Design of Feedback Control Systems

Description

Design of Feedback Control Systems is designed for electrical and mechanical engineering students in advanced undergraduate control systems courses. Now in its fourth edition, this tutorial-style textbook has been completely updated to include the use of modern analytical software, especially MATLAB®. It thoroughly discusses classical control theory and state variable control theory, as well as advanced and digital control topics. Each topic is preceded by analytical considerations that provide a well-organized parallel treatment of analysis and design. Design is presented in separate chapters devoted to root locus, frequency domain, and state space viewpoints. Treating the use of computers as a means rather than as an end, this student-friendly book contains new "Computer-Aided Learning" sections that demonstrate how MATLAB® can be used to verify all figures and tables in the text. Clear and accessible, Design of Feedback Control Systems, Fourth Edition, makes complicated methodology comprehensible to a wide spectrum of students.

Features

Table of Contents

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