There’s a particular kind of intuition that classical control engineers develop after enough years of tuning loops — a sense for what a phase-lead compensator feels like, what happens to the step response when you double an integrator’s gain, why a notch at the resonant frequency works better than a brute-force gain reduction. That intuition is hard to convey in writing because it’s fundamentally about moving a parameter and watching everything respond at once.
This studio is an attempt to convey it directly. Pick a controller. Pick a plant. Drag the parameters. The Bode plot, the closed-loop step response, and the performance metrics all update live.
What it covers
Five sections, all interactive, about twenty-five minutes to work through.
§1 — Foundations and Feedback Architecture. The structure of a unity-feedback loop, why we draw it the way we do, and where the compensator sits relative to plant, sensor, and disturbance.
§2 — Performance Specifications. The numbers we tune against — rise time, settling time, overshoot, gain and phase margins, steady-state error. What each one means in time domain and frequency domain, and how they trade off.
§3 — The Compensator Zoo. Live demos for each classical controller: proportional, PI (with windup), PD (with derivative filtering), PID, lead, lag, lead-lag. Every parameter is a slider; every change is reflected on the Bode plot and the step response instantly.
§4 — Tuning Reference. Ziegler-Nichols and friends. The classical recipes you can fall back on when nothing else works, with the caveat sheet about when each one breaks.
§5 — Notes from practice. The small handful of gotchas (numerical derivative, sample-rate aliasing, derivative kick on setpoint changes) that distinguish a textbook tuning from a deployable one.
If you’ve taken a classical control course and wanted to feel the tradeoffs rather than just calculate them, this is the kind of tool I wish I’d had then.
Read it
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