基于LQR的直线二级倒立摆最优控制系统研究

Research on an Optimal Linear Double Inverted Pendulum Control System Based on LQR

倒立摆系统是一个典型的多变量、非线性、强耦合和快速运动的高阶不稳定系统,是检验各种新的控制理论和方法有效性的典型理想模型。在其控制过程中,能有效地反映诸如镇定性、鲁棒性、随动性以及跟踪等许多关键问题。通过研究直线二级倒立摆LQR控制方法,首先建立了二级倒立摆的数学模型,然后设计LQR控制器,并对系统进行仿真,最后使用Windows动态链接库调用技术和多媒体定时器技术设计了VC和Simulink两种版本的控制程序,系统成功实现了稳摆控制。

The inverted pendulum is a typical high order system with multi -variable, non -linear, strong -coupling, fleet and absolutely instable properties. It is a typical ideal model to prove new control theory and techniques. During the control process, pendulum can effectively reflect many key problems such as equanimity, robust, follow - up and track. This paper studies the LQR control method of the straight line double inverted pendulum. First, the mathematical model of the double inverted pendulum is established, a LQR controller is designed and then the system simulation is conducted. Finally,two versions of the VC and Simulink control program based on the technology of Windows dynamic link library calls and multimedia timer technology are designed. The system successfully achieves steady sway control.