Frequency Estimation and Noise Reduction in Homodyne Grating Interferometer Based on Third-Order Generalized Integrator-Frequency-Locked Loop With Damping Ratio Adaptation

A phase-locked loop (PLL)-based subdivision module can provide distance and velocity information to the homodyne grating interferometer (HGI) integrated with a servo control system. However, the received sinusoidal signal pair from the HGI is degraded by considerable low-frequency noise, harmonic components, and white noise, limiting displacement measurement accuracy. In this article, a fast signal filtering method is proposed for HGI based on the combination of two third-order generalized integrators (TOGIs) and a frequency-locked loop (FLL). FLL is designed with damping ratio adaption to obtain high-accuracy estimation of time-varying frequency of the HGI signal, while two TOGIs are employed as frequency-adaptive bandpass filters using the FLL estimated frequency as the center frequency. Therefore, the proposed method enables accurate tracking of the fundamental components within the HGI signals, thereby effectively reducing noise. The performance of the proposed method is evaluated through simulations and physical experiments under various conditions, including frequency step changes, white noise, low-frequency noise, harmonics, and sinusoidal motions covering constant velocity and acceleration regimes. The results demonstrated that the proposed method generally outperformed other methods, namely, second-order generalized integrator-frequency-locked loop (SOGI-FLL), SOGI-FLLWPF, and SOGI-FLL-WIF. This study contributes to enabling more accurate and reliable displacement measurement using HGIs.