关键词: 二级直线倒立摆, 线性二次最优控制, 滑模控制

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）