Control Theory for the Masses

A book of explorable models. The shared project is "small masses in the 1 - and 2-D planes."

Control Theory for the Masses is an interactive book and site for learning how dynamic systems move through time — and how feedback changes what they do. Instead of only reading equations, you poke at live models: change a force, a gain, or a cost weight, and watch trajectories, plots, and trade-offs update.

It is written for undergraduates meeting feedback for the first time, engineers who want intuition more than another textbook recitation, and curious technical readers who like to play with models. Calculus and a bit of linear algebra help; a prior controls course does not. Start inModule 0 with a pizza run to a door, then follow the outline into classical, modern, and optimal control as chapters land.

Outline

• 0 — Our playground: Small masses in 1-D and 2-D
• 0.1 Pizza Delivery Driver in a Rush
• 0.2 Proper Pizza Delivery
• 0.3 Optimizing for Gas Instead of Time
• 0.4 Optimize for Gas, Time, and Comfort
• 0.5 What's Next
• 1 — Intuition of dynamic systems and feedback
• 1.1 Why control? Open-loop vs closed-loop
• 1.2 Modeling from first principles
• 1.3 Laplace domain and transfer functions
• 2 — Classical control (SISO and frequency domain)
• 2.1 PID
• 2.2 Stability and root locus
• 2.3 Frequency response: Bode and Nyquist
• 2.4 Robustness and design margins
• 3 — Modern control (state-space and MIMO)
• 3.1 State-space
• 3.2 Controllability and observability
• 3.3 Full-state feedback and pole placement
• 3.4 State estimation
• 4 — Optimal, nonlinear, and digital
• 4.1 LQR
• 4.2 MPC
• 4.3 Nonlinear dynamics
• 4.4 Digital implementation