Design of Feedback Control Systems

'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

• 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