Design of Optimized FOPID Controller for Performance and Stability Enhancement in Nonlinear Wind–Hydro Turbine Systems

ABSTRACT Nonlinear wind–hydro systems exhibit strong coupling, stochastic wind and inflow variations, and multi‐objective control needs for stability, power balance, and cost optimization. Fractional‐order proportional‐integral‐derivative (FOPID) controllers develop tuning flexibility, dynamic response, and robustness for wind–hydro systems using fractional calculus. However, combined wind–hydro operation introduces nonlinear coupling, uncertainty, and rapid environmental variations, challenging stability and optimal parameter tuning. Conventional optimization approaches suffer from slow convergence and local minima entrapment. To address this, a novel hybrid FAT–AOS algorithm is proposed for optimized FOPID tuning. It combines feedback artificial tree (FAT) global exploration with atomic orbital search (AOS) local exploitation, improving convergence and solution accuracy. It aims to improve stability, reduce nonlinear errors, and minimize operational cost. FAT estimates optimal FOPID gains, while AOS refines them for minimal error. MATLAB implementation uses yearly Indian electricity data for evaluation. Performance is compared with particle swarm optimization, salp swarm algorithm, and ant lion optimizer algorithms. Comparative analysis is also carried out with conventional controllers like sliding mode control, model predictive control, and fuzzy controller to further validate the superiority of the proposed FAT–AOS. Results show 0.11 s settling time, 0.001 s rise time, 0.015% overshoot, and 4235.24 € cost. Efficiency reaches 98%, outperforming existing methods in stability and performance. Overall, FAT–AOS FOPID significantly improves response speed, efficiency, and stability. Compared with conventional optimization approaches, it provides superior robustness and better handling of nonlinear wind–hydro system uncertainties under varying environmental conditions demonstrating improved control performance overall.