Dynamic systems with self-excited periodic motion have a wide range of applications in mechanical systems. For instance, a class of non-minimum phase underactuated and nonprehensile systems require self-oscillations instead of tracking an external reference signal. To solve this problem, we proposed a two fuzzy inference system, which is based on fuzzy logic theory, in order to generate a periodic output. The idea is to enforce the conditions that ensure the orbital asymptotic stability of the periodic solution of the closed-loop system. In this study, we considered Euler-Lagrange systems, with emphasis in underactuated systems. The describing function method was used to design the fuzzy controller and set the desired frequency and amplitude of the periodic output. Moreover, in accordance with Loeb's criteria, we established sufficient conditions for orbital stability. Finally, we tested and validated our proposal, via simulation and experiments on two laboratory platforms: a single-link pendulum and an underactuated non-minimum-phase rotational inverted pendulum.

具有自激周期运动的动态系统在机械系统中有着广泛的应用。例如，一类非最小相位欠驱动和非抓握系统需要自振荡而不是跟踪外部参考信号。为了解决这个问题，我们提出了一种基于模糊逻辑理论的二次模糊推理系统，以产生周期性的输出。这个想法是强制执行确保闭环系统周期解的轨道渐近稳定性的条件。在这项研究中，我们考虑了欧拉-拉格朗日系统，重点是欠驱动系统。采用描述函数法设计了模糊控制器，并设定了所需的周期输出频率和幅值。此外，根据勒布的标准，我们为轨道稳定建立了充分条件。最后，我们通过在两个实验室平台上的模拟和实验测试并验证了我们的提议：单连杆摆和欠驱动的非最小相位旋转倒立摆。