一类小车倒立摆的起摆稳摆时滞控制研究  

Delayed Swing up and Stability Control of a Class of Cart-Pendulum System

作　　者：冯欣炜 胥奇 杨正兵 李映辉[1] Feng Xinwei;Xu Qi;Yang Zhengbing;Li Yinghui(School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 610031,China;Sichuan Gas Turbine Establishment,Aero Engine Corporation of China,Chengdu 610500,China)

机构地区：[1]西南交通大学力学与航空航天学院,成都610031 [2]中国航发四川燃气涡轮研究院,成都610500

出　　处：《动力学与控制学报》2023年第8期82-91,共10页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12072292);四川省科技计划重点研发项目(2022YFG0083);四川省自然科学基金项目(2022NSFSC0275,2023NSFSC0067)。

摘　　要：主动控制中不可避免地存在时滞现象.本文研究了一级小车倒立摆由起摆到稳摆的时滞切换控制,包括非线性时滞起摆控制和线性时滞串级PD控制两种控制方法.为分析时滞对系统瞬态时域性能的影响,本文使用含时滞的线性表达式对特定运动时刻的Lyapunov函数导数进行近似,得到了时滞影响系统能量输入的简单判别式,发现时滞可优化非线性起摆控制阶段的能量输入.同时,使用定积分法分析了稳摆阶段的稳定性,得到了时滞的稳定性区间.针对本文所研究的小车倒立摆系统,综合起摆阶段和稳摆阶段的时滞取值范围,以引入适当的时滞,可以同时实现优化瞬态时域特性和稳定性的效果.Time delay is an inevitable factor in the active-control loop.This paper studies the delayed switching control of an inverted single pendulum on a cart,by using the delayed nonlinear swing up control and the delayed linear cascade PD stability control.To analyze the delay effect on the transient time-domain performance of the system,the derivative of the Lyapunov function at a specific moment of motion is linearized,and a simple criterion is then proposed for judging the transient performance based on the derivative.It is found that the time delay can decrease the energy input rate of the swing up control,and hence improve the transient performance.The definite integral method is then used to study the stability of the single pendulum,and the stable interval of the delay value is obtained.Case study shows that,with considering the delay effect of both the swing up control and the stability control,an appropriate time-delay value can be identified to improve the control performances for both transient and stability performance of the system.

关 键 词：倒立摆 时滞 瞬态时域特性 串级PD控制 稳定性分析 

分 类 号：O317.2[理学—一般力学与力学基础]