Sample-tracking vibration isolation with rigid negative stiffness for broad bandwidth

Sample-tracking vibration isolators position their mover such that the distance to a targeted sample is constant to provide a vibration-free environment, for example, for inline metrology with high resolution. To achieve high vibration isolation and rejection especially at low frequencies, this paper proposes a sample-tracking vibration isolator that integrates a flexure-guided hybrid reluctance actuator (HRA) with a negative stiffness for quasi-zero stiffness (QZS). The negative stiffness cancels the flexure stiffness for QZS, by which vibrations transmitted from the actuator’s stator can be significantly reduced. Unlike conventional QZS systems, the negative stiffness is magnetically realized with rigid components such as a permanent magnet and ferromagnetic cores. Consequently, the proposed vibration isolator has mechanical resonant frequencies of around 2.5 kHz and higher. This hardware design with a feedback controller realizes a motion with nanometer resolution and a high closed-loop control bandwidth of 991 Hz for further vibration isolation and sample tracking. To evaluate the performances of the proposed vibration isolator, the negative stiffness is tuned to cancel a flexure stiffness at experiments. Experimental results show that the fine tuning decreases transmissibility from $-30$  dB to $-62$  dB by a factor of 40 at a low frequency of 10 Hz. Furthermore, the tracking error of the mover position is measured for a demonstration of the vibration rejection performance in the time domain. The results also show that the stiffness cancellation decreases the tracking error with feedback control from 2.7 nm (rms) to 1.3 nm (rms) by 52% at a steady state. The proposed sample-tracking vibration isolator successfully demonstrates high vibration isolation performance by utilizing the rigid negative stiffness of the HRA.