Design of Feedback Control Systems

• Preface Chapter 1. Continuous-Time System Description 1.1: Preview 1.2: Basic Concepts 1.2.1: Control System Terminology 1.2.2: The Feedback Concept 1.3: Modeling 1.4: System Dynamics 1.5: Electrical Components 1.5.1: Mesh Analysis 1.5.2: State Variables 1.5.3: Node Analysis 1.5.4: Analyzing Operational Amplifier Circuits 1.5.5: Operational Amplifier Applications 1.6: Translational Mechanical Components 1.6.1: Free Body Diagrams 1.6.2: State Variables 1.7: Rotational Mechanical Components 1.7.1: Free Body Diagrams 1.7.2: Analogies 1.7.3: Gear Trains and Transformers 1.8: Electromechanical Components 1.9: Aerodynamics 1.9.1: Nomenclature 1.9.2: Dynamics 1.9.3: Lateral and Longitudinal Motion 1.10: Thermal Systems 1.11: Hydraulics 1.12: Transfer Function and Stability 1.12.1: Transfer Functions 1.12.2: Response Terms 1.12.3: Multiple Inputs and Outputs 1.12.4: Stability 1.13: Block Diagrams 1.13.1: Block Diagram Elements 1.13.2: Block Diagram Reductions 1.13.3: Multiple Inputs and Outputs 1.14: Signal Flow Graphs 1.14.1: Comparison and Block Diagrams 1.14.2: Mason's Rule 1.15: A Positioning Servo 1.16: Controller Model of the Thyroid Gland 1.17: Stick-Slip Response of an Oil Well Drill 1.18: Summary References Problems Chapter 2. Continuous-Time System Response 2.1: Preview 2.2: Response of First-Order Systems 2.3: Response of Second-Order Systems 2.3.1: Time Response 2.3.2: Overdamped Response 2.3.3: Critically Damped Response 2.3.4: Underdamped Response 2.3.5: Undamped Natural Frequency and Damping Ratio 2.3.6: Rise Time, Overshoot and Settling Time 2.4: Higher-Order System Response 2.5: Stability Testing 2.5.1: Coefficient Tests 2.5.2: Routh-Hurwitz Testing 2.5.3: Significance of the Array Coefficients 2.5.4: Left-Column Zeros 2.5.5: Row of Zeros 2.5.6: Eliminating a Possible Odd Divisor 2.5.7: Multiple Roots 2.6: Parameter Shifting 2.6.1: Adjustable Systems 2.6.2: Khartinov's Theorem 2.7: An Insulin Delivery System 2.8: Analysis of an Aircraft Wing 2.9: Summary References Problems Chapter 3. Performance Specifications 3.1: Preview 3.2: Analyzing Tracking Systems 3.2.1: Importance of Tracking Systems 3.2.2: Natural Response, Relative Stability and Damping 3.3: Forced Response 3.3.1: Steady State Error 3.3.2: Initial and Final Values 3.3.3: Steady State Errors to Power-of-Time Inputs 3.4: Power-of-Time Error Performance 3.4.1: System Type Number 3.4.2: Achieving a Given Type Number 3.4.3: Unity Feedback Systems 3.4.4: Unity Feedback Error Coefficients 3.5: Performance Indices and Optimal Systems 3.6: System Sensitivity 3.6.1: Calculating the Effects of Changes in Parameters 3.6.2: Sensitivity Functions 3.6.3: Sensitivity to Disturbance Signals 3.7: Time Domain Design 3.7.1: Process Control 3.7.2: Ziegler-Nichols Compensation 3.7.3: Chien-Hrones-Reswick Compensation 3.8: An Electric Rail Transportation System 3.9: Phase-Locked Loop for a CB Receiver 3.10: Bionic Eye 3.11: Summary References Problems Chapter 4. Root Locus Analysis 4.1: Preview 4.2: Pole-Zero Plots 4.2.1: Poles and Zeros 4.2.2: Graphical Evaluation 4.3: Root Locus for Feedback Systems 4.3.1: Angle Criterion 4.3.2: High and Low Gains 4.3.3: Root Locus Properties 4.4: Root Locus Construction 4.5: More About Root Locus 4.5.1: Root Locus Calibration 4.5.2: Computer-Aided Root Locus 4.6: Root Locus for Other Systems 4.6.1: Systems with Other Forms 4.6.2: Negative Parameter Ranges 4.6.3: Delay Effects 4.7: Design Concepts (Adding Poles and Zeros) 4.8: A Light-Source Tracking System 4.9: An Artificial Limb 4.10: Control of a Flexible Spacecraft 4.11: Bionic Eye 4.12: Summary References Problems Chapter 5. Root Locus Design 5.1: Preview 5.2: Shaping a Root Locus 5.3: Adding and Canceling Poles and Zeros 5.3.1: Adding a Pole or Zero 5.3.2: Canceling a Pole or Zero 5.4: Second-Order Plant Models 5.5: An Uncompensated Example System 5.6: Cascade Proportional Plus Integral (PI) 5.6.1: General Approach to Compensator Design 5.6.2: Cascade PI Compensation 5.7: Cascade Lag Compensation 5.8: Cascade Lead Compensation 5.9: Cascade Lag-Lead Compensation 5.10: Rate Feedback Compensation (PD) 5.11: Proportional-Integral-Derivative Compensation 5.12: Pole Placement 5.12.1: Algebraic Compensation 5.12.2: Selecting the Transfer Function 5.12.3: Incorrect Plant Transmittance 5.12.4: Robust Algebraic Compensation 5.12.5: Fixed-Structure Compensation 5.13: An Unstable High-Performance Aircraft 5.14: Control of a Flexible Space Station 5.15: Control of a Solar Furnace 5.16: Summary References Problems Chapter 6. Frequency Response Analysis 6.1: Preview 6.2: Frequency Response 6.2.1: Forced Sinusoidal Response 6.2.2: Frequency Response Measurement 6.2.3: Response at Low and High Frequencies 6.2.4: Graphical Frequency Response Methods 6.3: Bode Plots 6.3.1: Amplitude Plots in Decibels 6.3.2: Real Axis Roots 6.3.3: Products of Transmittance Terms 6.3.4: Complex Roots 6.4: Using Experimental Data 6.4.1: Finding Models 6.4.2: Irrational Transmittances 6.5: Nyquist Methods 6.5.1: Generating the Nyquist (Polar) Plot 6.5.2: Interpreting the Nyquist Plot 6.6: Gain Margin 6.7: Phase Margin 6.8: Relations between Closed-Loop and Open-Loop Frequency Response 6.9: Frequency Response of a Flexible Spacecraft 6.10: Summary References Problems Chapter 7. Frequency Response Design 7.1: Preview 7.2: Relation between Root Locus, Time Domain, and Frequency Domain 7.3: Compensation Using Bode Plots 7.4: Uncompensated System 7.5: Cascade Proportional Plus Integral (PI) and Cascade Lag Compensations 7.6: Cascade Lead Compensation 7.7: Cascade Lag-Lead Compensation 7.8: Rate Feedback Compensation 7.9: Proportional-Integral-Derivative Compensation 7.10: An Automobile Driver as a Compensator 7.11: Summary References Problems Chapter 8. State Space Analysis 8.1: Preview 8.2: State Space Representation 8.2.1: Phase-Variable Form 8.2.2: Dual Phase-Variable Form 8.2.3: Multiple Inputs and Outputs 8.2.4: Physical State Variables 8.2.5: Transfer Functions 8.3: State Transformations and Diagonalization 8.3.1: Diagonal Forms 8.3.2: Diagonalization Using Partial-Fraction Expansion 8.3.3: Complex Conjugate Characteristic Roots 8.3.4: Repeated Characteristic Roots 8.4: Time Response from State Equations 8.4.1: Laplace Transform Solution 8.4.2: Time-Domain Response of First-Order Systems 8.4.3: Time-Domain Response of Higher-Order Systems 8.4.4: System Response Computation 8.5: Stability 8.5.1: Asymptotic Stability 8.5.2: BIBO Stability 8.5.3: Internal Stability 8.6: Controllability and Observability 8.6.1: The Controllability Matrix 8.6.2: The Observability Matrix 8.6.3: Controllability, Observability and Pole-Zero Cancellation 8.6.4: Causes of Uncontrollability 8.7: Inverted Pendulum Problems 8.8: Summary Chapter 9. State Space Design 9.1: Preview 9.2: State Feedback and Pole Placement 9.2.1: Stabilizability 9.2.2: Choosing Pole Locations 9.2.3: Limitations of State Feedback 9.3: Tracking Problems 9.3.1: Integral Control 9.4: Observer Design 9.4.1: Control Using Observers 9.4.2: Separation Property 9.4.3: Observer Transfer Function 9.5: Reduced-Order Observer Design 9.5.1: Separation Property 9.5.2: Reduced-Order Observer Transfer Function 9.6: A Magnetic Levitation System 9.7: Summary Chapter 10. Advanced State Space Methods 10.1: Preview 10.2: The Linear Quadratic Regulator Problem 10.2.1: Properties of the LQR Design 10.2.2: Return Difference Inequality 10.2.3: Optimal Root Locus 10.3: Optimal Observers--The Kalman Filter 10.4: The Linear Quadratic Gaussian (LQG) Problem 10.4.1: Critique of LGQ 10.5: Robustness 10.5.1: Feedback Properties 10.5.2: Uncertainty Modeling 10.5.3: Robust Stability 10.6: Loop Transfer Recovery (LTR) 10.7: H¥ Control 10.7.1: A Brief History 10.7.2: Some Preliminaries 10.7.3: H¥ Control: Solution 10.7.4: Weights in H¥ Control Problem 10.8: Summary References Problems Chapter 11. Digital Control 11.1: Preview 11.2: Computer Processing 11.2.1: Computer History and Trends 11.3: A/D and D/A Conversion 11.3.1: Analog-to-Digital Conversion 11.3.2: Sample and Hold 11.3.3: Digital-to-Analog Conversion 11.4: Discrete-Time Signals 11.4.1: Representing Sequences 11.4.2: Z-Transformation and Properties 11.4.3: Inverse z-Transform 11.5: Sampling 11.6: Reconstruction of Signals from Samples 11.6.1: Representing Sampled Signals with Impulses 11.6.2: Relation between the z-Transform and the Laplace Transform 11.6.3: The Sampling Theorem 11.7: Discrete-Time Systems 11.7.1: Difference Equations Response 11.7.2: Z-Transfer Functions 11.7.3: Block Diagrams and Signal Flow Graphs 11.7.4: Stability and the Bilinear Transformation 11.7.5: Computer Software 11.8: State-Variable Descriptions of Discrete-Time Systems 11.8.1: Simulation Diagrams and Equations 11.8.2: Response and Stability 11.8.3: Controllability and Observability 11.9: Digitizing Control Systems 11.9.1: Step-Invariant Approximation 11.9.2: z-Transfer Functions of Systems with Analog Measurements 11.9.3: A Design Example 11.10: Direct Digital Design 11.10.1: Steady State Response 11.10.2: Deadbeat Systems 11.10.3: A Design Example 11.11: Summary References Problems Appendix A. Matrix Algebra A.1: Preview A.2: Nomenclature A.3: Addition and Subtraction A.4: Transposition A.5: Multiplication A.6: Determinants and Cofactors A.7: Inverse A.8: Simultaneous Equations A.9: Eigenvalues and Eigenvectors A.10: Derivative of a Scalar with Respect to a Vector A.11: Quadratic Forms and Symmetry A.12: Definiteness A.13: Rank A.14: Partitioned Matrices Problems Appendix B. Laplace Transform B.1: Preview B.2: Definition and Properties B.3: Solving Differential Equations B.4: Partial Fraction Expansion B.5: Additional Properties of the Laplace Transform Real Translation Second Independent Variable Final Value and Initial Value Theorems Convolution Integral Index

'An excellent text book that explains the basic concepts to the beginner in a very lucid way, yet goes on to cover many advanced topics in sufficient detail.'Ajeet Singh, DeVry Technical Institute