二次型最优控制在小车倒立摆控制系统中的应用  

Application of Quadratic Optimal Control System for Vehicle Inverted Pendulum

作　　者：彭锦 黄为 熊欢 PENG Jin;HUANG Wei;XIONG Huan(School of Information Science and Engineering,Hunan Institute of Science and Technology,Yueyang 414006,China)

机构地区：[1]湖南理工学院信息科学与工程学院,湖南岳阳414006

出　　处：《湖南理工学院学报（自然科学版）》2020年第1期17-23,共7页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：湖南省教育厅科学研究项目(18C0642)。

摘　　要：二级直线倒立摆是一个典型的不稳定系统,同时又具有非线性、多变量、强耦合的特性,因此对其稳定性的研究具有重要的意义.本文主要通过对直线二级倒立摆系统进行分析并进行了数学建模,得出了二级直线倒立摆系统的状态空间表达式,并分析了系统的稳定性、可控性和可观测性.研究了线性二次型最优控制在二级直线倒立摆中的应用,给出了其原理及公式推导过程.建立了二级倒立摆的线性二次型最优控制的Simulink仿真模型,对其进行仿真,最后对仿真结果进行分析,得出二次型最优控制能够实现二级直线倒立摆的稳定控制,而且有较强的抗干扰能力和较好的鲁棒性.Two-stage linear inverted pendulum is a typical unstable system,and it has the characteristics of non-linearity,multi-variable and strong coupling.Therefore,the research on its stability control performance is mainly based on the analysis and mathematical modeling of the two-stage linear inverted pendulum system,and the state of the two-stage linear inverted pendulum system was obtained.The stability,controllability and observability of the system were analyzed.The application of linear quadratic optimal control in two-stage linear inverted pendulum was studied,and its principle and formula derivation process were given.Simulation model of linear quadratic optimal control for two-stage inverted pendulum was established and simulated.Finally,the simulation results were analyzed.It is concluded that the quadratic optimal control can realize the stable control of two-stage linear inverted pendulum,and has strong anti-jamming ability and good robustness.

关 键 词：二级倒立摆 数学模型 拉格朗日方程 LQR控制 抗干扰 鲁棒性 

分 类 号：TM46[电气工程—电器]