针对压电悬臂梁的振动问题, 该文提出了一种模糊滑模主动控制策略, 以在抑制悬臂梁振动的基础上减小抖振。根据均质梁单元和压电梁单元运动方程引入状态向量,建立了压电悬臂梁的状态空间方程。通过平衡截断法对压电悬臂梁模型进行降阶,以提高计算效率, 并以降阶模型为对象设计了模糊滑模控制器。运用模糊规则调节切换增益,饱和函数替换符号函数, 有效地减小了滑模控制的抖振现象, 利用Lyapunov函数证明其稳定性。结果表明, 基于饱和函数的模糊滑模控制不仅能控制压电悬臂梁的振动, 还能降低抖振现象。

Aiming at the vibration problem of piezoelectric cantilever beams, a fuzzy sliding mode active control strategy is proposed so as to reduce the buffeting based on the suppressing of the vibration of cantilever beams. The state space equation of the piezoelectric cantilever beam is established by introducing the state vector into the motion equation of the homogeneous beam element and the piezoelectric beam element. The order of the piezoelectric cantilever beam model is reduced by the equilibrium truncation method so as to improve the calculation efficiency, and the fuzzy sliding mode controller is designed based on the reduced-order model. The buffeting phenomenon introduced by the sliding mode control can be reduced effectively by using the fuzzy rule to adjust the switching gain and using the saturation function to replace the sign function, and its stability is proved by using the Lyapunov function. The results show that the fuzzy sliding mode control based on the saturation function can not only control the vibration of piezoelectric cantilever, but also reduce the buffeting phenomenon.