针对传统正位置反馈（PPF）与一阶PPF控制器控制效果与鲁棒性不足，难以适用于结构动力学特性存在摄动的问题，提出一种新的基于分数阶微积分理论和一阶PPF的分数阶（FOPPF1）控制器，增加了一阶PPF控制器的可设计空间。综合考虑随机响应的频域特性与整体波动强弱，构造了控制器优化设计的目标函数。以粘有宏纤维压电复合材料（MFC）压电片的垂尾模型为被控对象，设计了相应的FOPPF1控制器。该控制器在控制目标频段内的相频特性变化平缓，可有效实现控制相位补偿，且闭环极点对参数摄动不敏感，使得控制器的鲁棒性强。通过试验研究了FOPPF1控制器对于自由振动与窄带随机振动的抑制性能。相比一阶PPF控制器，对标称垂尾模型，FOPPF1控制器在自由振动抑制试验中的等效阻尼系数提高了约50%。当给垂尾模型的一阶弯曲固有频率引入一定量的离线摄动或在线摄动后，窄带随机振动控制试验的结果表明，FOPPF1控制器的鲁棒性、控制效果及控制能耗率明显优于经典的一阶PPF控制器，因此对垂尾结构的振动主动控制具有良好应用潜力。
Traditional Positive Position Feedback (PPF) and first-order PPF controllers are inadequate in control effectiveness and robustness, and is thus difficult to be applied to the structures with perturbation effect. A novel Fractional Order (FOPPF1) controller is proposed based on the fractional calculus theory and the first-order PPF to increase the designable space of the controller. Considering the frequency domain characteristic and global vibration amplitude of random response, an optimization design of the objective function for the FOPPF1 controller is constructed. A scale model of the vertical tail with Macro Fiber Composite (MFC) piezoelectric patches is manufactured, and the corresponding FOPPF1 controller is designed based on the proposed method. The phase frequency property of this controller in the target frequency band is changed gently, and the phase compensation can be effectively realized. Furthermore, the poles in the closed-loop system are insensitive to parameter perturbation; therefore, the proposed FOPPF1 controller has good robustness. The free vibration and narrow-band random vibration control experiments are performed to validate the proposed control method. The free vibration response test results show that the equivalent damping coefficient of the FOPPF1 controller for the nominal model is improved by about 50% of that of the first-order PPF controller. When a certain amount of offline or online perturbation is introduced into the first-order natural frequency of the vertical tail, results of the narrow-band random vibration control experiment show that the robustness, control efficiency and energy consumption ratio of the proposed FOPPF1 controller is significantly better than those of the classical first-order PPF. Therefore, the proposed controller has great potential for application in vibration control of the vertical tail.
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