Abstract: In view of the double linear inverted pendulum system, the theoretical model is built based on Lagrange equation method, and the balanced control is achieved by adopting Linear Quadratic Regulator（LQR） approach and Sliding Mode Control（SMC） approach respectively in the case of the presence of interference. The qualitative relationship between matrix [Q, R] and feedback control matrix [K] is studied for LQR algorithm. After repeated experiments and continuous trying, a good set of control parameters are got to achieve the stable control of inverted pendulum. SMC algorithm based on exponential reaching law control method is applied to design sliding mode variable structure controller, and the chattering is further weakened by using boundary layer method. Finally, physical balanced control of the inverted pendulum is implemented through simulation and experiments.

Key words: double linear inverted pendulum, Linear Quadratic Regulator（LQR）, Sliding Mode Control（SMC）

摘要： 针对二级直线倒立摆系统，采用拉格朗日方程法建立其理论模型，分别使用线性二次最优控制（Linear Quadratic Regulator，LQR）及基于趋近律的滑模控制（Sliding Mode Control，SMC）算法来实现干扰存在情况下倒立摆的平衡控制。对于LQR算法，研究了矩阵[Q]和矩阵[R]与反馈控制矩阵[K]的定性关系，并经过反复多次实验，不断试凑，得到一组良好的控制参数，实现了倒立摆的稳定控制。SMC算法采用基于指数趋近律的控制方法进行了滑模变结构控制器的设计，并利用边界层法来进一步削弱抖振。最后通过仿真及实验，实现了倒立摆的实物平衡控制。

关键词: 二级直线倒立摆, 线性二次最优控制, 滑模控制