基于Lie理论的倒立摆系统的控制算法研究

该文通过能量反馈和最优控制相结合的方法实现倒立摆系统的自摆起和稳定控制。在摆起阶段采用能量反馈方法实现快速摆起，而在平衡稳定控制阶段，采用一种非线性系统微分几何方法一李理论，对倒立摆系统进行近似线性化，此种线性化方法使模型更多包含原系统主要的非线性部分，更能逼近实际系统，针对采用李理论得到的近似线性化模型，对倒立摆系统进行最优稳定控制设计。仿真和实时控制试验结果表明，文中提出的李理论近似模型线性化方法对于控制器设计结果是有效的，而且采用的能量反馈和最优控制相结合的联合控制策略能够成功实现倒立摆系统的自摆起和稳定控制过程。

Research on Control Algorithm of an Inverted Pendulum System Based on Lie Theory

In this paper an effective control approach for self swinging - up and stabilization of an inverted pendulum system is carried out successfully by combining energy feedback control method with optimum control method. During the self swinging up phase, energy feedback control is adopted to help the inverted pendulum swing up quickly. While during the stabilization phase, differential geometric structure theory of nonlinear system, Lie - theory, is employed to derive the approximate linearized model of the inverted pendulum. This method can keep the main non - linear mode in the system so that the linearized model can simulate the actual system more exactly. Based on the linearized model, an optimum control method is designed to stabilize the system. Both simulation and real -time test resuits show that the linearization method based on Lie -theory is effective for designing control law, and the control strategy which combines energy feedback control with optimum control can implement self swinging - up and stabilization of the inverted pendulum system successfully.