随机振动最优非连续跳变控制的界限与跳变频率作用机制分析  

Effect Mechanism Analysis of Control Bound and Switch Frequency of Optimal Non-continuous Switch Control for Random Vibrations

作　　者：张巍[1] 应曌中 应祖光[3] ZHANG Wei;YING Zhaozhong;YING Zuguang(Laboratory Center,School of Economics and Management,Zhejiang Sci-Tech University,Hangzhou 310018,China;Shanghai Cambricon Information Technology Company,Shanghai 201210,China;Department of Mechanics,School of Aeronautics and Astronautics,Zhejiang University,Hangzhou 310027,China)

机构地区：[1]浙江理工大学经济管理学院实验中心,杭州310018 [2]上海寒武纪信息科技有限公司,上海201210 [3]浙江大学航空航天学院力学系,杭州310027

出　　处：《噪声与振动控制》2020年第5期9-14,32,共7页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(11572279)。

摘　　要：结构系统的随机振动控制是一个重要实际问题,最优限界跳变控制是一个常用的简便方法,控制界限与跳变频率是决定非连续跳变控制效果的主要因素。然而,控制效果是否随控制界限增大单调地提高、跳变频率如何影响控制作用或控制效果、两者之间具有何种制约关系等,这些限界跳变控制的关键问题尚未有结果。以随机最优限界跳变控制的界限与跳变频率关于控制效果的作用机制为研究对象,为该控制设计与优化提供理论基础。首先介绍非连续最优限界跳变控制,基于随机动态规划原理建立随机最优控制的动态规划方程,结合控制界限约束条件,确定最优界限跳变控制律的一般表达式;再对于最优控制的随机振动系统,推导响应协方差方程的一般式,分析控制界限与跳变频率对控制效果的影响;进一步以单自由度随机振动系统为例,给出最优界限跳变控制律与随机响应协方差的表达式,讨论控制界限与跳变频率对于控制效果的作用机制,并通过数值结果说明两者对于控制效果的影响规律,最终得到随机振动控制效果随跳变频率提高而提高,但随控制界限增大先提高后降低的结论。Random vibration control of structural systems is an important realistic problem.The optimal bounded switch control is a common convenient method.The control bound and switch frequency are main factors in determining non-continuous switch control effectiveness.However,some key problems for bounded switch control,such as whether the control effectiveness increases always with the control bound,how the switch frequency affects the control effectiveness and which relation between them exists,have not been investigated yet.In this study,the effect mechanism of control bound and switch frequency of the optimal bounded switch control for random vibrations are analyzed.Firstly,the non-continuous optimal bounded switch control is introduced.The dynamical programming equation for the optimal control is established based on the stochastic dynamical programming principle.The optimal bounded switch control law is obtained by solving the equation with the constraint conditions of the control bound.For the controlled random vibration system,the response covariance equation is formulated,and the effects of the control bound and switch frequency on the control effectiveness are analyzed.By considering a single degree-of-freedom random system as an example,the expressions of the optimal bounded switch control law and random response covariance are obtained and the inherent action manner of the control bound and the switch frequency on the control effectiveness are discussed.Numerical results are given to illustrate the effects of the control bound and the switch frequency on the control effectiveness.It is shown that the control effectiveness increases with the switch frequency increasing,but increases initially then decreases later with the control bound increasing.

关 键 词：振动与波 随机最优控制 限界跳变 随机振动响应 

分 类 号：O324[理学—一般力学与力学基础]