Hybrid metaheuristic optimization for Bouc–Wen hysteresis modeling and robust control of piezoelectric actuators

This paper proposes a hybrid optimization algorithm combining the adaptive Marine Predators Algorithm (aMPA) and adaptive Differential Evolution (aDE) for parameter identification of the Bouc–Wen hysteresis model in piezoelectric actuators. The proposed aMPA–aDE algorithm improves the balance between global exploration and local exploitation, thereby enhancing convergence performance and identification robustness compared with standalone optimization methods. To evaluate its effectiveness, the proposed algorithm is compared with several optimization approaches, including MPA, aMPA, DE, CMA-ES, and aDE–Jaya. Comparative results show that the proposed aMPA–aDE algorithm achieves competitive convergence speed and identification accuracy. The proposed method is then applied to identify the Bouc–Wen hysteresis model using experimental input–output data obtained from a piezoelectric actuator. Furthermore, the identified hysteresis model is incorporated into a Sliding Mode Controller (SMC) for trajectory tracking and experimental verification under different reference signals. Experimental results demonstrate that the proposed method can effectively characterize the nonlinear hysteresis behavior of the piezoelectric actuator and provide satisfactory tracking performance.