Improved Ivy Algorithm for an Enhanced Fractional Order Proportional‐Integral‐Derivative Controller: Applications From Winding Tension Control to Hybrid System

ABSTRACT The multi‐filament carbon fiber winding technique is an advanced and novel process, where tension control and regulation during winding play a crucial role in determining product performance. Based on this, this paper introduces fractional‐order modeling to derive the physical model of the fiber winding process and optimizes the design of the traditional fractional‐order proportional‐integral‐derivative (FOPID) controller, to obtain the self‐coupling time delay fractional‐order proportional‐integral‐derivative control strategy (ST‐FOPID). The stability region of the tension control system is numerically computed and visually analyzed. Furthermore, this study improves the metaheuristic Ivy algorithm (IVYA) and proposes an improved version, the improved Ivy algorithm (IIVYA). Large‐scale benchmark function experiments and performance comparisons with various algorithms, including the original Ivy algorithm, demonstrate significant improvements in convergence speed, global search capability, and avoidance of local optima. As a result, we propose a self‐coupling time delay fractional‐order proportional‐integral‐derivative control strategy (IIVYA‐ST‐FOPID) based on the improved Ivy algorithm, which is successfully applied to industrial systems such as simple mathematical model, DC motor speed control system, servo tension control system, and hybrid multi‐area power system. Comparative analyses with various existing control strategies confirm the superior performance and broad applicability of the proposed method. Finally, both numerical simulations and experimental results show that the tension control system has excellent dynamic performance and stability under the proposed control strategy, with a significant performance improvement. Tension fluctuations can be controlled within 5% in slow winding conditions, while in fast winding scenarios, they remain around 6%. Moreover, the proposed control strategy reduces the settling time by more than 0.1 s, demonstrating the excellent performance of the proposed control strategy in complex industrial control systems.