基于能量控制与近似输出调节的二级倒立摆起摆和跟踪控制

Swing-up and tracking control of double inverted pendulum based on energy control and approximate output regulation

中文关键词  二级倒立摆  起摆  跟踪控制  能量控制  近似输出调节

英文关键词  double inverted pendulum  swing-up  tracking control  energy control  approximate output regulation

中文摘要

      二级倒立摆是一个典型的欠驱动非线性系统, 其控制问题具有一定的挑战性. 为了解决时变参考信号下二 级倒立摆的起摆和跟踪控制问题, 本文提出了一种基于能量控制与近似输出调节方法的起摆和三阶控制器设计方 案. 首先, 采用能量控制方法将第1级摆杆从下垂位置摆起到倒立位置附近; 其次, 采用滑模控制方法将第1级摆杆稳 定在倒立位置, 同时, 采用等效小车与能量控制相结合的方法将第2级摆杆摆起到倒立位置附近; 最后, 采用基于近 似输出调节理论的多项式近似方法设计三阶控制器实现二级倒立摆的位置跟踪控制. 仿真和实验结果均验证了该 控制方案的有效性.

英文摘要

      The control problem of double inverted pendulum is challenging since it is a typical underactuated nonlinear system. In this paper, a swing-up and third-order controller design scheme based on energy control and approximate output regulation method is proposed to solve the swing-up and tracking control problem of double inverted pendulum with time-varying reference signal. First, the energy control method is adopted to swing up the first pendulum from the downward position to the neighborhood of the upright position. Second, the sliding mode control method is adopted to stabilize the first pendulum at the upright position. Meanwhile, a method combining “equivalent cart” and energy control is adopted to swing up the second pendulum to the neighborhood of the upright position. Third, a polynomial approximation method based on approximate output regulation theory is adopted to design a third-order controller to realize the position tracking control of the double inverted pendulum. Both simulation and experimental results verify the effectiveness of the proposed control scheme.