基于LQR算法的三级倒立摆控制系统的仿真研究

倒立摆是智能控制的理想实验对象.本文首先建立了直线三级倒立摆的非线性数学模型,然后在平衡点处对其线性化,再利用二次型最优控制理论,导出控制规律.本文以MATLAB为仿真工具,设计了一系列稳定摆动和加扰实验,通过分析三级摆仿真实验曲线,明确了加权矩阵Q中各权系数对倒立摆稳定影响的相对重要程度,由此来优化加权系数的选择.实验表明,这样选择参数后,系统显示出较好的鲁棒性及动态特性.

Simulation Study on Triple Inverted-pendulum Control System Based on LQR Arithmetic

Inverted-pendulum is an ideal experimental object in intelligent control study. This paper sets up a mathematical model of triple inverted-pendulum in the first place,and linearize it at the balance point,then control rules are deduced using the quadratic optimal control theory.By(using) MATLAB as the simulation tool,a series of experiments are designed to control the stable swing of the poles and to carry out disturbance experiments.By analyzing the simulated curves of the triple inverted-pendulum,the comparative significance of each coefficient of the weighted matrix Q to the stability of the inverted pendulum can be determined,and thereby the choice of weighted coefficients can be optimized.The experiments indicate that the system will have fine robust and(dynamic) performance with these chosen parameters.