Authors: Sachin Umans, Sander Bregman.

Contents

Block A: Time domain

1. Basics
   1. Characteristic Polynomial
   2. State Space
   3. Block Diagram Intro
   4. Equilibria
2. State Space
   1. Linearisation
   2. Stability
   3. State Transforms
   4. Reachability
   5. Second Order Systems
3. Control Synthesis
   1. Impulse and Step Responses
   2. State Feedback
   3. Integral Action
   4. Linear Quadratic Regulators
4. Observers
5. Observer and Integral Action Implementation

Block B: Frequency domain

1. Basics
   1. Laplace Transform
   2. State Space to Transfer Function
   3. Zeros, Poles, and Gain
   4. General Control Scheme Transfer Functions
2. System Visualisation
   1. Bode Plot
   2. Nyquist Plot
   3. Nyquist Criterion
   4. Relation between Bode and Nyquist Plots
3. First and Second Order Systems
4. System Analysis
   1. Stability Margins
   2. Minimum Phase Systems
   3. Bode’s Phase-Gain Relation for MPS
   4. Sensitivity Function
   5. Margin Bounds for Performance and Robustness
5. Control Synthesis - Loop Shaping and PID

Contents (Sachin’s Remix) [Not recommended]

1. Block Diagram Intro
2. From Time Domain to Frequency Domain and Back Again
   1. The ODE multitool: Laplace transform
   2. Model to Transfer Function
3. State Space System Framework
   1. State Space
   2. Equilibria
   3. Linearisation
   4. State Transforms
   5. State Space to Transfer Function
4. System Visualisation
   1. Bode Plot
   2. Nyquist Plot
   3. Relation between Bode and Nyquist Plots
5. Systems Exploration
   1. Impulse and Step Responses
   2. Second Order Systems - Time Domain
   3. First and Second Order Systems - Frequency Domain
6. System Properties
   1. Zeros, Poles, and Gain
   2. Stability
   3. Controllability
   4. Observability
   5. Minimum Phase Systems
      1. Bode’s Phase-Gain Relation for MPS
7. State Feedback Design
   1. State Feedback
   2. Linear Quadratic Regulators
8. Output Feedback Design
   1. General Control Scheme Transfer Functions
   2. Time Domain PID Tuning (Work in Progress)
   3. Controller Analysis
      1. Nyquist Criterion
      2. Stability Margins
   4. Sensitivity Function
   5. Loop Shaping and Frequency Domain PID
9. Robust Control
   1. Margin Bounds for Performance and Robustness
   2. Integral Action
   3. Observer and Integral Action Implementation