考虑作动器饱和的结构振动多层级分布式瞬时最优控制  

Multi-level distributed instantaneous optimal control for structural vibration with actuator saturation

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

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

出　　处：《振动工程学报》2020年第6期1253-1262,共10页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11922203,11772074)。

摘　　要：针对结构振动主动控制问题,提出了一种含作动器饱和约束的多层级分布式瞬时最优控制方法。首先,基于Newmark-β法动态子结构技术,将整体系统分解为一系列多层级分布的子系统,并建立面向分布式控制的子系统动力学模型。然后,基于不同层级的动力学模型,采用瞬时最优控制策略,以出口节点状态作为各相邻子系统之间的信息交互,对各子系统设计独立的局部子控制器。最后,基于参变量变分原理,将具有作动器饱和约束的瞬时最优控制问题转化为线性互补问题,求解该线性互补问题,从而获得相应的子系统控制律。为验证所提算法的有效性,以平面简支梁和大型空间智能索网天线结构振动控制为例进行数值仿真,结果表明:所提多层级分布式瞬时最优控制方法能有效地抑制结构的振动响应,其设计灵活、具有良好的容错性,并且作动器饱和约束可直接通过求解线性互补问题而得以满足。In this paper,a multi-level distributed instantaneous optimal control method(MDIOC)with actuator saturation is proposed for solving the active structural vibration control problems.Firstly,based on the dynamic substructuring technique of the Newmark-βalgorithm,the entire structure system is decomposed into a series of multi-level subsystems,and the dynamic models for distributed control of each subsystem can be established.Then,based on these models from different level grids,the local subcontrollers can be independently designed by the IOC method with interaction of the connected boundary node states between adjacent subsystems.Finally,based on the parametric variational principle,the original problem with actuator saturation is transformed into a series of linear complementary problems(LCPs),and each local control law can be obtained by solving these LCPs.Numerical simulations,including aplanar simply supported beam and a large spatial intelligent cable antenna structure,illustrate that the proposed method is effective,flexible to implement,and has high fault tolerance.In addition,the actuator saturation constraints can be directly satisfied just by solving a linear complementary problem.

关 键 词：结构振动 振动主动控制 子结构技术 作动器饱和 分布式控制 瞬时最优控制 

分 类 号：O327[理学—一般力学与力学基础] TB535[理学—力学]