一级倒立摆系统设计与LQR最优控制仿真

摘要

By using the Lagrange mechanics, the mathematical model of a single inverted pendulum is built and state space equation is obtained. A controlled inverted pendulum system is designed, and system performance is analysed. A linear inverted pendulum optimal controller based on LQR is designed. Simulation and experiment proved that the LQR has good real-time control effects,and ensure that the system has good stability and robustness.%应用Lagrange力学,对一级倒立摆系统进行数学建模,得出了状态空间方程；设计了一级可控倒立摆系统,并对系统进行了性能分析；设计了直线一级倒立摆的LQR控制器,通过仿真和实验证明,LQR实时控制效果好,保证了系统具有良好的稳定性和鲁棒性.