Skip to content

Model and control workflow

Define the model

  1. Enter the usable rail half travel for the cart center.
  2. Enter cart mass and ordered links from the cart outward. Each link needs a length and tip mass. Add rod mass, inertia, damping, and friction as needed.
  3. Set one initial angle per link. Angle 0 is upright; π is hanging.
  4. Enter a command-to-cart-force actuator model, command bounds, force limit, and delay.
  5. Run a balance or swing-up example with a new output directory.

The exact JSON keys, units, and defaults are in configuration. A gearbox can be part of the transfer function. Current feedback alone does not give a command-to-cart-force model.

Tune balance control

Run balance from small initial angles. Check balance_terminal, peak cart travel, applied force, command saturation, and force saturation in summary.json. Use the per-link angle_weights to adjust angle priority, position_weight for cart centering, and force_weight for force request cost. Change one weight at a time and compare the resulting trajectories.

The mechanical LQR requests force. With a transfer-function actuator, a local inversion converts that request to a bounded command. actuator_force_weight applies to the augmented legacy force-lag and DC controllers; it does not tune the transfer-function inversion.

Run and check swing-up

Set simulation.mode to swingup, start near hanging, and install [opt]. The solver searches from the supplied seeds with free final winding. plan.csv stores a nominal ideal-force path. trajectory.csv stores the result after actuator dynamics, delay, and limits.

Check plan.success, each attempt's reason, terminal catch values, peak cart travel, and saturation fractions. Change plan_duration_s, plan_nodes, seeds, or cart_margin_m if the nominal solve fails. If the closed-loop catch fails, inspect the requested and applied forces before changing LQR weights or actuator limits.

For numerical sensitivity, reduce dt_s and compare the result. The Numba backend speeds mechanical steps; the optimizer remains in CasADi/IPOPT.

Model limits

Rail impact, static sticking, backlash, flexible rods, sensor noise, thermal limits, and hardware safety logic are outside the model. Parameters in the included examples are not measured hardware specifications. See scope and actuator validation.