Analog and Digital Control System Design Transfer-Function, State-Space, and Algebraic Methods,9780030940705

Analog and Digital Control System Design Transfer-Function, State-Space, and Algebraic Methods

by
ISBN13: 9780030940705
ISBN10: 0030940702
Format: Hardcover
Pub. Date: 1993-01-01
Publisher(s): Oxford University Press
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Summary

This text's contemporary approach focuses on the concepts of linear control systems, rather than computational mechanics. Straightforward coverage includes an integrated treatment of both classical and modern control system methods. The text emphasizes design with discussions of problemformulation, design criteria, physical constraints, several design methods, and implementation of compensators. Discussions of topics not found in other texts--such as pole placement, model matching and robust tracking--add to the text's cutting-edge presentation. Students will appreciate theapplications and discussions of practical aspects, including the leading problem in developing block diagrams, noise, disturbances, and plant perturbations. State feedback and state estimators are designed using state variable equations and transfer functions, offering a comparison of the twoapproaches. The incorporation of MATLAB throughout the text helps students to avoid time-consuming computation and concentrate on control system design and analysis.

Table of Contents

Introduction
1(13)
Empirical and Analytical Methods
1(1)
Control Systems
2(7)
Position Control Systems
2(2)
Velocity Control Systems
4(2)
Temperature Control Systems
6(1)
Trajectory Control and Autopilot
6(1)
Miscellaneous Examples
7(2)
Problem Formulation and Basic Terminology
9(2)
Scope of the Text
11(3)
Mathematical Preliminary
14(55)
Physical Systems and Models
14(2)
Linear Time-Invariant Lumped Systems
16(8)
Mechanical Systems
17(3)
RLC Networks
20(2)
Industrial Process---Hydraulic tanks
22(2)
Zero-Input Response and Zero-State Response
24(3)
Zero-Input Response---Characteristic Polynomial
25(2)
Zero-State Response---Transfer Function
27(12)
Proper Transfer Functions
30(4)
Poles and Zeros
34(5)
Block Representation---Complete Characterization
39(6)
The Loading Problem
43(2)
State-Variable Equations
45(5)
Solutions of State Equations---Laplace Transform Method
50(7)
Time-Domain Solutions
52(2)
Transfer Function and Characteristic Polynomial
54(3)
Discretization of State Equations
57(12)
Problems
60(9)
Development of Block Diagrams for Control Systems
69(42)
Introduction
69(1)
Motors
70(8)
Field-Controlled DC Motor
70(2)
Armature-Controlled DC Motor
72(3)
Measurement of Motor Transfer Functions
75(3)
Gears
78(3)
Transducers
81(3)
Operational Amplifiers (Op-Amps)
84(4)
Block Diagrams of Control Systems
88(6)
Reaction Wheels and Robotic Arms
91(3)
Manipulation of Block Diagrams
94(17)
Mason's Formula
98(3)
Open-Loop and Closed-Loop Transfer Functions
101(1)
Problems
102(9)
Quantitative and Qualitative Analyses of Control Systems
111(43)
Introduction
111(1)
First-Order Systems---The Time Constant
111(5)
Effects of Feedback
115(1)
Second-Order Systems
116(7)
Time Responses of Poles
123(2)
Stability
125(4)
The Routh Test
129(9)
Stability Range
135(3)
Steady-State Response of Stable Systems---Polynomial Inputs
138(16)
Steady-State Response of Stable Systems---Sinusoidal Inputs
141(3)
Infinite Time
144(3)
Problems
147(7)
Computer Simulation and Realization
154(34)
Introduction
154(1)
Computer Computation of State-Variable Equations
155(4)
Existing Computer Programs
159(3)
Basic Block Diagrams and Op-Amp Circuits
162(3)
Realization Problem
165(12)
Realizations of N(s)/D(s)
167(5)
Tandem and Parallel Realizations
172(5)
Minimal Realizations
177(11)
Minimal Realization of Vector Transfer Functions
179(4)
Problems
183(5)
Design Criteria, Constraints, and Feedback
188(35)
Introduction
188(1)
Choice of a Plant
188(1)
Performance Criteria
189(8)
Steady-State Performance---Accuracy
191(3)
System Types---Unity-Feedback Configuration
194(1)
Transient Performance---Speed of Response
195(2)
Noise and Disturbances
197(1)
Proper Compensators and Well-Posedness
198(4)
Total Stability
202(5)
Imperfect Cancellations
203(3)
Design Involving Pole-Zero Cancellations
206(1)
Saturation---Constraint on Actuating Signals
207(2)
Open-Loop and Closed-Loop Configurations
209(7)
Two Basic Approaches in Design
216(7)
Problems
217(6)
The Root-Locus Method
223(47)
Introduction
223(1)
Quadratic Systems with a Constant Numerator
223(8)
Desired Pole Region
225(3)
Design using Desired Pole Region
228(3)
More on Desired Pole Region
231(2)
The Plot of Root Loci
233(17)
Properties of Root Loci---Phase Condition
236(10)
Complexities of Root Loci
246(1)
Stability Range from Root Loci---Magnitude Condition
247(3)
Design using the Root-Locus Method
250(5)
Discussion
254(1)
Proportional-Derivative (PD) Controller
255(5)
Phase-Lead and Phase-Lag Networks
260(2)
Concluding Remarks
262(8)
Problems
263(7)
Frequency-Domain Techniques
270(69)
Introduction
270(1)
Frequency-Domain Plots
271(4)
Plotting Bode Plots
275(14)
Non-Minimum-Phase Transfer Functions
284(2)
Identification
286(3)
Stability Test in the Frequency Domain
289(11)
Principle of Argument
289(1)
The Nyquist Plot
290(4)
Nyquist Stability Criterion
294(3)
Relative Stability---Gain Margin and Phase Margin
297(3)
Frequency-Domain Specifications for Overall Systems
300(5)
Frequency-Domain Specifications for Loop Transfer Functions---Unity-Feedback Configuration
305(7)
Why Use Bode Plots?
310(1)
Design from Measured Data
311(1)
Design on Bode Plots
312(3)
Gain Adjustment
314(1)
Phase-Lag Compensation
315(6)
Phase-Lead Compensation
321(6)
Proportional-Integral (PI) Compensators
327(5)
Concluding Remarks
332(7)
Problems
332(7)
The Inward Approach---Choice of Overall Transfer Functions
339(45)
Introduction
339(1)
Implementable Transfer Functions
340(6)
Asymptotic Tracking and Permissible Pole-Zero Cancellation Region
345(1)
Various Design Criteria
346(4)
Quadratic Performance Indices
350(11)
Quadratic Optimal Systems
350(4)
Computation of Spectral Factorizations
354(4)
Selection of Weighting Factors
358(3)
Three More Examples
361(6)
Symmetric Root Loci
365(2)
ITAE Optimal Systems
367(8)
Applications
371(4)
Selection Based on Engineering Judgment
375(3)
Summary and Concluding Remarks
378(6)
Problems
380(4)
Implementation---Linear Algebraic Method
384(48)
Introduction
384(1)
Unity-Feedback Configuration---Model Matching
385(3)
Unity-Feedback Configuration---Pole Placement by Matching Coefficients
388(14)
Diophantine Equations
390(7)
Pole Placement with Robust Tracking
397(3)
Pole Placement and Model Matching
400(2)
Two-Parameter Compensators
402(9)
Two-Parameter Configuration---Model Matching
405(6)
Effect of Dp(s) on Disturbance Rejection and Robustness
411(11)
Model Matching and Disturbance Rejection
419(3)
Plant Input/Output Feedback Configuration
422(3)
Summary and Concluding Remarks
425(7)
Problems
428(4)
State-Space Design
432(43)
Introduction
432(1)
Controllability and Observability
432(8)
Pole-Zero Cancellations
438(2)
Equivalent State-Variable Equations
440(2)
Pole Placement
442(7)
Quadratic Optimal Regulator
449(4)
State Estimators
453(6)
Reduced-Dimensional Estimators
456(3)
Connection of State Feedback and State Estimators
459(6)
Comparison with Linear Algebraic Method
461(4)
Lyapunov Stability Theorem
465(5)
Application---A Proof of the Routh Test
467(3)
Summary and Concluding Remarks
470(5)
Problems
471(4)
Discrete-Time System Analysis
475(36)
Introduction
475(1)
Why Digital Compensators?
476(2)
A/D and D/A Conversions
478(3)
The z-Transform
481(9)
The Laplace Transform and the z-Transform
484(3)
Inverse z-Transform
487(1)
Time Delay and Time Advance
488(2)
Solving LTIL Difference Equations
490(5)
Characteristic Polynomials and Transfer Functions
491(3)
Causality and Time Delay
494(1)
Discrete-Time State Equations
495(2)
Controllability and Observability
496(1)
Basic Block Diagrams and Realizations
497(3)
Realizations of N(z)/D(z)
499(1)
Stability
500(3)
The Final-Value and Initial-Value Theorems
502(1)
Steady-State Responses of Stable Systems
503(4)
Frequency Responses of Analog and Digital Systems
506(1)
Lyapunov Stability Theorem
507(4)
Problems
508(3)
Discrete-Time System Design
511(40)
Introduction
511(1)
Digital Implementations of Analog Compensators---Time-Domain Invariance
512(10)
Frequency-Domain Transformations
516(6)
An Example
522(4)
Selection of Sampling Periods
524(2)
Equivalent Digital Plants
526(8)
Hidden Dynamics and Non-Minimum-Phase Zeros
528(6)
Root-Locus Method
534(6)
Frequency-Domain Design
540(1)
State Feedback, State Estimator and Dead-Beat Design
541(3)
Model Matching
544(3)
Concluding Remarks
547(4)
Problems
548(3)
PID Controllers
551(16)
Introduction
551(1)
PID Controllers in Industrial Processes
552(9)
Rules of Ziegler and Nichols
558(1)
Rational Approximations of Time Delays
559(2)
PID Controllers for Linear Time-Invariant Lumped Systems
561(2)
Digital PID Controllers
563(4)
Appendix A The Laplace Transform 567(12)
A.1 Definition
567(3)
A.2 Inverse Laplace Transform---Partial Fraction Expansion
570(1)
A.3 Some Properties of the Laplace Transform
571(2)
A.4 Solving LTIL Differential Equations
573(4)
A.5 Time Delay
577(2)
Appendix B Linear Algebraic Equations 579(11)
B.1 Matrices
579(1)
B.2 Determinant and Inverse
580(2)
B.3 The Rank of Matrices
582(2)
B.4 Linear Algebraic Equations
584(2)
B.5 Elimination and Substitution
586(2)
B.6 Gaussian Elimination with Partial Pivoting
588(2)
References 590(5)
Index 595

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