Controller Rankings Shift When Uncertainty Is Weighted Differently

A simulation study comparing five fixed control algorithms found that statistically detectable performance differences did not always establish a unique engineering preference for a nonlinear rotary inverted pendulum. Across 30,000 closed-loop simulations, PID controllers recorded the lowest controller robustness index in every tested uncertainty band, yet the four leading indices were separated by no more than 3.87%. The results illustrate how closely matched controllers can differ significantly in a numerical score without possessing a clear, practically meaningful advantage.

The researchers evaluated the controllers on a numerically verified nonlinear rotary inverted pendulum model. They represented uncertainty using two independent Latin-hypercube realizations within matched ±10%, ±15% and ±20% bands. A four-metric score combined the controllers’ simulated performance, while a prespecified 5% practical margin defined whether one controller was separated sufficiently from another to support a unique preference. The benchmark therefore assessed not only whether controller scores differed, but also whether those differences exceeded its threshold for practical separation.

In the pooled ±15% uncertainty domain, all ten paired controller comparisons were detectable after Holm correction for multiple comparisons. The statistical result did not, however, yield a consistent practical winner: 69.40% of 2,000 scenario blocks lacked a unique practical preference under the common uncertainty score. A controller could therefore occupy a clear position in a statistical ranking while remaining effectively tied with alternative controllers under the study’s practical-separation criterion.

PID’s apparent lead was sensitive to the weighting of uncertainty in the analysis. It retained first rank in 99.95% of paired-bootstrap replicates, but its rank-one frequency fell to 63.16% and 43.06% in two weight-variation analyses. Post-review analyses showed that the principal practical-separation finding was robust to the tested controller robustness index coefficient, realization-specific median normalization and heavier-tailed dependence models. Command delay behaved differently: changing it altered separation among controllers that were otherwise near-tied. Because this was a simulation study, its findings are specific to the five-controller portfolio, chosen score definition, rotary inverted pendulum model and simulated uncertainty domain; they do not establish the controllers’ performance on physical systems or under unmodeled operating conditions.

Subject of Research: Reliability of controller preferences in a simulated rotary inverted pendulum under uncertainty

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

Article References: Coşkun, Y., Özyılmaz, L., & Aydın, M. (2026). Quantifying controller preference reliability under uncertainty in a rotary inverted pendulum benchmark. Scientific Reports. https://doi.org/10.1038/s41598-026-76797-y

Image Credits: AI Generated

DOI: 10.1038/s41598-026-76797-y

Keywords: rotary inverted pendulum, controller comparison, uncertainty quantification, robustness index, Latin hypercube sampling, sensitivity analysis, practical significance, control engineering, Quantifying, controller, preference, reliability