平面两级倒立摆的分析、控制器设计与实现

对基于XY平台的平面两级倒立摆进行了运动学和动力学分析，由于系统具有很强的非线性以及耦合等特性，需要在其平衡点附近线性化，以得到系统的近似线性状态方程。然后分析了系统的可控性，并根据状态方程采用线性二次最优控制LQR方法设计控制器。仿真结果说明，倒立摆系统可以得到很好的稳定效果。最后进行了多次实验，倒立摆都可以稳定很长时间，而且可以施加一定的干扰，具有较好的鲁棒性。实验结果说明，此方法是有效可行的。

Analysis and Controller Design of Plane Double Inverted Pendulum

The dynamics and kinematics of a plane double inverted pendulum over an XY table is analyzed. For the system has strong characters of nonlinear and coupling, to gain the approximate linear state equation, the system need to been linearized round the balanceable point. The controllability of the state equation is analyzed, and an LQR controller is designed. Simulate results show that the stabilization of the inverted pendulum is satisfactory. The pendulum can balance for hours, and it can burden some disturbance, which shows that it has a good character of robust . The effectiveness of the method is proved.