The achievable performance of the complementary-filter-based parallel control for a compound dual-stage nano-positioning system is limited by its model-based sequential design structure. This study proposes a frequency-response-data-based optimization approach for the simultaneous and systematic design of the complementary-filter-based dual-feedback controller. The design procedure and corresponding Nyquist stability analysis are presented in detail. By directly utilizing frequency response data, the proposed method mitigates the effects of system identification errors. The controller design objective is formulated as a constrained optimization problem to achieve a flat amplitude frequency response with high control bandwidth. Comparative experiments conducted on a dual-stage nano-positioning system verify the effectiveness of the proposed approach. The proposed method reduces the root-mean-square tracking error from 70.6 nm using the baseline integral controller to 21.3 nm at 50 Hz sinusoidal tracking, demonstrating its clear superiority.
Yu et al. (2026) studied this question.