Design of a novel and robust 2-DOF PIDA controller based on enzyme action optimizer for ball position regulation in magnetic levitation systems

Abstract

Magnetic levitation (maglev) systems are characterized by strong nonlinearities and inherent open-loop instability, making precise position regulation of levitating bodies exceptionally challenging. These systems are highly sensitive to model uncertainties, parameter variations, and external disturbances. This demands advanced control strategies beyond conventional PID techniques. To address these challenges, this study introduces a novel two-degree-of-freedom proportional-integral-derivative-acceleration (2-DOF PIDA) controller, specifically designed to stabilize and regulate ball position in magnetic levitation systems. The controller`s structure is augmented with acceleration feedback and reference input weighting, enabling decoupled tuning for transient and steady-state performance and ensuring enhanced damping, disturbance rejection, and tracking accuracy. A core innovation of this work is integration of the controller with the enzyme action optimizer (EAO)—a recently developed bio-inspired metaheuristic algorithm that emulates adaptive catalytic behavior observed in enzymatic reactions. The EAO algorithm balances global exploration and local exploitation to efficiently optimize the 2-DOF PIDA controller parameters, minimizing the integral of absolute error (IAE) as the objective function. This optimization framework is evaluated against two recent metaheuristics: the horned lizard optimization algorithm (HLOA) and the sea-horse optimizer (SHO), using extensive time-domain simulations. Quantitative results confirm the superior performance of the proposed method, achieving 0% overshoot, a rise time of 0.0121 s, and a settling time of 0.0365 s the optimal response speed and stability among all tested algorithms. Additionally, robustness is rigorously validated under multiple scenarios of parameter perturbations, including variations in resistance and inductance, simulating real-world effects such as component aging and thermal drift. The EAO-tuned controller consistently maintains superior regulation and stability across all test cases, exhibiting high resilience to system uncertainties. Furthermore, a comprehensive comparative analysis involving 12 state-of-the-art control strategies, including PID, FOPID, and RPIDD2 variants optimized via diverse evolutionary algorithms, confirms the proposed controller`s dominance across all critical performance indices, including IAE, rise time, settling time, and overshoot. These findings underscore the effectiveness of combining 2-DOF control architectures with bio-inspired optimization algorithms for real-time implementation in nonlinear, unstable systems. Overall, the proposed EAO-optimized 2-DOF PIDA controller offers a computationally efficient, auto-tunable, and robust solution for high-precision maglev control.