基于二级倒立摆的数学建模及系统性能分析  

Mathematical modeling and analysis on system performance based on two-stage inverted pendulum

作　　者：吉红[1] 王颖丽[1] 赵忠义 孙宏图 JI Hong;WANG Yingli;ZHAO Zhongyi;SUN Hongtu(School of Mechanical and Electrical Engineering,Tianjin Bohai Vocational Technical College,Tianjin 300402;Tianjin Welding Research Institute Co.,Ltd.,Tianjin 300110)

机构地区：[1]天津渤海职业技术学院机电工程学院,天津300402 [2]天津市焊接研究所有限公司,天津300110

出　　处：《机械设计》2023年第7期137-142,共6页Journal of Machine Design

摘　　要：基于二级倒立摆非线性、强耦合、多变量和自然不稳定的高阶系统特点,文中采用Lagrange数学建模方法对二级倒立摆模型数学建模并进行系统分析。分析二级倒立摆系统结构及阐述其工作原理,并基于Lagrange方程建立该系统的非线性模型;考虑系统工作特点对建模过程中次要因素进行忽略,并在此基础上对数学模型线性化处理;对二级倒立摆模型的稳定性、可控性及可观性进行分析。结果表明:二级倒立摆模型是一个单输入多输出系统,具有高度不稳定性,但具有良好的可控性和可观性,这为二级倒立摆模型的控制系统研究奠定了坚实的理论基础。Based on the characteristics of nonlinear,strongly coupled,multivariable,and naturally unstable high-order systems of the secondary inverted pendulum,the Lagrangian mathematical modeling method is used to model the secondary inverted pendulum model and conduct system analysis.Analyze the structure of the two-stage inverted pendulum system and explain its working principle,and establish a nonlinear model of the system based on the Lagrange equation;Neglecting secondary factors in the modeling process considering the characteristics of the system's work,and linearizing the mathematical model based on this;Analyze the stability,controllability,and observability of the two-stage inverted pendulum model.The results indicate that the two-stage inverted pendulum model is a single input multiple output system with high instability but good controllability and observability,laying a solid theoretical foundation for the research of the control system of the two-stage inverted pendulum model.

关 键 词：二级倒立摆 数学建模 线性化 可控性 可观性 

分 类 号：TP24[自动化与计算机技术—检测技术与自动化装置]