Purpose

Corbin's World: Making Systems Behave

A PID controller drives a system to its setpoint. Tune the gains: too low = slow, too high = oscillation. This is EXACTLY what Corbin's dissertation addresses -- can we PROVE which gains are stable?

The Physics

PID Controller

u = Kp*e + Ki*integral(e) + Kd*de/dt

Kp: proportional (spring-like, reacts to current error)

Ki: integral (eliminates steady-state offset)

Kd: derivative (damping, prevents overshoot)

Stability

Stable: output settles to setpoint. Unstable: output grows or oscillates forever.

Key Insight: Corbin's Chapter 4 studies EXACTLY this: a PI controller (Kp + Ki/s) on a gas turbine engine. Backlash causes limit cycling. His verification task: PROVE which (Kp, Ki) values are safe. Drag the sliders to feel the problem.

Historical

James Watt (1736-1819)
Centrifugal governor for steam engines -- first feedback controller. Rudolf Kalman (1930-2016): state-space theory + Kalman filter. Apollo navigation used the Kalman filter to reach the Moon.

References

Nise, Control Systems Engineering, Ch 1-6 | Corbin Klett dissertation, Ch 3-4 | MIT OCW 6.302