"""Bench-grade simulators used by Sprint 2+ to validate the PID without
the AR-NMEA-IO board attached.

Modules:

- :mod:`~arautopilot.studio.simulator.rudder_dynamics`
    Minimal physical model of a hydraulic rudder actuator: rotational
    inertia, viscous friction, hydraulic deadband, port/stbd asymmetry,
    mechanical end-stops.

- :mod:`~arautopilot.studio.simulator.pid_inner`
    Pure-Python reference implementation of the inner (rudder-position)
    PID. Used to iterate on the algorithm and cross-validate the C++
    firmware port.
"""