A piecewise frequency control (PFC) strategy is proposed in this paper for coordinating vibration isolation and positioning of supporting systems under complex disturbance conditions, such as direct and external disturbances. This control strategy is applied in an active-passive parallel supporting system, where relative positioning feedback for positioning and absolute velocity feedback for active vibration isolation. The analysis of vibration and deformation transmissibility shows that vibration control increases low-frequency position error while positioning control amplifies high-frequency vibration amplitude. To overcome this contradiction across the whole control bandwidth, a pair of Fractional-Order Filters (FOFs) is adopted in the PFC system, which increases the flexibility in the PFC design by introducing fraction orders. The system stability analysis indicates that the FOFs can provide a better stability margin than the Integral-Order Filters (IOFs), so the control gains are increased to get a better performance on the AVI and positioning. The PFC based on FOFs can suppress the peak amplitude at the natural frequency which cannot be avoided when using the IOFs. The constrained nonlinear multivariable function is formed by the required performance and the stability of the system, then the controller parameters are optimized effectively. Lastly, the effectiveness of the proposed method is verified by experiments.

中文翻译：

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基于分数阶滤波器的新型分段频率控制策略，用于协调隔振与支撑系统的定位。

提出了一种分段频率控制（PFC）策略，用于协调复杂干扰条件下（如直接和外部干扰）的支撑系统的隔振和定位。该控制策略应用于主动-被动并联支撑系统，其中相对定位反馈用于定位，绝对速度反馈用于主动隔振。对振动和变形传递率的分析表明，振动控制会增加低频位置误差，而定位控制则会放大高频振动幅度。为了克服整个控制带宽上的这种矛盾，PFC系统中采用了一对分数阶滤波器（FOF），通过引入分数阶来增加PFC设计的灵活性。系统稳定性分析表明，FOF可以提供比积分阶滤波器（IOF）更好的稳定性裕度，因此可以增加控制增益以在AVI和定位上获得更好的性能。基于FOF的PFC可以抑制固有频率下的峰值幅度，这在使用IOF时无法避免。通过所需的性能和系统的稳定性形成约束非线性多元函数，然后对控制器参数进行有效优化。最后，通过实验验证了该方法的有效性。基于FOF的PFC可以抑制固有频率下的峰值幅度，这在使用IOF时无法避免。通过所需的性能和系统的稳定性形成约束非线性多元函数，然后对控制器参数进行有效优化。最后，通过实验验证了该方法的有效性。基于FOF的PFC可以抑制固有频率下的峰值幅度，这在使用IOF时无法避免。通过所需的性能和系统的稳定性形成约束非线性多元函数，然后对控制器参数进行有效优化。最后，通过实验验证了该方法的有效性。