通过Washout滤波算法对自振荡系统进行反馈镇定  

Feedback Stabilization of the Self-oscillatory System Based on Washout Filter Algorithm

作　　者：柴莘茗 易云帆 翟持 CHAI Xinming;YI Yunfan;ZHAI Chi(Faculty of Chemical Engineering,Kunming University of Science and Technology,Kunming 650500)

机构地区：[1]昆明理工大学化工学院,昆明650500

出　　处：《工程数学学报》2024年第3期577-586,共10页Chinese Journal of Engineering Mathematics

基　　金：云南省基础研究计划基金(202001AU070048).

摘　　要：由Andronov-Hopf分岔演化而成的自振荡系统与对应的线性化系统在结构上不再具有相同的微分流型,而是会表现出多维非线性耦合特征。有研究借助Washout滤波的瞬态保留特性构建控制策略对自振荡系统进行反馈镇定,但所需的滤波器个数一直无法定量确定。基于Andronov-Hopf分岔标准形式的分析,探讨使用两个Washout滤波对造成自振荡的二维非稳态变量进行反馈镇定化。考虑到基于状态空间法的反馈设计可能会导致滤波算法具有高阶特性,进而使设计结果与Washout滤波元件提供的模拟信号不匹配,通过分析闭环系统Laplace变换的极值问题将多维、高阶滤波系统对角化并降维。研究发现,通过向形成共轭复数特征值的两个状态量引入两个Washout滤波,将原n维自振荡系统转化成n+2维增广系统,状态–输出通道需构建的Washout滤波具有相同的滤波参数,其值为辅助矩阵P的迹。一个自振荡反应过程仿真实例进一步验证了所得控制方案的可行性与有效性。Considering the self-oscillating system evolved from Andronov-Hopf bifurcation and the corresponding linearized system no longer share the same differential manifold,but would exhibit multi-dimensional nonlinear coupling characteristics.Previous study adopts Washout filter to stabilize the oscillatory system,while,the number of filters needed for a particular system is still unsolved.Based on normal form analysis of the Andronov-Hopf bifurcation system,this work explores to connect two filters on the dual-unstable eigenspace,however,feedback design based on state-space method may cause the results being high ordered,which cannot be realized by a Washout filter compartment physically.Through transient dynamics analysis on the Laplace transfer function,we propose to decouple the feedback loop and reduce the Washout algorithm to 1-ordered,which is able to be realized by stable Washout filters physically.A simulation example of the self-oscillation reaction process further verifies the feasibility and effectiveness of the obtained control scheme.

关 键 词：Andronov-Hopf分岔 瞬态特征 滤波个数 增广系统 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]