Course Notes - Reading Order

These notes are organized as a beginner-friendly path through linear systems and control. Start with open-loop and second-order system ideas, then move into closed-loop intuition, MATLAB/state-space tools, controllability, observers, and finally integral control/LQR.

0. Preface / References

0.1 00.1 Reference - Introduction to Modern Controls

0.2 00.2 Case Study - ALC Final Project Description

1. Open Loop and Second-Order System Basics

1.1 01.1 Basics of Open Loop

1.2 01.2 DC Gain Explained

1.3 01.3 Natural Frequency, Poles, Damping (2nd Order System)

1.4 01.4 Damping Ratio and Resonance

1.5 01.5 Bandwidth Definition

1.6 01.6 Decibel Interpretation

2. Closed Loop and Frequency-Domain Thinking

2.1 02.1 Basics of Closed Loop

2.2 02.2 Closed Loop System with Feedback Control

2.3 02.3 Gain Margin and Phase Margin

2.4 02.4 Controller or Compensator Design

3. MATLAB / LTI Object Toolbox

3.1 03.1 Creating a LTI Object in MATLAB - Part 1

3.2 03.2 Creating a LTI Object in MATLAB - Part 2 (Conversion)

3.3 03.3 State-Space Info from LTI Object

3.4 03.4 Impulse Response Function Plotting

3.5 03.5 sgrid Code for s-plane

3.6 03.6 Pole Placement (Const Damping and Const Freq Line) s-plane

3.7 03.7 Drawing Block Diagram in LaTeX

4. Why State-Space Matters

4.1 04.1 Why Do We Bother with State-Space Realization

4.2 04.2 Intuition (Mapping) of State-Space Realization

4.3 04.3 Transfer Function Matrix - A Misconception

5. Controllability and Full-State Feedback

5.1 05.1 Controllability 1

5.2 05.2 Controllability 2

5.3 05.3 Draft - Why Observability and Controllability are Dual Problems

5.4 05.4 Full State Feedback - Part 1

6. Observers and Augmented Systems

6.1 06.1 Luenberger Observer (State Estimation) - Full State Feedback - 2

6.2 06.2 Luenberger Observer - 2

6.3 06.3 Observer (State Estimator) and Augmented System

6.4 06.4 Augmented System - 2 with Control Command

7. Integral Control / LQR / Wrap-Up

7.1 07.1 Integral Control (LQR) - Part 1

7.2 07.2 Integral Control (LQR) - Part 2

7.3 07.3 Draft - Summary Equations for Closed Loop, Observer, Controller

7.4 07.4 Wrapping Up - 1

7.5 07.5 Draft - Wrapping Up - 2

Future Appendix

8.1 08.1 Future Appendix - ODE Solving in MATLAB (with Function)

Not in This Sequence

ADC and DAC Explained is intentionally left out of this reading path.