直 线 倒 立 摆 系 统 的 LQR控 制 器 设 计 与 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、鲁棒性问题以与跟踪问题等。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讨论具有重要的理论讨论和实际应用价值。本文以固高公司直线倒立摆为讨论对象，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。关键词：直线倒立摆；建模；稳定性；LQR ；仿真ABSTRACTInverted pendulum system is non-linear, strongly coupled, multivariable andnaturally instable. In the control process this system can reflect some keyproblemsof control theory, such asstabilization problem,nonlinear problems, robustness, andtracking problem. It’s a typicallyexperimental facility which can verifythemethodsofmodern control theory, moreover thecontrol methods andthoughtsplay an important role in dealing withthegeneral industrialprocess. So the studies of inverted pendulum system are theoretically andpractically valued.Googolcompanylinearinverted pendulum, Newton's methodtocreatea straight lineaninverted pendulumdynamic modelusingtheLagrange equationdeducedstraight linedouble inverted pendulummathematical modelof analytical mechanicsmethods. This thesis adopts Googolcompanylinearinverted pendulum as the study object,. Firstcontrollabilityand observabilityanalysis of system state equation should be analyzed, afterwards, with theGoogolhigh-techMatlabreal-timecontrol softwareexperimental platform, LQR controller can be designed andLQR controlmeth...
