单级倒立摆LQR最优控制及其嵌入式系统实现

LQR Optimal Control and Embedded System Implementation for a Single Inverted Pendulum

倒立摆以其非线性特点成为控制理论分析和设计的典型实验设备。针对单级倒立摆系统,建立其数学模型,设计了线性二次型最优控制器,利用Matlab进行了仿真验证。同时,搭建了控制系统的实物实验平台,利用Z-World公司的嵌入式系统实现了该控制算法,并进行了调试,完成了倒立摆的平衡控制。并作了一些干扰实验来验证系统性能。仿真研究和实物实验的结果,表明在嵌入式控制系统中实现的LQR最优控制算法具有很好的控制效果,使倒立摆具有良好的动态性能和稳态性能。

For the nonlinear characteristics, the inverted pendulum is the typical experimental equipment in control system analysis and design. A mathematical model of the single inverted pendulum system is presented and a LQR optimal controller is designed. After the algorithm simulation and verification under the Matlab environment, the inverted pendulum control system is constructed to accomplish the equilibrium control, and the control algorithm is realized on an embedded system of Z-world company. In order to verify the system anti-disturbing performance, experiment is designed and accomplished. The comparison resuh between experiment and simulation shows that the LQR optimal control based on embedded system can regulate the inverted pendulum effectively, and the control system has a good dynamic and static performance.