车轨长度受限的并行双摆能量控制

Energy control for parallel-type double inverted pendulums with restricted cart rail length

采用牛顿-欧拉方法建立并行二级倒立双摆系统的数学模型.针对车轨长度受限的并行二级倒立摆系统,本文提出了一种基于能量控制思想和直接李雅普诺夫函数方法的摆起控制策略.所设计的控制器保证了小车的速度收敛到零和摆杆在达到垂直向上的位置时摆杆的能量为零.同时,它能实现对并行双摆的稳摆控制.控制器简单易行,参数调节方便.在并行二级倒立摆摆起控制器设计的基础上,简述了三级车摆的摆起控制器设计过程.最后,通过计算机仿真验证了控制方法在工作效率和抗干扰方面能保持良好的控制性能.

The Newton-Euler approach is used to build the mathematical model of a parallel-type double inverted pendulums system（PDIPS）.A new swinging up controller is proposed for the PDIPS with restricted cart rail length by making use of energy-based control ideal and direct Lyapunov function method.The designed controller guarantees that the speed of the cart converges to zero even in the presence of the restriction on the rail length,and the energy of the inverted pendulums is zero when the pendulums is in vertical position.Moreover,the swing angles of the PDIP can be regulated to their steady-state values,respectively.Based on the controller design for PDIPS,the swinging controller development for the triple pendulums is summarized briefly.In addition,the proposed controller is convenient for implementing and adjusting designed parameters.Simulation results show that the proposed control method can achieve satisfactory control performance in terms of working efficiency and robustness with respect to disturbances.