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.

Active vibration isolation system (AVIS) using the traditional vibration isolation technology, such as reducing suspending stiffness and adding absolute damping, has performance defects due to the residual low-frequency disturbances which still severely restrict the precision machine accuracy. This paper proposes a novel vibration control method combining inertial absolute sensor feedback (ASF) and positive relative sensor feedback (RSF), which can highly improve the low-frequency vibration isolation performance, and the blending control method is analyzed according to the vibration transmission. The results show that ASF strengthens the connection between the payload and the absolute space, while positive RSF weakens the connection between the payload and the base. By introducing ASF and positive RSF blended, the stiffness and damping between the payload and the absolute space can be increased to near infinity, while the stiffness and damping between the payload and the base can be attenuated to near zero. The blending control method includes absolute displacement feedback (ADF), positive relative displacement feedback (RDF), absolute velocity feedback (AVF), and positive relative velocity feedback (RVF). ADF combined with RDF improves the vibration isolation performance at low-frequency, while AVF combined with RVF improves the performance around the inherent frequency and high-frequency. In this way, the payload is hard to be affected by disturbances in a broad frequency region. Finally, the proposed method is verified by experiments and compared with the commonly used sky-hook damping method. It shows that the initial frequency of vibration isolation is reduced from 5.6 Hz (sky-hook damping method) to 1 Hz (the proposed method), the magnitude of vibration transmission starts with −11.1 dB (at 1 HZ), and the maximum magnitude is always below 0 dB from 1 Hz to 50 Hz.