平面倒立摆建模与最优控制算法的研究

Modeling And Research of Optimal Control Algorithm On Planar Inverted Pendulum

倒立摆系统是一个多变量、非线性、高阶次、强耦合、欠驱动的自然不稳定系统,是自动控制理论教学和研究中典型的物理模型。本文以平面倒立摆系统为研究对象,使用拉格朗日方程建立了多级平面倒立摆的数学模型。采用线性二次最优控制算法,分别设计了LQR及LQR-模糊控制器,实现平面多级倒立摆的平衡控制,结论证明了本文设计的LQR控制器有很好的稳定性、鲁棒性和适应性。

The inverted pendulum is characterized as a typical nonlinear,high order,strong coupling,underactuated and unstable absolutely system. Is the typical physical model in teaching and research of automatic control theory. As planar inverted pendulum system for the research object,The Lagrangian equations are chosen to establish the nonlinear mathematical model of the single,doubleand triple inverted pendulum system,Based on optimal control theory,linear quadratic optimal regulator （LQR） control algorithm isdesigned and realized the balance control of the three level inverted pendulum. the conclusion that the linear quadratic optimal control algorithm is applied to the stability of the planar inverted pendulum control to control effectively.