LQR在单级倒立摆系统中的应用

摘要

单级倒立摆控制是一个即复杂而又对准确性、快速性要求很高的非线性不稳定系统控制问题。单级倒立摆数学模型的建立对研究其稳定性具有指导作用。针对多变量、非线性、强耦合性的倒立摆系统，运用牛顿动力学方法建立其动力学方程，并进行线性化处理，得到状态空间模型。然后对该模型分别进行LQR控制，在MATLAB环境下进行仿真。实验结果表明，二次型最优控制具有良好的响应性能和算法简单等特点，在实际应用中具有重要意义。%Single-stage inverted pendulum control is a nonlinear and unstable system control problem that is complicated and of high accuracy and rapidity remands.The mathematical model of single stage inverted pendulum have guidance to study its stability.For multi-variable,nonlinear,strong coupling inverted pendulum system,using Newtonian dynamics method to establish the dynamic equation,and linearization processing to get the state space model.Then using LQR control the model of respectively,under the environment of MATLAB simulation. The experimental results show that quadratic optimal control has the characteristics of good response performance and the algorithm is simple,it is of great signiifcance in practical application.