← antimony labs

controls

Ten short lessons, three applied capstones. Every page leads with a plot you can poke. Math sits one tap below in a drawer. Built in order — start at 01 if you're new, or jump to the widget that looks interesting.

Feedback Why measure-and-correct beats open-loop, even when your model is wrong.

PID Three knobs that go further than they deserve. Step response, live.

Transfer functions What a system is, written in s. Same plant, three different inputs.

Poles & zeros Where stability lives. Drag a pole, watch the response.

Bode plots Gain and phase at every frequency, on log paper.

Nyquist The contour that tells you when the loop will sing.

Root locus How the closed-loop poles slide as you turn up the gain.

State-space Vectors instead of polynomials. ẋ = Ax + Bu, as a vector field.

Controllability & observability Can you steer it? Can you see it? Same matrix, two ranks.

Observers Estimating the state you can't measure — Luenberger, then Kalman.

applied

Motor speed Cordless drill bogging into wood. PI controller earns its keep.

Inverted pendulum Balancing a broom on a cart. LQR-style gain tuning, four sliders.

Quadrotor altitude 1-DOF hover. Double integrator with wind gusts.