A Practical Guide to Control Theory

中文 README

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What Is This?

This repository is a practical control-theory note aimed at real robotics engineering work. It is written around one core goal: helping you design, tune, and debug controllers on real hardware.

Rather than treating theory and application separately, the notes continuously answer: "What is this useful for when the robot is actually running?"

Who Is This For?

Undergraduate students (roughly year 1-3) with basic calculus and linear algebra. If you can follow derivatives and matrix multiplication, you are ready.

Table of Contents

Part I: Foundations

#	Chapter	Key Topics
-	Two Numbers: $e$ and $\pi$	Why $\pi$ governs periodicity and $e$ governs decay; Euler's formula
1	Introduction	Motivation, learning path, how to use this guide

Part II: Theory Pipeline

#	Chapter	Key Topics
2	Digital Signal Processing	Laplace/Fourier/Z-transforms, poles & zeros, LPF/BPF/HPF/notch filters
3	System Description	Transfer functions, state-space, stability, 2nd-order systems, motor modeling
4	Classical Control	Bode plots, PID (single/cascade/parallel), positive-feedback diagnosis, tuning, feedforward, sysid
5	Discretization & Implementation	ZOH, Tustin, FIR/IIR filter design, fixed-point, embedded implementation
6	Modern Control	LQR (+ PID-as-state-space insight), MPC, NMPC, TinyMPC, Kalman/EKF, LQG, trajectory planning
7	Nonlinear Control	Feedback linearization, sliding mode, gain scheduling, Lyapunov design, NMPC comparison

Part III: Practice

#	Chapter	Key Topics
8	Multi-Loop Architecture	Full control stack, cascade architecture, bandwidth separation, state machines, RTOS
9	Debugging & Tuning Cookbook	Diagnostic flowcharts, failure mode signatures, PID tuning on real hardware

Part IV: Frontiers & Reference

#	Chapter	Key Topics
10	Outlook	Data-driven control, Koopman, adaptive control, RL, diffusion policies, VLAs, neural ODEs
A	Appendix: C++ Modules	Header-only, embedded-friendly algorithm modules
B	Appendix: Attitude & Rotation	Coordinate frames (NWU), rotation matrices, Euler angles, gimbal lock, quaternions

Structure

The notes follow an engineering workflow: theory first (uninterrupted from DSP through nonlinear control), then practical chapters on architecture and debugging, then frontier topics and reference appendices.

Project Structure

Control-Note/
├─ main.tex                  # English main document
├─ main_zh.tex               # Chinese main document
├─ sections_zh/              # Chinese chapter source files
├─ include/                  # Shared include resources
├─ figures/                  # English figures
├─ figures_zh/               # Chinese figures
├─ scripts/                  # Figure generation scripts
├─ build/                    # Built PDF outputs
├─ README.md                 # English README
└─ README_zh.md              # Chinese README

How to Build

Overleaf

Import this repository and compile with XeLaTeX.

Local Build (Recommended)

A build script is provided for local compilation. Prerequisites:

1. Install TeX Live (user-space, no sudo required):

   # Download the installer
   cd /tmp && wget https://mirror.ctan.org/systems/texlive/tlnet/install-tl-unx.tar.gz
   tar xzf install-tl-unx.tar.gz && cd install-tl-*/
   
   # Run the installer (choose "small" scheme to save space)
   perl install-tl
   
   # After installation, add TeX Live to your PATH (adjust the year as needed)
   echo 'export PATH="$HOME/texlive/2026/bin/x86_64-linux:$PATH"' >> ~/.bashrc
   source ~/.bashrc
   
   # Install required packages
   tlmgr install latexmk ctex mdframed zref needspace booktabs enumitem float caption

2. Build PDFs using the provided script:

   # Build both English and Chinese PDFs
   ./scripts/build.sh all
   
   # Build English only
   ./scripts/build.sh en
   
   # Build Chinese only
   ./scripts/build.sh zh
   
   # Clean auxiliary files
   ./scripts/build.sh clean

   Output files:

   • build/Control_Theory_Note.pdf (English)
   • build/Control_Theory_Note_cn.pdf (Chinese)

Manual Build

If you prefer to compile manually:

# English (pdflatex)
latexmk -pdf -interaction=nonstopmode main.tex

# Chinese (xelatex)
latexmk -xelatex -interaction=nonstopmode main_zh.tex

Regenerate Figures

pip install matplotlib numpy
python scripts/generate_figures_zh.py
python scripts/generate_advanced_figures_zh.py

See scripts/ for the complete list of figure generation scripts.

Contributing

Issues and pull requests are welcome for typo fixes, technical corrections, and structural improvements.