Quantifying controller preference reliability under uncertainty in a rotary inverted pendulum benchmark

Simulation-based controller comparisons can report a single winner even when score differences are too small to justify a unique engineering preference. We assessed preference reliability for five fixed controllers on a numerically verified nonlinear rotary inverted pendulum model using two independent Latin-hypercube realizations across matched ± 10%, ± 15%, and ± 20% uncertainty bands (30,000 closed-loop simulations). A four-metric score and a prespecified 5% practical margin quantified controller separation. Under the common uncertainty score, PID had the lowest controller robustness index in every band, but the four leading indices remained within 3.87%. In the pooled ± 15% domain, all ten paired comparisons were detectable after Holm correction, yet 69.40% of 2,000 scenario blocks lacked a unique practical preference. PID retained rank one in 99.95% of paired-bootstrap replicates but only 63.16% and 43.06% under two weight-variation analyses. Post-review sensitivity analyses showed that the principal practical-separation conclusion was robust to the tested CRI coefficient, realization-specific median normalization, and heavier-tail dependence models, while command delay altered separation among near-tied controllers. These findings are specific to the fixed controller portfolio, score definition, RIP model, and simulated uncertainty domain.