Applied Linear Systems
These are notes I jotted down for my own reference when I was new to this field. I took the graduate-level Applied Linear Systems course taught by Dr. Steve Southward, an amazing professor, and the snippets here come from his class notes.
At first, I just wanted a reference I could return to whenever I needed to refresh the ideas. Later, I decided to organize the notes a bit more and put them on my website.
This whole thing is still under improvement.
1. Open Loop and Second-Order System Basics
Natural Frequency, Poles, Damping (2nd Order System)
2. Closed Loop and Frequency-Domain Thinking
Closed Loop System with Feedback Control
Controller or Compensator Design
3. MATLAB / LTI Object Toolbox
Creating a LTI Object in MATLAB - Part 1
Creating a LTI Object in MATLAB - Part 2 (Conversion)
State-Space Info from LTI Object
Impulse Response Function Plotting
Pole Placement (Const Damping and Const Freq Line) s-plane
4. Why State-Space Matters
Why Do We Bother with State-Space Realization
Intuition (Mapping) of State-Space Realization
Transfer Function Matrix - A Misconception
5. Controllability and Full-State Feedback
TODO - Why Observability and Controllability are Dual Problems
6. Observers and Augmented Systems
Luenberger Observer (State Estimation) - Full State Feedback - 2
Observer (State Estimator) and Augmented System
Augmented System - 2 with Control Command
7. Integral Control / LQR / Wrap-Up
Integral Control (LQR) - Part 1
Integral Control (LQR) - Part 2