摘要
大变形结构动力学模型常用于模拟大型化、轻量化结构的瞬态响应,但其几何非线性特征使高效而精确的建模与控制面临挑战.基于数据驱动的本征正交分解(POD)与Hellinger-Reissner变分原理,可构造大变形结构的双场动力学降阶模型.该模型引入先验的应力信息,并将位移基推导的刚度不变量阶数由四阶降低至三阶,由此提升了瞬态动力学降阶计算的精度与效率.在双场动力学降阶模型基础上,进一步探讨柔性结构动响应的高效预测与最优控制问题,嵌入模型预测控制框架,实现轨迹优化控制.通过细长杆系与机翼骨架两个结构算例表明,该方法在保证精度的同时显著降低了在线计算成本,相较于传统位移POD降阶方法,在精度与实时性方面均表现出更优性能,并展现出良好的模型预测控制适用性.
Dynamic models of large-deformation structures are widely used to simulate transient response of large-scale and lightweight structures,but their geometric nonlinearity poses significant challenges for efficient and accurate modeling and control.A two-field reduced-order model(ROM)for large-deformation structures can be constructed,via data-driven Proper Orthogonal Decomposition(POD)with the Hellinger-Reissner variational principle.This model incorporates prior stress information and reduces the order of stiffness invariants derived from displacement bases from fourth to third order,thereby improving both accuracy and efficiency of transient dynamic model reduction.Based on the two-field ROM,this work further investigates efficient prediction and optimal control of flexible structural responses by embedding the ROM into a model predictive control(MPC)framework to achieve trajectory optimization and tracking.Case studies on a slender beam system and a wing skeleton demonstrate that the proposed approach significantly reduces online computational cost while maintaining accuracy,and outperforms traditional displacement-based POD methods in both efficiency and accuracy,showing strong applicability to MPC-based control of nonlinear flexible structures.
作者
周文祥
罗凯
Zhou Wenxiang;Luo Kai(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;State Key Laboratory of Environment Characteristics and Effects for Near-space,Beijing Institute of Technology,Beijing 100081,China)
出处
《动力学与控制学报》
2025年第11期72-80,共9页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(12522201,12494563)。
