Ball-beam via composable-model-graph (transfer function + PD/fuzzy control)

[bigboateng]

What

Adds a headless, runnable take on the ball-beam from this repo, expressed through
composable-model-graph,
plus three browser visualizations (no VPython needed).

• ballbeam_cmg.py — the same physics as inclinedplane.py / main.py, run
  headless, then two cmg variations: (1) the plant is a transfer function — the
  forward-Euler ball-beam is exactly a discrete double integrator G(q) with
  b=[0,0,dt²], a=[-2,1], and running the tilt input through a cmg TransferFunction
  reproduces the hand-written loop to ~1e-11; (2) a PD controller closes the loop and
  balances the ball at a setpoint. Deterministic and self-checking (PASS/FAIL).
• ballbeam_sim.html — live animated ball-beam: a PD controller tilts the beam to
  keep the ball on the center mark; click/nudge to disturb it.
• ballbeam_compare.html — the same beam under PD vs a Sugeno fuzzy controller
  (error + rate-of-error inputs), getting the same disturbances, so the difference in
  behaviour is visible side by side.
• ballbeam_cmg.html — a chart of the trajectories (Euler vs transfer function
  overlay; the controller settling curve).

Why

It makes the implicit structure explicit: the integration loop in the original sim is a
transfer function, and the fuzzy controller is mathematically the same blend (local
linear consequents weighted by membership). Old files are untouched; these are additive.

Run

# headless script (needs the cmg python package on the path)
PYTHONPATH=/path/to/composable-model-graph/python/src python3 ballbeam_cmg.py
# visualizations: just open the .html files in a browser

🤖 Generated with Claude Code