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Cover
TOC
Preface
Chapter 1 - An Overview and Brief History of Feedback Control
A Perspective on Feedback Control
Chapter Overview
1.1 A Simple Feedback System
1.2 A First Analysis of Feedback
1.3 Feedback System Fundamentals
1.4 A Brief History
1.5 An Overview of the Book
Summary
Review Questions
Problems
Chapter 2 - Dynamic Models
A Perspective on Dynamic Models
Chapter Overview
2.1 Dynamics of Mechanical Systems
2.1.1 Translational Motion
2.1.2 Rotational Motion
2.1.3 Combined Rotation and Translation
2.1.4 Complex Mechanical Systems (W)**
2.1.5 Distributed Parameter Systems
2.1.6 Summary: Developing Equations of Motionfor Rigid Bodies
2.2 Models of Electric Circuits
2.3 Models of Electromechanical Systems
2.3.1 Loudspeakers
2.3.2 Motors
2.3.3 Gears
2.4 Heat and Fluid-Flow Models
2.4.1 Heat Flow
2.4.2 Incompressible Fluid Flow
2.5 Historical Perspective
Summary
Review Questions
Problems
Chapter 3 - Dynamic Response
A Perspective on System Response
Chapter Overview
3.1 Review of Laplace Transforms
3.1.1 Response by Convolution
3.1.2 Transfer Functions and Frequency Response
3.1.3 The G_ Laplace Transform
3.1.4 Properties of Laplace Transforms
3.1.5 Inverse Laplace Transform by Partial-Fraction Expansion
3.1.6 The Final Value Theorem
3.1.7 Using Laplace Transforms to Solve Differential Equations
3.1.8 Poles and Zeros
3.1.9 Linear System Analysis Using Matlab®
3.2 System Modeling Diagrams
3.2.1 The Block Diagram
3.2.2 Block-Diagram Reduction Using Matlab
3.2.3 Mason's Rule and the Signal Flow Graph (W)
3.3 Effect of Pole Locations
3.4 Time-Domain Specifications
3.4.1 Rise Time
3.4.2 Overshoot and Peak Time
3.4.3 Settling Time
3.5 Effects of Zeros and Additional Poles
3.6 Stability
3.6.1 Bounded Input—Bounded Output Stability
3.6.2 Stability of LTI Systems
3.6.3 Routh's Stability Criterion
3.7 Obtaining Models from Experimental Data: System Identification (W)
3.8 Amplitude and Time Scaling (W)
3.9 Historical Perspective
Summary
Review Questions
Problems
Chapter 4 - A First Analysis of Feedback
A Perspective on the Analysis of Feedback
Chapter Overview
4.1 The Basic Equations of Control
4.1.1 Stability
4.1.2 Tracking
4.1.3 Regulation
4.1.4 Sensitivity
4.2 Control of Steady-State Error to Polynomial Inputs: System Type
4.2.1 System Type for Tracking
4.2.2 System Type for Regulation and DisturbanceRejection
4.3 The Three-Term Controller: PID Control
4.3.1 Proportional Control (P)
4.3.2 Integral Control (I)
4.3.3 Derivative Control (D)
4.3.4 Proportional Plus Integral Control (PI)
4.3.5 PID Control
4.3.6 Ziegler—Nichols Tuning of the PID Controller
4.4 Feedforward Control by Plant Model Inversion
4.5 Introduction to Digital Control (W)
4.6 Sensitivity of Time Response to Parameter Change (W)
4.7 Historical Perspective
Summary
Review Questions
Problems
Chapter 5 - The Root-Locus Design Method
A Perspective on the Root-Locus Design Method
Chapter Overview
5.1 Root Locus of a Basic Feedback System
5.2 Guidelines for Determining a Root Locus
5.2.1 Rules for Determining a Positive (1800) Root Locus
5.2.2 Summary of the Rules for Determining a Root Locus
5.2.3 Selecting the Parameter Value
5.3 Selected Illustrative Root Loci
5.4 Design Using Dynamic Compensation
5.4.1 Design Using Lead Compensation
5.4.2 Design Using Lag Compensation
5.4.3 Design Using Notch Compensation
5.4.4 Analog and Digital Implementations (W)
5.5 A Design Example Using the Root Locus
5.6 Extensions of the Root-Locus Method
5.6.1 Rules for Plotting a Negative (0°) Root Locus
5.6.2 Consideration of Two Parameters
5.6.3 Time Delay (W)
5.7 Historical Perspective
Summary
Review Questions
Problems
Chapter 6 - The Frequency Response Design Method
A Perspective on the Frequency-Response Design Method
Chapter Overview
6.1 Frequency Response
6.1.1 Bode Plot Techniques
6.1.2 Steady-State Errors
6.2 Neutral Stability
6.3 The Nyquist Stability Criterion
6.3.1 The Argument Principle
6.3.2 Application of The Argument Principle to Control Design
6.4 Stability Margins
6.5 Bode's Gain—Phase Relationship
6.6 Closed-Loop Frequency Response
6.7 Compensation
6.7.1 PD Compensation
6.7.2 Lead Compensation (W)
6.7.3 PI Compensation
6.7.4 Lag Compensation
6.7.5 PID Compensation
6.7.6 Design Considerations
6.3.7 Specifications in Terms of the Sensitivity Function
6.7.8 Limitations on Design in Terms of the Sensitivity Function
6.8 Time Delay
6.8.1 Time Delay via the Nyquist Diagram (W)
6.9 Alternative Presentation of Data
6.9.1 Nichols Chart
6.9.2 The Inverse Nyquist Diagram (W)
6.10 Historical Perspective
Summary
Review Questions
Problems
Chapter 7 - State-Space Design
A Perspective on State-Space Design
Chapter Overview
7.1 Advantages of State-Space
7.2 System Description in State-Space
7.3 Block Diagrams and State-Space
7.4 Analysis of the State Equations
7.4.1 Block Diagrams and Canonical Forms
7.4.2 Dynamic Response from the StateEquations
7.5 Control-Law Design for Full-State Feedback
7.5.1 Finding the Control Law
7.5.2 Introducing the Reference Input with Full-StateFeedback
7.6 Selection of Pole Locations for Good Design
7.6.1 Dominant Second-Order Poles
7.6.2 Symmetric Root Locus (SRL)
7.6.3 Comments on the Methods
7.7 Estimator Design
7.7.1 Full-Order Estimators
7.7.2 Reduced-Order Estimators
7.7.3 Estimator Pole Selection
7.8 Compensator Design: Combined Control Law and Estimator (W)
7.9 Introduction of the Reference Input with the Estimator (W)
7.9.1 General Structure for the Reference
7.9.2 Selecting the Gain
7.10 Integral Control and Robust Tracking
7.10.1 Integral Control
7.10.2 Robust Tracking Control: The Error-SpaceApproach
7.10.3 Model-Following Design
7.10.4 The Extended Estimator
7.11 Loop Transfer Recovery
7.12 Direct Design with Rational Transfer Functions
7.13 Design for Systems with Pure Time Delay
7.14 Solution of State Equations (W)
7.15 Historical Perspective
Summary
Review Questions
Problems
Chapter 8 - Digital Control
A Perspective on Digital Control
Chapter Overview
8.1 Digitization
8.2 Dynamic Analysis of Discrete Systems
8.2.1 z-Transform
8.2.2 z-Transform Inversion
8.2.3 Relationship Between s and z
8.2.4 Final Value Theorem
8.3 Design Using Discrete Equivalents
8.3.1 Tustin's Method
8.3.2 Zero-Order Hold (ZOH) Method
8.3.3 Matched Pole—Zero (MPZ) Method
8.3.4 Modified Matched Pole—ZeroMMPZ) Method
8.3.5 Comparison of Digital ApproximationMethods
8.3.6 Applicability Limits of the Discrete EquivalentDesign Method
8.4 Hardware Characteristics
8.4.1 Analog-to-Digital (A/D) Converters
8.4.2 Digital-to-Analog Converters
8.4.3 Anti-Alias Prefilters
8.4.4 The Computer
8.5 Sample-Rate Selection
8.5.1 Tracking Effectiveness
8.5.2 Disturbance Rejection
8.5.3 Effect of Anti-Alias Prefilter
8.5.4 Asynchronous Sampling.
8.6 Discrete Design
8.6.1 Analysis Tools
8.6.2 Feedback Properties
8.6.3 Discrete Design Example
8.6.4 Discrete Analysis of Designs
8.7 Discrete State-Space Design Methods (W)
8.8 Historical Perspective
Summary
Review Questions
Problems
Chapter 9 - Nonlinear Systems
A Perspective on Nonlinear Systems
Chapter Overview
9.1 Introduction and Motivation: Why Study Nonlinear Systems?
9.2 Analysis by Linearization
9.2.1 Linearization by Small-Signal Analysis
9.2.2 Linearization by Nonlinear Feedback
9.2.3 Linearization by Inverse Nonlinearity
9.3 Equivalent Gain Analysis Using the Root Locus
9.3.1 Integrator Antiwindup
9.4 Equivalent Gain Analysis Using Frequency Response: Describing Functions
9.4.1 Stability Analysis Using Describing Functions
9.5 Analysis and Design Based on Stability
9.5.1 The Phase Plane
9.5.2 Lyapunov Stability Analysis
9.5.3 The Circle Criterion
9.6 Historical Perspective
Summary
Review Questions
Problems
Chapter 10 - Control System Design: Principles and Case Studies
A Perspective on Design Principles
Chapter Overview
10.1 An Outline of Control Systems Design
10.2 Design of a Satellite's Attitude Control
10.3 Lateral and Longitudinal Control of a Boeing 747
10.3.1 Yaw Damper
10.3.2 Altitude-Hold Autopilot
10.4 Control of the Fuel—Air Ratio in an Automotive Engine
10.5 Control of the Read/Write Head Assembly of a Hard Disk
10.6 Control of RTP Systems in Semiconductor Wafer Manufacturing
10.7 Chemotaxis or How E. Coll Swims Away from Trouble
10.8 Historical Perspective
Summary
Review Questions
Problems
Appendix
A.1 The r_ Laplace Transform
A.I.1 Properties of Laplace Transforms
A.1.2 Inverse Laplace Transform by Partial-Fraction Expansion
A.1.3 The Initial Value Theorem
A.1.4 Final Value Theorem
Appendix A Laplace Transforms
Appendix B Solutions to the Review Questions
Appendix C Mattab Commands
Bibliography
Index
FEEDBACK CONTROL OF DYNAMIC SYSTEMS
Table of Laplace Transforms Number l 2 3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 f(s) I I s 1 s2 2! s3 3! s4 m! sm+1 1 (s+a) I (s + a)2 (s + a)3 (s + a)m l I a s(s +a) a s2(s+ a) b-a (s + a)(s + b) s (s + a)2 a2 s(s + a)2 (b- a)s (s + a)(s + b) a (s2 + a2) s (s2 + a2) s+a (s +a)2 + b2 b (s + a)2 + b2 a2 +,;. s [ (.s + a)2 + b2] /(t), t?: 0 .S(t) l (t) I ,2 13 Im e-at te-at _!_ 12e-a1 2! 1 ,m-1e-at (m - 1)! l -at -e - 1 -(at - I+ e at) a -at -bt -e e (I - at)e-at 1 - e-at (I + at) be-bt - ae-at sin at cos at e-at cosbt e-at sin bt I - e-at (cos bt + ~ sin bt)
Chronological History of Feedback Control Driverless car - Automotive stability augmentation systems - Farm tractor auto-steering via GPS - GPS Unmanned aircraft - High precision disk drive control - Computer-aided control design - Internal model control - Feedback control of automotive engines - Aircraft auto-landing - Apollo digital autopilot - Aircraft stability augmentation - LQG design - Inertial navigation - Microprocessor - Maximum principle - Dynamic programming - Numerical optimization - Optimal filtering - Sampled data systems - Root locus - Nyquist stability - Frequency-response tools - Feedback amplifier - Autopilot - lbility analysis of governor - Routh stability - Fly-ball governor l lncubatorl +- I 1600s 1700s I I I 1800s 1910 I 1920 I 1930 I 1940 I 1950 I 1960 I 1970 I 1980 1990 2000 2010 • I I I
Feedback Control of Dynamic Systems Seventh Edition Gene F. Franklin Stanford University J. oav;d Powell Stanford University Abbas Emami-Naeini SC Solutions, Inc. PEARSON Boston Columbus Indianapolis New York San Francis\.'o l1pper SadJle Rher AntMcrdam Cape Town Dubai London Madrid Milan Munkh P.aris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
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To the memory of Gene F. Franklin
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