欠驱动旋转双摆系统的模糊控制

摘要

Double rotating pendulums system consists of an actuated rotating arm and two unactuated rotating pendulums. A fuzzy controller is designed to keep the two rotating pendulums upright and bring the rotating arm to origin. The system' s dynamic model is derived by using Lagrange equations. And the dynamics is linearized around the unstable equilibrium under linearization conditions. During the fuzzy controller design, "rules explosion" problem emerges because of the system having 6 state variables. To overcome the problem, a fusion function is employed for the system variables such that the input number of the fuzzy controller decreases from 6 to 2. Consequently, the corresponding fuzzy rules are established and a practical fuzzy controller for the double rotating pendulums system is achieved. Finally, simulation results demonstrate the effectiveness of the designed fuzzy controller.%旋转双摆系统由一个单电机驱动的旋转臂和两根安装在旋转臂上的未驱动的旋转摆杆组成,是典型的欠驱动系统,模糊控制设计的目的是将两根摆杆稳定在倒立位置的同时将旋转臂控制到原点.首先,基于拉格朗日方程获得系统的非线性动力学模型,进而给出其在不稳定平衡点附近的线性化模型.在进行模糊控制器的设计过程中,由于旋转双摆系统有6个状态变量,为了避免模糊控制中“规则爆炸”问题,借助融合函数合并系统状态变量,将模糊控制器的输入数由6减少到2,再设计相应的控制规则,得到易于实现的模糊控制器.最后,数字仿真实验证明了所设计的模糊控制器的有效性.