Linear Control System Analysis and Design with MATLAB (Hardcover, 6)

Part I: Introductory Material
Introduction
Introduction
Introduction to Control Systems
Definitions
Historical Background
Control System: A Human Being
Digital Control Development
Mathematical Background
Engineering Control Problem
Computer Literacy
Outline of Text

Unmanned Aircraft Vehicles
Introduction
Twentieth-Century UAV R&D
Predator
Grim Reaper (US Air Force Fact Sheet MQ-9 Reaper, Posted on January 5, 2012)
RQ-4 Global Hawk (US Air Force Fact Sheet RQ-4 Global Hawk, Posted on January 19, 2012)

Wind Energy Control Systems
Introduction
Concurrent Engineering: A Road Map for Systems Design: Energy Example
QFT Controller Design CAD Toolbox

Frequency Domain Analysis
Introduction
Steel Mill Ingot
Electrocardiographic Monitoring
Control Theory: Analysis and Design of Control Systems

Part II: Analog Control Systems
Writing System Equations
Introduction
Electric Circuits and Components
State Concepts
Transfer Function and Block Diagram
Mechanical Translation Systems
Analogous Circuits
Mechanical Rotational Systems
Effective Moment of Inertia and Damping of a Gear Train
Thermal Systems
Hydraulic Linear Actuator
Liquid-Level System
Rotating Power Amplifiers
DC Servomotor
AC Servomotor
Lagrange’s Equation

Solution of Differential Equations
Introduction
Standard Inputs to Control Systems
Steady-State Response: Sinusoidal Input
Steady-State Response: Polynomial Input
Transient Response: Classical Method
Definition of Time Constant
Example: Second-Order System (Mechanical)
Example: Second-Order System (Electrical)
Second-Order Transients
Time-Response Specifications
CAD Accuracy Checks
State-Variable Equations
Characteristic Values
Evaluating the State Transition Matrix
Complete Solution of the State Equation

Laplace Transform
Introduction
Definition of the Laplace Transform
Derivation of Laplace Transforms of Simple Functions
Laplace Transform Theorems
CAD Accuracy Checks
Application of the Laplace Transform to Differential Equations
Inverse Transformation
Heaviside Partial-Fraction Expansion Theorems
MATLAB^® Partial-Fraction Example
Partial-Fraction Shortcuts
Graphical Interpretation of Partial-Fraction Coefficients
Frequency Response from the Pole?Zero Diagram
Location of Poles and Stability
Laplace Transform of the Impulse Function
Second-Order System with Impulse Excitation
Solution of State Equation
Evaluation of the Transfer-Function Matrix
MATLAB^® Script For MIMO Systems

System Representation
Introduction
Block Diagrams
Determination of the Overall Transfer Function
Standard Block-Diagram Terminology
Position-Control System
Simulation Diagrams
Signal Flow Graphs
State Transition Signal Flow Graph
Parallel State Diagrams from Transfer Functions
Diagonalizing the A Matrix
Use of State Transformation for the State-Equation Solution
Transforming A Matrix with Complex Eigenvalues
Transforming an A Matrix into Companion Form
Using MATLAB^® to Obtain the Companion A Matrix

Control-System Characteristics
Introduction
Routh’s Stability Criterion
Mathematical and Physical Forms
Feedback System Types
Analysis of System Types
Example: Type 2 System
Steady-State Error Coefficients
CAD Accuracy Checks: CADAC
Use of Steady-State Error Coefficients
Nonunity-Feedback System

Root Locus
Introduction
Plotting Roots of a Characteristic Equation
Qualitative Analysis of the Root Locus
Procedure Outline
Open-Loop Transfer Function
Poles of the Control Ratio C(s)/R(s)
Application of the Magnitude and Angle Conditions
Geometrical Properties (Construction Rules)
CAD Accuracy Checks
Root Locus Example
Example of Section 10.10: MATLAB^® Root Locus
Root Locus Example with an RH Plane Zero
Performance Characteristics
Transport Lag
Synthesis
Summary of Root-Locus Construction Rules for Negative Feedback

Frequency Response
Introduction
Correlation of the Sinusoidal and Time Response
Frequency-Response Curves
Bode Plots (Logarithmic Plots)
General Frequency?Transfer?Function Relationships
Drawing the Bode Plots
Example of Drawing a Bode Plot
Generation of MATLAB^® Bode Plots
System Type and Gain as Related to Log Magnitude Curves
CAD Accuracy Check
Experimental Determination of Transfer Function
Direct Polar Plots
Summary: Direct Polar Plots
Nyquist Stability Criterion
Examples of the Nyquist Criterion Using Direct Polar Plots
Nyquist Stability Criterion Applied to a System Having Dead Time
Definitions of Phase Margin and Gain Margin and Their Relation to Stability
Stability Characteristics of the Log Magnitude and Phase Diagram
Stability from the Nichols Plot (Log Magnitude?Angle Diagram)

Closed-Loop Tracking Performance Based on Frequency Response
Introduction
Direct Polar Plot
Determination of Mm and ωm for a Simple Second-Order System
Correlation of Sinusoidal and Time Responses
Constant M(ω) and α(ω) Contours of C(Jω)/R(Jω) on the Complex Plane (Direct Plot) Constant 1/M and α Contours (Unity Feedback) in the Inverse Polar Plane
Gain Adjustment of a Unity-Feedback System for a Desired Mm: Direct Polar Plot
Constant M and α Curves on the Log Magnitude?Angle Diagram (Nichols Chart) Generation of MATLAB^® Bode and Nyquist Plots
Adjustment of Gain by Use of the Log Magnitude?Angle Diagram (Nichols Chart)
Correlation of the Pole?Zero Diagram with Frequency and Time Responses

Part III: Compensation: Analog Systems
Root-Locus Compensation: Design
Introduction to Design
Transient Response: Dominant Complex Poles
Additional Significant Poles
Root-Locus Design Considerations
Reshaping the Root Locus
CAD Accuracy Checks
Ideal Integral Cascade Compensation (PI Controller)
Cascade Lag Compensation Design Using Passive Elements System
Ideal Derivative Cascade Compensation (PD Controller)
Lead Compensation Design Using Passive Elements
General Lead-Compensator Design
Lag?Lead Cascade Compensation Design System
Comparison of Cascade Compensators
PID Controller
Introduction to Feedback Compensation
Feedback Compensation: Design Procedures
Simplified Rate Feedback Compensation: A Design Approach
Design of Rate Feedback
Design: Feedback of Second Derivative of Output
Results of Feedback-Compensation Design
Rate Feedback: Plants with Dominant Complex Poles

Frequency-Response Compensation Design
Introduction to Feedback Compensation Design
Selection of a Cascade Compensator
Cascade Lag Compensator
Design Example: Cascade Lag Compensation
Cascade Lead Compensator
Design Example: Cascade Lead Compensation
Cascade Lag?Lead Compensator
Design Example: Cascade Lag?Lead Compensation
Feedback Compensation Design Using Log Plots
Design Example: Feedback Compensation (Log Plots)
Application Guidelines: Basic Minor-Loop Feedback Compensators

Part IV: Advanced Topics
Control-Ratio Modeling
Introduction
Modeling a Desired Tracking Control Ratio
Guillemin ? Truxal Design Procedure
Introduction to Disturbance Rejection
Second-Order Disturbance-Rejection Model
Disturbance-Rejection Design Principles for SISO Systems
Disturbance-Rejection Design Example
Disturbance-Rejection Models

Design: Closed-Loop Pole?Zero Assignment (State-Variable Feedback)
Introduction
Controllability and Observability
State Feedback for SISO Systems
State-Feedback Design for SISO Systems Using the Control Canonical (Phase-Variable) Form
State-Variable Feedback (Physical Variables)
General Properties of State Feedback (Using Phase Variables)
State-Variable Feedback: Steady-State Error Analysis
Use of Steady-State Error Coefficients
State-Variable Feedback: All-Pole Plant
Plants with Complex Poles
Compensator Containing a Zero
State-Variable Feedback: Pole?Zero Plant
Observers
Control Systems Containing Observers

Parameter Sensitivity and State-Space Trajectories
Introduction
Sensitivity
Sensitivity Analysis
Sensitivity Analysis Examples
Parameter Sensitivity Examples
Inaccessible States
State-Space Trajectories
Linearization (Jacobian Matrix)

Part V: Digital Control Systems
Sampled-Data Control Systems
Introduction
Sampling
Ideal Sampling
Z Transform Theorems
Differentiation Process
Synthesis in the z Domain (Direct Method)
Inverse Z Transform
Zero-Order Hold
Limitations
Steady-State Error Analysis for Stable Systems
Root-Locus Analysis for Sampled-Data Control Systems

Digital Control Systems
Introduction
Complementary Spectra
Tustin Transformation: s- to z-Plane Transformation
z-Domain to the w- and w’-Domain Transformations
Digitization Technique
Digitization Design Technique
Pseudo-Continuous-Time Control System
Design of Digital Control System
Direct Compensator
PCT Lead Cascade Compensation
PCT Lag Compensation
PCT Lag?Lead Compensation
Feedback Compensation: Tracking
Controlling Unwanted Disturbances
Extensive Digital Feedback Compensator Example
Controller Implementation
Appendix A: Table of Laplace Transform Pairs
Appendix B: Matrix Linear Algebra
Appendix C: Introduction to MATLAB® and Simulink®
Appendix D: Conversion of Units
Problems
Answers to Selected Problems
Index