Robust Position Control of an Electro-Hydraulic Actuator via Metaheuristic Optimization of a Fractional-Order PID Controller

In this study, a robust position control strategy is presented for a two-stage electro-hydraulic actuator system using a fractional-order proportional–integral–derivative (FOPID) controller tuned by Kirchhoff's law algorithm (KLA). Electro-hydraulic systems exhibit strong nonlinearities, parameter uncertainties, and external disturbances, making accurate position control challenging. Classical integer-order controllers such as PI and PID often provide limited flexibility in shaping transient dynamics under such conditions, leading to performance degradation when system parameters vary. Although advanced nonlinear and adaptive control strategies can improve robustness, their implementation complexity and tuning burden may restrict their practical applicability. In addition, many existing metaheuristic-based tuning approaches rely on algorithm-specific parameters and may exhibit inconsistent convergence behavior across different operating conditions. To address these limitations, a control-oriented mathematical model of the electro-hydraulic positioning system is first derived from linearized valve flow relations, actuator continuity equations, and load dynamics, and a reduced-order transfer function preserving the dominant behavior is obtained for controller design. The FOPID controller is adopted to enlarge the tuning space through fractional integral and derivative orders, enabling finer dynamic shaping than classical integer-order structures. The controller parameters are determined automatically by formulating a multi-term time-domain objective function that penalizes overshoot, settling time, and accumulated tracking error. The KLA metaheuristic, inspired by electrical circuit laws, is employed to solve this constrained optimization problem without introducing algorithm-specific control parameters. Under identical optimization settings (population size 25, 40 iterations, 20 independent runs), the proposed KLA approach achieves the best statistical performance among the tested optimizers, with a minimum fitness value of 1.2511, mean value of 1.2881, and standard deviation of 0.0258, outperforming APO, PSO, and DE according to Wilcoxon signed-rank tests (p ≈ 8.86 × 10^–5). For a 20 cm step command, the KLA-tuned FOPID controller yields a rise time of 0.1664 s, settling time of 0.3034 s, overshoot of 0.0124%, and IAE of 1.5244 cm·s, improving all metrics relative to both competing optimizers and KLA-tuned PI, PIDF, and 2-DOF PID controllers. Additional simulations demonstrate stable and accurate tracking under multi-level and time-varying references, parametric variations from $$ to $$, and combined disturbance and measurement noise. The results indicate that the KLA-based FOPID design provides a fast, accurate, and robust control solution for electro-hydraulic positioning systems.