基于LQR对直线倒立摆的稳摆控制研究及实现  

Research and Realization of Stable Pendulum Control of Linear Inverted Pendulum Based on LQR

作　　者：张慧慧[1] 侯伯杰[1] 高建设[1] 郭明[1] ZHANG Hui-hui;HOU Bo-jie;GAO Jian-she;GUO Ming(School of Mechanical and Power Engineering,Zhengzhou University,He’nan Zhengzhou 450001,China)

机构地区：[1]郑州大学机械与动力工程学院,河南郑州450001

出　　处：《机械设计与制造》2024年第1期186-190,共5页Machinery Design & Manufacture

基　　金：河南省高等学校重点科研项目(19A460008)。

摘　　要：针对倒立摆的稳摆控制问题,研究设计了一个LQR控制器。首先,考虑摆杆摆动的阻力矩,采用牛顿力学分析方法推导出直线倒立摆的数学模型,建立了其线性状态空间模型,并分析了系统的稳定性、能控性与能观性。通过采用仿真试凑确定加权矩阵Q、R,得到状态反馈增益矩阵K,完成LQR控制器的设计。之后,搭建了以开放式运动控制器为核心的倒立摆实验平台,在计算机上开发了实时人机交互程序,在运动控制器里编写了倒立摆控制算法。最后,进行了仿真与实测实验,验证了所设计的LQR控制器的有效性和可行性。Aiming at the stabilization control problem of the inverted pendulum,an LQR controller was researched and designed.First,considered the resistance moment of the swing of the pendulum rod,the mathematical model of the linear inverted pendulum is derived by Newtonian mechanics analysis method.The linear state space model is established,and the stability,controllability and observability of the system are analyzed.By using methods of simulation and trial to determine the weighting matrix Q and R,the state feedback gain matrix K is obtained,thus completing the design of the LQR controller.After that,an inverted pendulum ex-periment platform with an open motion controller as the core was designed and built,a real-time human-computer interaction program was developed on the computer,and an inverted pendulum control algorithm was written in the motion controller.Fi-nally,simulation and actual measurement experiments are carried out to verify the effectiveness and feasibility of the designed LQR controller.

关 键 词：直线倒立摆 LQR 运动控制器 最优控制 

分 类 号：TH16[机械工程—机械制造及自动化] TP273[自动化与计算机技术—检测技术与自动化装置]