考虑局部非线性结构振动的模型预测控制  

The model predictive control for structural vibration with local nonlinearity

作　　者：李飞[1] 张盛[1] 彭海军[1] 陈飙松[1] LI Fei;ZHANG Sheng;PENG Hai-jun;CHEN Biao-song(Department of Engineering Mechanics,State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室工程力学系,大连116024

出　　处：《计算力学学报》2018年第5期582-588,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11472069);111引智计划(B14013);国家重点研发计划(2016YFB0200702)资助项目

摘　　要：针对具有局部非线性的结构振动主动控制问题,首先,利用Newmark-β法推导了局部非线性结构动力响应的时域显式递推表达式。然后,基于该表达式,一方面建立了局部非线性结构振动预测模型,并借鉴模型的线性化思想对非线性环节进行处理,提出考虑局部非线性结构振动的模型预测控制算法;另一方面,在获取各仿真时刻的预测初始状态时,为避免直接对非线性动力学方程所有维度的完全迭代求解,推导了时域显式降维迭代方法,从而使在线计算效率得到显著提高。最后,分别以局部非线性弹簧振子系统在简谐激励作用下的无控动力学分析和含粘滞阻尼器毗邻框架建筑结构在地震激励作用下的受控振动为例,进行数值仿真,结果表明,本文算法计算准确且控制效果较好。In this paper,for the problem of structural vibration control with local nonlinearity,a dynamic explicit recursive formulation in time-domain for locally nonlinear structures is derived by using the Newmark-βmethod firstly.Then,based on this formulation,a novel model predictive control algorithm for vibration of the locally nonlinear structure is proposed,which is followed by the establishment of the predictive model for this problem.It should be pointed out that the nonlinear component in the control process can be dealt with using the model linearization method.Besides,to avoid a full iteration of all dimensions for the nonlinear dynamic equations when the initial state values in each predictive period need to be computed,an explicit dimension-reduced iteration method in time-domain for locally nonlinear structures is also derived,which can greatly improve the online computation efficiency.Lastly,numerical simulations of a local nonlinear mass-spring system subjected to a harmonic excitation and an adjacent frame building with viscous dampers subjected to seismic excitation show that the proposed method is quite accurate and satisfactory in control performance.

关 键 词：局部非线性 显式递推表达式 模型线性化 模型预测控制 显式降维迭代 

分 类 号：O327[理学—一般力学与力学基础]