Yan Yonggang, Duan Kangqiao, Cui Jianjun, Guo Shiwei, Cui Can, Zhou Yongsheng, Huang Junjie, Wang Geng, Zhang Dengpan, Zhang Fumin
School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454003, China.
National Institute of Metrology, Beijing 100029, China.
Micromachines (Basel). 2025 Apr 23;16(5):492. doi: 10.3390/mi16050492.
Piezoelectric tilt mirrors are crucial components of precision optical systems. However, the intrinsic hysteretic nonlinearity of the piezoelectric actuator severely restricts the control accuracy of these mirrors and the overall performance of the optical system. This paper proposes an improved Gray Wolf Optimization (GWO) algorithm for high-accuracy identification of hysteresis model parameters based on the Bouc-Wen (BW) differential equation. The proposed algorithm accurately describes the intrinsic hysteretic nonlinear behavior of piezoelectric tilt mirrors. A logistic chaotic mapping method is introduced for population initialization, while a nonlinear convergence factor and a Levy flight strategy are incorporated to enhance global search capabilities during the later stages of optimization. These modifications enable the algorithm to effectively identify BW model parameters for piezoelectric nonlinear systems. Compared to conventional Particle Swarm Optimization (PSO) and standard GWO, the improved algorithm demonstrates faster convergence, higher accuracy, and superior ergodicity, making it a promising tool for solving optimization problems, such as parameter identification in piezoelectric hysteresis systems. This work provides a robust approach for improving the precision and reliability of piezoelectric-driven optical systems.
压电倾斜镜是精密光学系统的关键部件。然而，压电致动器固有的滞后非线性严重限制了这些镜子的控制精度以及光学系统的整体性能。本文提出了一种基于布赫 - 温（BW）微分方程的改进灰狼优化（GWO）算法，用于高精度识别滞后模型参数。所提出的算法准确地描述了压电倾斜镜固有的滞后非线性行为。引入逻辑斯谛混沌映射方法进行种群初始化，同时在优化后期纳入非线性收敛因子和莱维飞行策略以增强全局搜索能力。这些改进使算法能够有效地识别压电非线性系统的BW模型参数。与传统粒子群优化（PSO）和标准GWO相比，改进算法具有更快的收敛速度、更高的精度和更好的遍历性，使其成为解决优化问题（如压电滞后系统中的参数识别）的有前途的工具。这项工作为提高压电驱动光学系统的精度和可靠性提供了一种稳健的方法。
