含有采样反馈的二连杆系统稳定性  

Stability of Double Pendulum System with Sampling Feedback

作　　者：曹天成 张舒[1] Cao Tiancheng;Zhang Shu(The School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《动力学与控制学报》2023年第11期10-18,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11872277,12072237,11932015)。

摘　　要：当今主流的控制方法大都基于采样反馈得到的离散的状态量从而进行控制参数设计,然而对于采样反馈本身对系统的影响鲜有研究.本文以采样比例-微分控制反馈作用下的二连杆系统为研究对象,研究了采样周期对于混杂系统稳定性的影响.首先,通过数值模拟,发现了二连杆非线性混杂系统可以通过近似线性系统进行定性表征;其次,构造了状态量的离散映射,以反映二连杆混杂系统在目标位置附近的动态响应;最后,提出了二连杆混杂系统的稳定性判据,并以数值仿真的结果验证了判据的准确性.The majority of common control methods focus on control parameter design based on discrete state variables obtained by digital sampling currently.In this study,the influence of sampling period on the stability of hybrid systems is studied by studying a double pendulum system controlled with digital proportional differential feedback.Firstly,through numerical simulation,it is found that the double pendulum nonlinear hybrid system can be qualitatively characterized by an approximate linearized system.The discrete mapping of state variables is then constructed to reveal the dynamic behavior of double pendulum hybrid system near the target position.Furthermore,a stability criterion of the double pendulum hybrid system is purposed.The criteria’s accuracy is verified with numerical simulation results.

关 键 词：二连杆 混杂系统 稳定性 反馈控制 

分 类 号：O317[理学—一般力学与力学基础]