Velocity-Sensor-Based Dual-ESO Reconstruction for Feedforward-Feedback Low-Frequency Active Micro-Vibration Isolation

Low-frequency base vibration transmitted through supporting platforms can degrade the stability of precision payloads, optical instruments, and inertial measurement systems. In velocity-sensor-based active isolation platforms, displacement-related feedback states are unavailable. Direct velocity integration can drift under sensor bias, while raw lower-platform velocity feedforward can introduce measurement noise and out-of-band components. This paper proposes a dual extended state observer (ESO) reconstruction method combining equivalent-displacement feedback and lower-platform feedforward. The upper-platform ESO reconstructs feedback velocity and a bounded equivalent-displacement state, while the lower-platform ESO provides a smoothed velocity reference for feedforward compensation. The method was implemented on a plate-type active vibration isolation platform and evaluated using lower-to-upper-platform acceleration transmissibility over 0.1-10 Hz. Across three repeated 200 s records, the proposed ESO feedback-feedforward condition achieved an integrated input-output suppression ratio of 38.67±0.46 dB, reduced the upper-platform output acceleration RMS to (1.31±0.09)×10-7 g, and provided a 48.92±2.12 dB RMS reduction relative to the passive baseline. Direct nominal-measured comparisons further showed that the reduced model captured the dominant passive and feedback-controlled dynamics. These results demonstrate that low-frequency active micro-vibration isolation can be achieved using only velocity measurements, without additional displacement sensors.