虑及时变时滞的伺服电机传动系统稳定性分析  

Stability analysis of servo motor drive systems with time-varying delay

作　　者：陈子欢 周占民 王鑫[1] 于齐 李旭 Chen Zihuan;Zhou Zhanmin;Wang Xin;Yu Qi;Li Xu(Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,Changchun 130033,China;School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]中国科学院长春光学精密机械与物理研究所,长春130033 [2]大连理工大学机械工程学院,大连116024

出　　处：《电子测量技术》2025年第3期26-34,共9页Electronic Measurement Technology

基　　金：吉林省科技发展计划项目(SKL202402024)资助。

摘　　要：针对伺服电机传动系统建模过程对时滞的考虑不够充分、控制增益的整定缺乏以系统稳定为前提给出的分析、系统稳定判据保守性相对较高的问题,本文提出了一个具有更低保守性的时滞相关稳定判据。首先在惯量结构模型考虑时变时滞并通过设计相应的控制器建立了时滞闭环系统状态空间方程,然后利用Lyapunov泛函分析法结合自由权矩阵、时滞分割、积分不等式等技术以降低稳定判据的保守性。通过运行MATLAB程序得出了由该稳定判据保证系统稳定的控制器增益适用时滞范围,并得出本文判据使系统稳定的最大时滞上界提高了46.33%,验证了本文判据具有更低的保守性。本文的稳定性分析研究为更复杂的伺服电机传动系统分析与控制提供理论参考。Aiming at the problems of insufficient consideration of time delay in the modeling process of servo motor drive system,lack of analysis given in the premise of system stability in the calibration of control gain,and relatively high conservatism of system stability criterion,this paper proposes a time delay related stability criterion with lower conservatism.Firstly,the time-varying delay is considered in the inertia structure model and the state space equations of the time-delayed closed-loop systems are established by designing the corresponding controllers,and then the Lyapunov generalized functional analysis method is used in combination with the techniques of free weight matrix,time delay splitting and integral inequality to reduce the conservatism of the stability criterion.The applicable time delay range of the controller gain for system stability guaranteed by this stability criterion is derived by running the MATLAB program,and it is concluded that this paper′s criterion improves the upper bound of the maximum time delay for system stability by 46.33%,which verifies that this paper′s criterion has a lower conservatism.The stability analysis of this paper provides theoretical reference for the analysis and control of more complex servo motor drive systems.

关 键 词：稳定性分析 LYAPUNOV-KRASOVSKII泛函 伺服电机传动系统 时变时滞 状态空间 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] TN03[自动化与计算机技术—控制科学与工程]