Top-down 2D view of the same first-order Nomoto maneuvering model used to relate rudder angle to yaw (turn) rate in ship control. A PID autopilot compares true heading to the bearing toward the active waypoint and commands a rudder angle to null that error.
Nomoto (1st order):
dr/dt = (K·δ − r) / T
dψ/dt = r
Autopilot (PID on heading error e):
e = wrap(bearing_wp − ψ)
δ_cmd = Kp·e + Kd·(de/dt), clamped ±35°
Position (with current drift c):
dx/dt = V·sin(ψ) + cx, dy/dt = V·cos(ψ) + cy
- Throttle — sets forward speed V.
- Manual rudder — commands δ directly (ignored while autopilot is engaged).
- Sea state / current — scales wave-induced heel and lateral current drift c.
- Autopilot — hands rudder control to the PID law above, steering toward the buoy.
- New waypoint — drops a fresh target and resets distance.