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Table of Contents

1. Getting Started      1
1.1 Using the Application for the First Time      1
1.2 The Structure of the Application      2
1.3 The Control Objects      3
1.4 Traditional Notations      5
1.5 The Control Format      7
1.6 The Notation for the Imaginary Unit      9
1.7 Numericalizing for Speed      9
1.8 Evaluating Examples in This Guide      10
2. Introduction: Extending Mathematica to Solve Control Problems      11
3. Description of Dynamic Systems      27
3.1 Transfer Function Representations      27
3.2 State-Space Representations      33
3.3 Continuous-Time versus Discrete-Time Systems      39
3.4 The Traditional Notations      41
3.5 Discrete-Time Models of Continuous-Time Systems      44
3.5.1 The Conversion Methods      48
3.6 Discrete-Time Models of Systems with Delay      53
3.7 Continuous-Time Models of Discrete-Time Systems      54
4. Time-Domain Response      57
4.1 Symbolic Approach      57
4.2 Simulating System Behavior      65
4.3 Step, Impulse, and Other Responses      74
5. Classical Methods of Control Theory      80
5.1 Root Loci      80
5.2 The Bode Plot      85
5.2.1 The Basic Function      85
5.2.2 Gain and Phase Margins      89
5.3 The Nyquist Plot      93
5.4 The Nichols Plot      95
5.5 The Singular-Value Plot      96
6. System Interconnections      98
6.1 Elementary Interconnections      98
6.1.1 Connecting in Series      98
6.1.2 Connecting in Parallel      103
6.1.3 Closing Feedback Loop      105
6.2 Arbitrary Interconnections      110
6.3 State Feedback      114
6.4 Manipulating a System's Contents      115
6.5 Using Interconnecting Functions for Controller Design      119
7. Controllability and Observability      122
7.1 Tests for Controllability and Observability      122
7.2 Controllability and Observability Constructs      126
7.3 Dual System      130
8. Realizations      132
8.1 Irreducible (Minimal) Realizations      133
8.2 Kalman Canonical Forms      136
8.3 Jordan Canonical (Modal) Form      138
8.4 Internally Balanced Realizations      140
8.5 Dominant Subsystem      142
8.6 Pole-Zero Cancellation      144
8.7 Similarity Transformation      146
8.8 Recovering the Transformation Matrix      148
9. Feedback Control Systems Design      150
9.1 Pole Assignment with State Feedback      150
9.1.1 Ackermann's Formula      154
9.1.2 Robust Pole Assignment      158
9.2 State Reconstruction      161
10. Optimal Control Systems Design      165
10.1 Linear Quadratic Regulator      166
10.2 Optimal Output Regulator      171
10.3 Riccati Equations      172
10.4 Discrete Regulator by Emulation of Continuous Design      178
10.5 Optimal Estimation      181
10.6 Discrete Estimator by Emulation of Continuous Design      184
10.7 Kalman Estimator      185
10.8 Optimal Controller      192
11. Nonlinear Control Systems      197
11.1 Local Linearization of Nonlinear Systems      197
11.2 Rational Polynomial Approximations      202
12. Miscellaneous      204
12.1 Ordered Schur Decomposition      204
12.2 Lyapunov Equations      206
12.3 Rank of Matrix      210
12.4 Part Count and Consistency Check      210
12.5 Displaying Graphics Array Objects Together      211
12.6 Systems with Random Elements      211
References      214
Index      215

Incompatible Changes between Version 1 and Version 2Overview



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