摘要：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，它是检验各种新的控制理论和方法有效性的典型理想模型。在对其控制过程中，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。本文以固高科技生产的直线二级倒立摆为研究对象，推导建立了该倒立摆系统的数学模型，并对其系统性能进行了分析。然后采用了PID控制方法和LQR(linear quadratic regulator）控制方法，对其系统进行了稳定性控制。仿真结果表明LQR比PID控制器的效果更好。并依据Q、R矩阵的物理意义以及多次试验的结果，给出了一组较好的Q、R参数矩阵。

关键词：二级倒立摆；LQR控制；PID控制

Abstract:The inverted pendulum system is a typical advanced unstable system, which is  multi-variable, nonlinear and strong-coupling with a rapid movement. It is an ideal model  to test all theories about controlling and the validity of the method. In the controlling process, it can effectively reflect many key issues, such as stabilization, robust, follow-up and track,etc.. The thesis tries to derive and establish the mathematical model of this inverted pendulum system and analyze its properties in detail, regarding the high-tech double linear inverted pendulum as the research target. The system is controlled with stability based on the controlling methods of PID and LQR ( linear quadratic regulator ). The results show that LQR has a better effect than PID controller. According to Q, R matrix physical meaning and many experiments,a group of good Q, R parameter matrix will be given.

Key words：Second-order inverted pendulum；LQR control；PID control