Preface xix
1 Introduction
1. 1 Problem Definition
1. 2 Overview of Design Approach
1. 3 Computer-Aided Design
1. 4 Suggestions for Further Reading
1. 5 Summary
1. 6 Problems
2 Review of Continuous Control
2. 1 Dynamic Response
2. 1. 1 Differential Equations
2. l. 2 Laplace Transforms and Transfer Functions
2. 1. 3 Output Time Histories
2. 1. 4 The Final Value Theorem
2. 1. 5 Block Diagrams
2. 1. 6 Response versus Pole Locations
2. 1. 7 Time-Domain Specifications
2. 2 Basic Properties of Feedback
2. 2. 1 Stability
2. 2. 2 Steady-State Errors
2. 2. 3 PID Control
2. 3 Root Locus
2. 3. 1 Problem Definition
2. 3. 2 Root Locus Drawing Rules
2. 3. 3 Computer-Aided Loci
2. 4 Frequency Response Design
2. 4. 1 Specifications
2. 4. 2 Bode Plot Techniques
2. 4. 3 Steady-State Errors
2. 4. 4 Stability Margins
2. 4. 5 Bode's Gain-Phase Relationship
2. 4. 6 Design
2. 5 Compensation
2. 6 State-Space Design
2. 6. 1 Control Law
2. 6. 2 Estimator Design
2. 6. 3 Compensation: Combined Control and Estimation
2. 6. 4 Reference Input
2. 6. 5 Integral Control
2. 7 Summary
2. 8 Problems
3 Introductory Digital Control
3. 1 Digitization
3. 2 Effect of Sampling
3. 3 PID Control
3. 4 Summary
3. 5 Problems
4 Discrete Systems Analysis
4. 1 Linear Difference Equations
4. 2 The Discrete Transfer Function
4. 2. 1 The z-Transform
4. 2. 2 The Transfer Function
4. 2. 3 Block Diagrams and State-Variable Descriptions
4. 2. 4 Relation of Transfer Function to Pulse Response
4. 2. 5 External Stability
4. 3 Discrete Models of Sampled-Data Systems
4. 3. 1 Using the z-Transform
4. 3. 2 *Continuous Time Delay
4. 3. 3 State-Space Form
4. 3. 4 *State-Space Models for Systems with Delay
4. 3. 5 *Numerical Considerations in Computing ? and ?
4. 3. 6 *Nonlinear Models
4. 4 Signal Analysis and Dynamic Response
4. 4. 1 The Unit Pulse
4. 4. 2 The Unit Step
4. 4. 3 Exponential
4. 4. 4 General Sinusoid
4. 4. 5 Correspondence with Continuous Signals
4. 4. 6 Step Response
4. 5 Frequency Response
4. 5. 1 *The Discrete Fourier Transform (DFT)
4. 6 Properties of the z-Transform
4. 6. 1 Essential Properties
4. 6. 2 *Convergence of z-Transform
4. 6. 3 *Another Derivation of the Transfer Function
4. 7 Summary
4. 8 Problems
5 Sampled-Data Systems
5. 1 Analysis of the Sample and Hold
5. 2 Spectrum of a Sampled Signal
5. 3 Data Extrapolation
5. 4 Block-Diagram Analysis of Sampled-Data Systems
5. 5 Calculating the System Output Between Samples: The Ripple
5. 6 Summary
5. 7 Problems
5. 8 Appendix
6 Discrete Equivalents
6. l Design of Discrete Equivalents via Numerical Integration
6. 2 Zero-Pole Matching Equivalents
6. 3 Hold Equivalents
6. 3. 1 Zero-Order Hold Equivalent
6. 3. 2 A Non-Causal First-Order-Hold Equivalent The Triangle-Hold Equivalent
6. 4 Summary
6. 5 Problems
7 Design Using Transform Techniques
7. 1 System Specifications
7. 2 Design by Emulation
7. 2. 1 Discrete Equivalent Controllers
7. 2. 2 Evaluation of the Design
7. 3 Direct Design by Root Locus in the z-Plane
7. 3. 1 z-Plane Specifications
7. 3. 2 The Discrete Root Locus
7. 4 Frequency Response Methods
7. 4. 1 Nyquist Stability Criterion
7. 4. 2 Design Specifications in the Frequency Domain
7. 4. 3 Low Frequency Gains and Error Coefficents
7. 4. 4 Compensator Design
7. 5 Direct Design Method of Ragazzini
7. 6 Summary
7. 7 Problems
8 Design Using State-Space Methods
8. 1 Control Law Design
8. 1. 1 Pole Placement
8. 1. 2 Controllability
8. 1. 3 Pole Placement Using CACSD
8. 2 Estimator Design
8. 2. 1 Prediction Estimators
8. 2. 2 Observability
8. 2. 3 Pole Placement Using CACSD
8. 2. 4 Current Estimators
8. 2. 5 Reduced-Order Estimators
8. 3 Regulator Design: Combined Control Law and Estimator
8. 3. 1 The Separation Principle
8. 3. 2 Guidelines for Pole Placement
8. 4 Introduction of the Reference Input
8. 4. 1 Reference Inputs for Full-State Feedback
8. 4. 2 Reference Inputs with Estimators: The State-Command Structure
8. 4. 3 Output Error Command
8. 4. 4 A Comparison of the Estimator Structure and Classical Methods
8. 5 Integral Control and Disturbance Estimation
8. 5. 1 Integral Control by State Augmentation
8. 5. 2 Disturbance Estimation
8. 6 Effect of Delays
8. 6. l Sensor Delays
8. 6. 2 Actuator Delays
8. 7 *Controllability and Observability
8. 8 Summary
8. 9 Problems
9 Multivariable and Optimal Control
9. 1 Decoupling
9. 2 Time-Varying Optimal Control
9. 3 LQR Steady-State Optimal Control
9. 3. 1 Reciprocal Root Properties
9. 3. 2 Symmetric Root Locus
9. 3. 3 Eigenvector Decomposition
9. 3. 4 Cost Equivalents
9. 3. 5 Emulation by Equivalent Cost
9. 4 Optimal Estimation
9. 4. 1 Least-5quares Estimation
9. 4. 2 The Kalman Filter
9. 4. 3 Steady-State Optimal Estimation
9. 4. 4 Noise Matrices and Discrete Equivalents
9. 5 Multivariable Control Design
9. 5. 1 Selection of Weighting Matrices Q1 and Q2
9. 5. 2 Pincer Procedure
9. 5. 3 Paper-Machine Design Example
9. 5. 4 Magnetic-Tape-Drive Design Example
9. 6 Summary
9. 7 Problems
10 Quantization Effects
10. 1 Analysis of Round-Off Error
10. 2 Effects of Parameter Round-Off
10. 3 Limit Cycles and Dither
10. 4 Summary
10. 5 Problems
11 Sample Rate Selection
11. 1 The Sampling Theorem's Limit
11. 2 Time Response and Smoothness
11. 3 Errors Due to Random Plant Disturbances
11. 4 Sensitivity to Parameter Variations
11. 5 Measurement Noise and Antialiasing Filters
11. 6 Multirate Sampling
11. 7 Summary
11. 8 Problems
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