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: HY Control
10.7.1: A Brief History
10.7.2: Some Preliminaries
10.7.3: HY Control: Solution
10.7.4: Weights in HY 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