6th Edition

Linear Control System Analysis and Design with MATLAB®

    729 Pages 558 B/W Illustrations
    by CRC Press

    Thoroughly classroom-tested and proven to be a valuable self-study companion, Linear Control System Analysis and Design: Sixth Edition provides an intensive overview of modern control theory and conventional control system design using in-depth explanations, diagrams, calculations, and tables.

    Keeping mathematics to a minimum, the book is designed with the undergraduate in mind, first building a foundation, then bridging the gap between control theory and its real-world application. Computer-aided design accuracy checks (CADAC) are used throughout the text to enhance computer literacy. Each CADAC uses fundamental concepts to ensure the viability of a computer solution.

    Completely updated and packed with student-friendly features, the sixth edition presents a range of updated examples using MATLAB®, as well as an appendix listing MATLAB functions for optimizing control system analysis and design. Over 75 percent of the problems presented in the previous edition have been revised or replaced.

    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

    Biography

    Constantine H. Houpis, Stuart N. Sheldon