Comparative Performance Analysis of an SMA-Optimized FOPID Controller for an Inverted Pendulum on a Cart

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Türktam M., Soylu S., Zorlu H.

Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.42, sa.2, ss.739-759, 2026 (Hakemli Dergi)

Özet

This study investigates the tuning of a Fractional-Order Proportional-Integral-Derivative (FOPID) controller for a cart–inverted pendulum system, which is an inherently nonlinear and unstable system requiring simultaneous stabilization of the pendulum angle and regulation of the cart position. Although various optimization methods have been widely employed in the literature for this problem, the performance of the Slime Mould Algorithm (SMA) in the context of inverted pendulum control has not been sufficiently investigated. Motivated by this gap, the five parameters of the controller were determined using SMA, Grey Wolf Optimization (GWO), and Artificial Hummingbird Algorithm (AHA), and all methods were comparatively evaluated under identical simulation conditions based on the Integral Time Absolute Error (ITAE) criterion. The obtained results demonstrate that the SMA-based design yields lower ITAE variability and higher repeatability compared to the other methods. The corresponding closed-loop responses also exhibit less oscillatory angle and position behavior. These findings indicate that SMA provides a more reliable and consistent FOPID tuning performance than GWO and AHA for the considered inverted pendulum problem.