1. Getting Started
1
1.1 Using the Package for the First Time
1
1.2 Structure of the Application
2
1.3 Robustness of Numerical Methods
3
2. Introduction
7
2.1 Quick Reference
7
Solutions of the Lyapunov and Sylvester Matrix Equations
8
Solutions of the Algebraic Riccati Equations
8
Reduction to Controller-Hessenberg and
Observer-Hessenberg Forms
9
Controllability and Observability Tests
9
Pole Assignment
9
Feedback Stabilization
10
Design of the Reduced-Order State Estimator (Observer)
10
Model Reduction
10
Model Identification
10
Miscellaneous Matrix Decompositions and Functions
11
2.2 An Industrial Application: Controlling the Drum Boiler
11
2.2.1 The State-Space Model of a Drum Boiler
11
2.2.2 System Responses, Stability, and Poles
12
2.2.3 Testing the Controllability
14
2.2.4 The Design of the LQR Controller
15
2.2.5 The Controller Design Using Constrained Feedback
Stabilization
19
2.2.6 The Observer Design
20
3. Matrix Equations and Control Applications
26
3.1 Lyapunov Equations
26
3.2 Riccati Equations
29
3.2.1 The Schur Methods for the Riccati Equations
30
3.2.2 The Inverse-Free Generalized Eigenvector and Schur
Methods for the Riccati Equations
32
3.2.3 The Matrix Sign-Function Methods for the Riccati Equations
34
3.2.4 The Newton Methods for the Riccati Equations
36
3.2.5 LQR and LQG Designs Using Riccati Equations
38
4. Block Hessenberg Forms
41
4.1 Controller-Hessenberg Forms
41
4.2 Observer-Hessenberg Forms
45
4.3 Controllability and Observability Tests Using
Block Hessenberg Forms
47
5. Pole Assignment and Stabilization by State Feedback
50
5.1 Pole Assignment Methods
50
5.1.1 The Recursive Algorithms
51
5.1.2 The Explicit and Implicit QR Algorithms
53
5.1.3 The Schur Method
56
5.2 Partial Pole Assignment
58
5.3 Constrained Feedback Stabilization
61
5.4 Lyapunov Feedback Stabilization
66
6. State Estimation
69
6.1 Full-Order State Estimation
69
6.2 Reduced-Order State Estimator
71
6.2.1 Reduced-Order State Estimator via Pole Assignment
74
6.2.2 Reduced-Order State Estimator via Sylvester-Observer
Equation
76
7. Model Reduction
80
7.1 Cholesky Factors of the Controllability and Observability Gramians
80
7.2 Model Reduction Using Schur and Square-Root Methods
84
8. Model Identification
89
8.1 Time-Domain System Identification
89
8.1.1 Identification Using Markov Parameters
89
8.1.2 Identification Using Input-Output Data (Subspace
System Identification Method)
93
8.2 Frequency Domain System Identification
97
9. Generalized Eigenvalue Problem
101
9.1 Generalized Eigenvalue Problem
101
9.2 Generalized Schur Decomposition
104
References
110
Appendix. Collection of Control Systems for Case Studies
115
A.1 Continuous-Time Models
115
A.1.1 The Absorption Column
115
A.1.2 The F-8 Aircraft
116
A.1.3 The L-1011 Aircraft
117
A.1.4 The Tubular Ammonia Reactor
118
A.1.5 The Fluid Catalytic Reactor
118
A.1.6 The Binary Distillation Column
119
A.1.7 The Drum Boiler
120
A.1.8 The Flight Control System
121
A.1.9 The Automobile Gas Turbine
121
A.1.10 The CH-47 Helicopter
122
A.1.11 The Magnetic Tape
123
A.1.12 The Electric Power System
123
A.1.13 The J-100 Jet Engine
124
A.1.14 The "Smart" Highway
125
A.1.15 The Generator Axle in a Power Plant
126
A.2 Discrete-Time Models
127
A.2.1 The Catalytic Cracker
127
A.2.2 The Chemical Plant
127
A.2.3 The Paper Machine
128
A.2.4 The Steam Power System
129
Index
130
