Abstract: Traditional research work on underactuated (Translational Oscillator with Rotational Actuator, TORA) system mainly focuses on stabilizing control of equilibrium points. In this article, a fuzzy control design scheme easy to realize is proposed to steer periodic oscillating trajectories of TORA system. Firstly, based on the dynamics of TORA, the frequency of translational oscillation platform is derived, and then the dynamic periodic orbits are followed, namely, the translational oscillation platform oscillating periodically while the rotational proof mass rotating with the fixed angular velocity. Secondly, based on the analysis of state variables, tracking error of system’s energy is employed as the inputs of fuzzy control system so as to reduce the dimension of the control system, membership function using one-side domain is applied to design fuzzy rules and the center of gravity method is used for defuzzification. Consequently, a practical fuzzy controller is achieved. Finally, simulation results and experimental results validate efficiency and practicability of the proposed control scheme.

Key words: Translational oscillators with rotating actuator, underactuated, trajectory tracking, fuzzy control

摘要： 欠驱动(Translational Oscillators with Rotating Actuator，TORA)系统的传统控制目标是实现平衡点的稳定控制，文中针对系统的周期性振荡轨迹给出易于实现的模糊控制设计方法。首先，基于欠驱动TORA系统的动力学分析，考虑振荡平台的振荡频率，设计一种振荡平台周期运动、转动小球匀速转动的周期性目标动态轨迹。其次，基于对状态变量的分析，选择能量误差作为模糊控制系统的输入量以降低模糊控制器的维度，采用单边论域隶属度函数设计模糊控制规则，采用重心法进行解模糊化，得到易于实现的模糊控制器。最后，仿真和实验结果验证了所提控制方案的有效性。

关键词: 旋转激励平移振荡器, 欠驱动, 轨迹跟踪, 模糊控制