Automatic control systems / Farid Golnaraghi , Benjamin C. Kuo.

Preface CHAPTER 1 Introduction to Control Systems 1-1 Basic Components of a Control System 1-2 Examples of Control-System Applications 1-2-1 Intelligent Transportation Systems 1-2-2 Steering Control of an Automobile 1-2-3 Idle-Speed Control of an Automobile 1-2-4 Sun-Tracking Control of Solar Collectors 1-3 Open-Loop Control Systems (Nonfeedback Systems) 1-4 Closed-Loop Control Systems (Feedback Control Systems) 1-5 What Is Feedback, and What Are Its Effects? 1-5-1 Effect of Feedback on Overall Gain 1-5-2 Effect of Feedback on Stability 1-5-3 Effect of Feedback on External Disturbance or Noise 1-6 Types of Feedback Control Systems 1-7 Linear versus Nonlinear Control Systems 1-8 Time-Invariant versus Time-Varying Systems 1-9 Continuous-Data Control Systems 1-10 Discrete-Data Control Systems 1-11 Case Study: Intelligent Vehicle Obstacle Avoidance-LEGO MINDSTORMS 1-12 Summary CHAPTER 2 Modeling of Dynamic Systems 2-1 Modeling of Simple Mechanical Systems 2-1-1 Translational Motion 2-1-2 Rotational Motion 2-1-3 Conversion between Translational and Rotational Motions 2-1-4 Gear Trains 2-1-5 Backlash and Dead Zone (Nonlinear Characteristics) 2-2 Introduction to Modeling of Simple Electrical Systems 2-2-1 Modeling of Passive Electrical Elements 2-2-2 Modeling of Electrical Networks 2-3 Introduction to Modeling of Thermal and Fluid Systems 2-3-1 Elementary Heat Transfer Properties 2-3-2 Elementary Fluid System Properties 2-4 Linearization of Nonlinear Systems 2-4-1 Linearization Using Taylor Series: Classical Representation 2-5 Analogies 2-6 Project: Introduction to LEGO MINDSTORMS NXT Motor-Mechanical Modeling 2-7 Summary References Problems CHAPTER 3 Solution of Differential Equations of Dynamic Systems 3-1 Introduction to Differential Equations 3-1-1 Linear Ordinary Differential Equations 3-1-2 Nonlinear Differential Equations 3-2 Laplace Transform 3-2-1 Definition of the Laplace Transform 3-2-2 Important Theorems of the Laplace Transform 3-2-3 Transfer Function 3-2-4 Characteristic Equation 3-2-5 Analytic Function 3-2-6 Poles of a Function 3-2-7 Zeros of a Function 3-2-8 Complex Conjugate Poles and Zeros 3-2-9 Final-Value Theorem 3-3 Inverse Laplace Transform by Partial-Fraction Expansion 3-3-1 Partial Fraction Expansion 3-4 Application of the Laplace Transform to the Solution of Linear Ordinary Differential Equations 3-4-1 First-Order Prototype System 3-4-2 Second-Order Prototype System 3-4-3 Second-Order Prototype System-Final Observations 3-5 Impulse Response and Transfer Functions of Linear Systems 3-5-1 Impulse Response 3-5-2 Time Response Using the Impulse Response 3-5-3 Transfer Function (Single-Input, Single-Output Systems) 3-6 Systems of First-Order Differential Equations: State Equations 3-6-1 Definition of State Variables 3-6-2 The Output Equation 3-7 Solution of the Linear Homogeneous State Equation 3-7-1 Transfer Functions (Multivariable Systems) 3-7-2 Characteristic Equation from State Equations 3-7-3 State Equations from the Transfer Function 3-8 Case Studies with MATLAB 3-9 Linearization Revisited-the State-Space Approach 3-10 Summary References Problems CHAPTER 4 Block Diagrams and Signal-Flow Graphs 4-1 Block Diagrams 4-1-1 Modeling of Typical Elements of Block Diagrams in Control Systems 4-1-2 Relation between Mathematical Equations and Block Diagrams 4-1-3 Block Diagram Reduction 4-1-4 Block Diagrams of Multi-Input Systems: Special Case-Systems with a Disturbance 4-1-5 Block Diagrams and Transfer Functions of Multivariable Systems 4-2 Signal-Flow Graphs 4-2-1 SFG Algebra 4-2-2 Definitions of SFG Terms 4-2-3 Gain Formula for SFG 4-2-4 Application of the Gain Formula between Output Nodes and Noninput Nodes 4-2-5 Simplified Gain Formula 4-3 State Diagram 4-3-1 From Differential Equations to State Diagrams 4-3-2 From State Diagrams to Transfer Functions 4-3-3 From State Diagrams to State and Output Equations 4-4 Case Studies 4-5 MATLAB Tools 4-6 Summary References Problems CHAPTER 5 Stability of Linear Control Systems 5-1 Introduction to Stability 5-2 Methods of Determining Stability 5-3 Routh-Hurwitz Criterion 5-3-1 Routh's Tabulation 5-3-2 Special Cases When Routh's Tabulation Terminates Prematurely 5-4 MATLAB Tools and Case Studies 5-5 Summary References Problems CHAPTER 6 Important Components of Feedback Control Systems 6-1 Modeling of Active Electrical Elements: Operational Amplifiers 6-1-1 The Ideal Op-Amp 6-1-2 Sums and Differences 6-1-3 First-Order Op-Amp Configurations 6-2 Sensors and Encoders in Control Systems 6-2-1 Potentiometer 6-2-2 Tachometers 6-2-3 Incremental Encoder 6-3 DC Motors in Control Systems 6-3-1 Basic Operational Principles of DC Motors 6-3-2 Basic Classifications of PM DC Motors 6-3-3 Surface-Wound DC Motors 6-3-4 Moving-Coil DC Motors 6-3-5 Brushless DC Motors 6-3-6 Mathematical Modeling of PM DC Motors 6-3-7 Relation between Ki and Kb 6-4 Speed and Position Control of a DC Motor 6-4-1 Speed Response and the Effects of Inductance and Disturbance: Open-Loop Response 6-4-2 Speed Control of DC Motors: Closed-Loop Response 6-4-3 Position Control 6-5 Case Studies: Practical Examples 6-6 The Control Lab: Introduction to LEGO MINDSTORMS NXT Motor-Modeling and Characterization 6-6-1 NXT Motor 6-6-2 Electrical Characteristics 6-6-3 Mechanical Characteristics 6-6-4 Speed Response and Model Verification 6-7 Summary References Problems CHAPTER 7 Time-Domain Performance of Control Systems 7-1 Time Response of Continuous-Data Systems: Introduction 7-2 Typical Test Signals to Evaluate Time-Response Performance of Control Systems 7-3 The Unit-Step Response and Time-Domain Specifications 7-4 Time Response of a Prototype First-Order System 7-5 Transient Response of a Prototype Second-Order System 7-5-1 Damping Ratio and Natural Frequency 7-5-2 Maximum Overshoot (0 < < 1) 7-5-3 Delay Time and Rise Time (0 < < 1) 7-5-4 Settling Time (5 and 2 Percent) 7-5-5 Transient Response Performance Criteria-Final Remarks 7-6 Steady-State Error 7-6-1 Definition of the Steady-State Error 7-6-2 Steady-State Error in Systems with a Disturbance 7-6-3 Types of Control Systems: Unity-Feedback Systems 7-6-4 Error Constants 7-6-5 Steady-State Error Caused by Nonlinear System Elements 7-7 Basic Control Systems and Effects of Adding Poles and Zeros to Transfer Functions 7-7-1 Addition of a Pole to the Forward-Path Transfer Function: Unity-Feedback Systems 7-7-2 Addition of a Pole to the Closed-Loop Transfer Function 7-7-3 Addition of a Zero to the Closed-Loop Transfer Function 7-7-4 Addition of a Zero to the Forward-Path Transfer Function: Unity-Feedback Systems 7-7-5 Addition of Poles and Zeros: Introduction to Control of Time Response 7-8 Dominant Poles and Zeros of Transfer Functions 7-8-1 Summary of Effects of Poles and Zeros 7-8-2 The Relative Damping Ratio 7-8-3 The Proper Way of Neglecting the Insignificant Poles with Consideration of the Steady-State Response 7-9 Case Study: Time-Domain Analysis of a Position-Control System 7-9-1 Unit-Step Transient Response 7-9-2 The Steady-State Response 7-9-3 Time Response of a Third-Order System-Electrical Time Constant Not Neglected 7-9-4 Unit-Step Transient Response 7-9-5 Steady-State Response 7-10 The Control Lab: Introduction to LEGO MINDSTORMS NXT Motor-Position Control 7-11 Summary References Problems CHAPTER 8 State-Space Analysis and Controller Design 8-1 State-Variable Analysis 8-2 Block Diagrams, Transfer Functions, and State Diagrams 8-2-1 Transfer Functions (Multivariable Systems) 8-2-2 Block Diagrams and Transfer Functions of Multivariable Systems 8-3 Systems of First-Order Differential Equations: State Equations 8-3-1 Definition of State Variables 8-3-2 The Output Equation 8-4 Vector-Matrix Representation of State Equations 8-5 State-Transition Matrix 8-5-1 Significance of the State-Transition Matrix 8-5-2 Properties of the State-Transition Matrix 8-6 State-Transition Equation 8-6-1 State-Transition Equation Determined from the State Diagram 8-7 Relationship between State Equations and High-Order Differential Equations 8-8 Relationship between State Equations and Transfer Functions 8-9 Characteristic Equations, Eigenvalues, and Eigenvectors 8-9-1 Characteristic Equation from a Differential Equation 8-9-2 Characteristic Equation from a Transfer Function 8-9-3 Characteristic Equation from State Equations 8-9-4 Eigenvalues 8-9-5 Eigenvectors 8-9-6 Generalized Eigenvectors 8-10 Similarity Transformation 8-10-1 Invariance Properties of the Similarity Transformations 8-10-2 Characteristic Equations, Eigenvalues, and Eigenvectors 8-10-3 Transfer-Function Matrix 8-10-4 Controllability Canonical Form 8-10-5 Observability Canonical Form 8-10-6 Diagonal Canonical Form 8-10-7 Jordan Canonical Form 8-11 Decompositions of Transfer Functions 8-11-1 Direct Decomposition 8-11-2 Direct Decomposition to CCF 8-11-3 Direct Decomposition to OCF 8-11-4 Cascade Decomposition 8-11-5 Parallel Decomposition 8-12 Controllability of Control Systems 8-12-1 General Concept of Controllability 8-12-2 Definition of State Controllability 8-12-3 Alternate Tests on Controllability 8-13 Observability of Linear Systems 8-13-1 Definition of Observability 8-13-2 Alternate Tests on Observability 8-14 Relationship among Controllability, Observability, and Transfer Functions 8-15 Invariant Theorems on Controllability and Observability 8-16 Case Study: Magnetic-Ball Suspension System 8-16-1 The Characteristic Equation 8-17 State-Feedback Control 8-18 Pole-Placement Design through State Feedback 8-19 State Feedback with Integral Control 8-20 MATLAB Tools and Case Studies 8-20-1 Description and Use of the State-Space Analysis Tool 8-20-2 Description and Use of tfsym for State-Space Applications 8-21 Case Study: Position Control of the LEGO MINDSTORMS Robotic Arm System 8-22 Summary References Problems CHAPTER 9 Root-Locus Analysis 9-1 Basic Properties of the Root Loci 9-2 Properties of the Root Loci 9-2-1 K = 0 and K = +/- Points 9-2-2 Number of Branches on the Root Loci 9-2-3 Symmetry of the RL 9-2-4 Angles of Asymptotes of the RL: Behavior of the RL at |s| = 9-2-5 Intersect of the Asymptotes (Centroid) 9-2-6 Root Loci on the Real Axis 9-2-7 Angles of Departure and Angles of Arrival of the RL 9-2-8 Intersection of the RL with the Imaginary Axis 9-2-9 Breakaway Points (Saddle Points) on the RL 9-2-10 Angles of Arrival and Departure of Root Loci at the Breakaway Point 9-2-11 Calculation of K on the Root Loci 9-2-12 Summary: Properties of the Root Loci 9-3 The Root Sensitivity 9-4 Design Aspects of the Root Loci 9-4-1 Effects of Adding Poles and Zeros to G(s)H(s) 9-4-2 Addition of Poles to G(s)H(s) 9-4-3 Addition of Zeros to G(s)H(s) 9-5 Root Contours: Multiple-Parameter Variation 9-6 MATLAB Tools 9-7 Summary References Problems CHAPTER 10 Frequency-Domain Analysis 10-1 Introduction to Frequency Response 10-1-1 Frequency Response of Closed-Loop Systems 10-1-2 Frequency-Domain Specifications 10-2 Mr, r, and Bandwidth of the Prototype Second-Order System 10-2-1 Resonant Peak and Resonant Frequency 10-2-2 Bandwidth 10-3 Effects of Adding Poles and Zeros to the Forward-Path Transfer Function 10-3-1 Effects of Adding a Zero to the Forward-Path Transfer Function 10-3-2 Effects of Adding a Pole to the Forward-Path Transfer Function 10-4 Nyquist Stability Criterion: Fundamentals 10-4-1 Stability Problem 10-4-2 Definitions of Encircled and Enclosed 10-4-3 Number of Encirclements and Enclosures 10-4-4 Principles of the Argument 10-4-5 Nyquist Path 10-4-6 Nyquist Criterion and the L(s) or the G(s)H(s) Plot 10-5 Nyquist Criterion for Systems with Minimum-Phase Transfer Functions 10-5-1 Application of the Nyquist Criterion to Minimum-Phase Transfer Functions That Are Not Strictly Proper 10-6 Relation between the Root Loci and the Nyquist Plot 10-7 Illustrative Examples: Nyquist Criterion for Minimum-Phase Transfer Functions 10-8 Effects of Adding Poles and Zeros to L(s) on the Shape of the Nyquist Plot 10-8-1 Addition of Poles at s = 0 10-8-2 Addition of Finite Nonzero Poles 10-8-3 Addition of Zeros 10-9 Relative Stability: Gain Margin and Phase Margin 10-9-1 Gain Margin 10-9-2 Gain Margin of Nonminimum-Phase Systems 10-9-3 Phase Margin 10-10 Stability Analysis with the Bode Plot 10-10-1 Bode Plots of Systems with Pure Time Delays 10-11 Relative Stability Related to the Slope of the Magnitude Curve of the Bode Plot 10-11-1 Conditionally Stable System 10-12 Stability Analysis with the Magnitude-Phase Plot 10-13 Constant-M Loci in the Magnitude-Phase Plane: The Nichols Chart 10-14 Nichols Chart Applied to Nonunity-Feedback Systems 10-15 Sensitivity Studies in the Frequency Domain 10-16 MATLAB Tools and Case Studies 10-17 Summary References Problems CHAPTER 11 Design of Control Systems 11-1 Introduction 11-1-1 Design Specifications 11-1-2 Controller Configurations 11-1-3 Fundamental Principles of Design 11-2 Design with the PD Controller 11-2-1 Time-Domain Interpretation of PD Control 11-2-2 Frequency-Domain Interpretation of PD Control 11-2-3 Summary of Effects of PD Control 11-3 Design with the PI Controller 11-3-1 Time-Domain Interpretation and Design of PI Control 11-3-2 Frequency-Domain Interpretation and Design of PI Control 11-4 Design with the PID Controller 11-5 Design with Phase-Lead and Phase-Lag Controllers 11-5-1 Time-Domain Interpretation and Design of Phase-Lead Control 11-5-2 Frequency-Domain Interpretation and Design of Phase-Lead Control 11-5-3 Effects of Phase-Lead Compensation 11-5-4 Limitations of Single-Stage Phase-Lead Control 11-5-5 Multistage Phase-Lead Controller 11-5-6 Sensitivity Considerations 11-5-7 Time-Domain Interpretation and Design of Phase-Lag Control 11-5-8 Frequency-Domain Interpretation and Design of Phase-Lag Control 11-5-9 Effects and Limitations of Phase-Lag Control 11-5-10 Design with Lead-Lag Controller 11-6 Pole-Zero-Cancellation Design: Notch Filter 11-6-1 Second-Order Active Filter 11-6-2 Frequency-Domain Interpretation and Design 11-7 Forward and Feedforward Controllers 11-8 Design of Robust Control Systems 11-9 Minor-Loop Feedback Control 11-9-1 Rate-Feedback or Tachometer-Feedback Control 11-9-2 Minor-Loop Feedback Control with Active Filter 11-10 MATLAB Tools and Case Studies 11-11 The Control Lab References Problems INDEX

600-699