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This paper aims to improve the robustness of the air-gap controller for a solid immersion lens (SIL)-based near-field (NF) storage system against dynamic disturbances, such as external shocks. The robust control system is essential in NF data storage technology because the nanoscale gap distance between the SIL and the disk is 50 nm or less. Also, the air-gap distance must be maintained without physical contact between the SIL and the disk to evaluate the efficient reading and recording signals when an external shock is applied. Therefore, we propose an improved air-gap control algorithm with an acceleration feedforward controller (AFC) using time delay to maintain the nanoscale air-gap distance without collision for a 5.76 G at 10 ms shock. Thus, the anti-shock control performance for the SIL-based NF storage system in the presence of external shocks is markedly improved. Furthermore, to enhance the performance of the anti-shock air-gap control with AFC using time delay, we use the AFC using time delay with a double disturbance observer (DOB). As a result, the air-gap distance is controlled without contact for a 6.85 G@10 ms shock.