直线倒立摆系统的LQR控制器设计及仿真设计.doc

直线倒立摆系统的LQR控制器设计及仿真 摘 要 倒立摆系统是非线形、强耦合、多变量和自然不稳定的系统。在控制过程中能反映控制理论中的许多关键问题，如镇定问题、非线性问题、鲁棒性问题以及跟踪问题等。不仅是验证现代控制理论方法的典型实验装置，而且其控制方法和思路对处理一般工业过程亦有广泛的用途，因此对倒立摆系统的研究具有重要的理论研究和实际应用价值。本文以固高公司直线倒立摆为研究对象，利用Newton法建立直线一级倒立摆的动力学模型。先对系统状态方程进行能控性和能观性分析，之后借助固高科技Matlab实时控制软件实验平台，设计LQR控制器，并利用LQR控制方法对直线一级倒立摆系统进行了Simulink在线实时仿真实验，并对实验结果分析，调节LQR参数，使之达到最佳稳定调节状态，通过在线对系统施加一定的扰动，系统均能在很短的时间里恢复平衡，取得了较好的实时控制效果。 直线倒立摆；建模；稳定性；LQR；仿真 ABSTRACT Inverted pendulum system is non-linear, strongly coupled, multivariable and naturally instable. In the control process this system can reflect some key problems of control theory, such as stabilization problem, nonlinear problems, robustness, and tracking problem. It’s a typically experimental facility which can verify the methods of modern control theory, moreover the control methods and thoughts play an important role in dealing with the general industrial process. So the studies of inverted pendulum system are theoretically and practically valued. Googol company linear inverted pendulum, Newtons method to create a straight line an inverted pendulum dynamic model using the Lagrange equation deduced straight line double inverted pendulum mathematical model of analytical mechanics methods. This thesis adopts Googol company linear inverted pendulum as the study object,. First controllability and observability analysis of system state equation should be analyzed, afterwards, with the Googol high-tech Matlab real-time control software experimental platform, LQR controller can be designed and LQR control method can conduct online real-time simulation experiment on straight line, double inverted pendulum Simulink, analyze results of experiment and adjust LQR parameters so as to achieve the best stability and regulation state. Some certain disturbance online imposed on the system enables it to restore the balance in a very short time, and achieve very good real-time control effects. linear inverted pendulum; modeling；stability；LQR；Simulation 目 录 第一章 绪 论 1 1.1