1. Introduction

2. Mathematical Modeling — Review of Heat & Material Balances

"Traditional" ODE Solution Techniques

• 3. Separation of Variables, Integration Factors, ...
• 4. Numerical Methods for ODE Solutions
• Solving problem numerically using POLYMATH
• Example given in class 
• Valve has non-linear flow characteristics

• Table of typical Laplace Transforms
• Special Modeling Techniques — Deviation variables & linearizing an ODE
• Use of Cramer's rule for simultaneous linear equations
• Spreadsheet to numerically split into partial fractions
  

• 6. Introduction to Transfer Functions
• Deriving transfer functions from the heat & material balances for a stirred tank heater
• 7. 1st Order Systems
• 8. 2nd Order Systems
• Equation Derivation for Underdamped Systems
• 9. Higher Order Systems
• 10. Table of Responses for 1st & 2nd order systems to standard input functions

• Data matching example spreadsheet

• 12. Analysis of Feedback Control Systems
• Numerical solution example
• 13. Stability Analysis of Feedback Control Systems
• 14. Design & Tuning of Feedback Control Systems
• Cohen & Coon Controller Tuning Example
• Excel spreadsheet (in ZIP file)
• Ziegler-Nichols Controller Tuning Example
• Direct Synthesis Tuning Method
• Associated Mathematica notebooks
• Frequency Response Methods

• Feedforward controllers
• Cascade control