Documentation Table of Contents

1. Getting Started

• Using the Application for the First Time
• The Structure of the Application
• The Control Objects
• Traditional Notations
• The Control Format
• The Notation for the Imaginary Unit
• Numericalizing for Speed
• Evaluating Examples in This Guide

2. Introduction: Extending Mathematica to Solve Control Problems

3. Description of Dynamic Systems

• Transfer Function Representations
• State-Space Representations
• Continuous-Time versus Discrete-Time Systems
• The Traditional Notations
• Discrete-Time Models of Continuous-Time Systems
• The Conversion Methods
• Discrete-Time Models of Systems with Delay
• Continuous-Time Models of Discrete-Time Systems

4. Time-Domain Response

• Symbolic Approach
• Simulating System Behavior
• Step, Impulse, and Other Responses

5. Classical Methods of Control Theory

• Root Loci
• The Bode Plot
• The Basic Function
• Gain and Phase Margins
• The Nyquist Plot
• The Nichols Plot
• The Singular-Value Plot

6. System Interconnections

• Elementary Interconnections
• Connecting in Series
• Connecting in Parallel
• Closing Feedback Loop
• Arbitrary Interconnections
• State Feedback
• Manipulating a System's Contents
• Using Interconnecting Functions for Controller Design

7. Controllability and Observability

• Tests for Controllability and Observability
• Controllability and Observability Constructs
• Dual System

8. Realizations

• Irreducible (Minimal) Realizations
• Kalman Canonical Forms
• Jordan Canonical (Modal) Forms
• Internally Balanced Realizations
• Dominant Subsystem
• Pole-Zero Cancellation
• Similarity Transformation
• Recovering the Transformation Matrix

9. Feedback Control Systems Design

• Pole Assignment with State Feedback
• Ackermann's Formula
• Robust Pole Assignment
• State Reconstruction

10. Optimal Control Systems Design

• Linear Quadratic Regulator
• Optimal Output Regulator
• Riccati Equations
• Discrete Regulator by Emulation of Continuous Design
• Optimal Estimation
• Discrete Estimator by Emulation of Continuous Design
• Kalman Estimator
• Optimal Controller

11. Nonlinear Control Systems

• Local Linearization of Nonlinear Systems
• Rational Polynomial Approximations

12. Miscellaneous

• Ordered Schur Decomposition
• Lyapunov Equations
• Rank of Matrix
• Part Count and Consistency Check
• Displaying Graphics Array Objects Together
• Systems with Random Elements