Regulator
568
12
General Second-Order System Optimal Controllers
574
1
Discrete Riccati Equation Solution
575
5
Optimal Control Variations
580
1
Sampling Time
581
1
Summary
582
1
Discrete Estimation and Stochastic Control
583
23
Introduction
583
1
Parameter Identification
584
6
Discrete Optimal Estimation
590
7
Additive Noise Model
590
1
Estimation Problem Formulation
591
1
Discrete Optimal Estimation
592
5
Solution to Optimal Filter Equations
597
1
Discrete Stochastic Control
597
3
Combined Model
597
1
Optimal Performance
598
2
H∞ Robust Optimal Control
600
3
Discrete Adaptive Control
603
2
Summary
605
1
Bibliography
606
7
Problems
613
101
Appendixes
A Fourier Transform
661
6
B Convolution
667
2
C Pade Approximation
669
3
D Power Series
672
2
E Computer-Aided-Design (CAD) Programs for Control
674
4
F Matrix Manipulations
678
11
G Signal Flow Graphs
689
6
H w-Transformation Characteristics
695
1
I Number Representations
696
5
J Theory of Probability
701
8
K Discrete QFT Design Process
709
5
Answers to Selected Problems
714
25
Index
739