Scenario-Based Robust Tuning and Generalization Analysis of PID and Fractional-Order PID Controllers for a Nonlinear Cart-Inverted Pendulum Under Parametric and Disturbance Uncertainty

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Zorlu H., Türktam M., Soylu S.

Applied Sciences (Switzerland), sa.17, ss.1-31, 2026 (SCI-Expanded, Scopus)

Özet

Robust controller tuning is essential for nonlinear systems operating under plant uncertainty

and external disturbances. This study proposes a scenario-based framework for

tuning PID and FOPID controllers for a nonlinear cart-inverted-pendulum system, using

separate training and test scenarios to assess generalization. Five training scenarios

incorporating parametric variations, disturbances, and noise are used during optimization,

while four unseen scenarios are reserved for evaluation. The Slime Mold Algorithm

(SMA), Artificial Hummingbird Algorithm (AHA), and GreyWolf Optimizer (GWO) are

compared under identical computational budgets and initial populations. The objective

combines weighted integral of time-weighted absolute error (ITAE) measures with a

standard-deviation penalty to promote consistent performance across scenarios. Robust

tuning reduces the mean unseen test cost of PID controllers by approximately 20% compared

with nominal tuning. Its effect is more pronounced for FOPID controllers: nominal

tuning causes instability in several unseen cases, whereas robust tuning eliminates failures

in the test set. Increasing the robustness penalty reduces the generalization gap by about

17% for PID and 46% for FOPID. Across fifteen unseen plant configurations, the robusttuned

FOPID-AHA controller remains stable, while the nominal counterpart fails under

the two most severe combined-stress conditions. These results show that scenario-based

tuning improves controller reliability beyond a single nominal operating point.