Stability Design of Resonance Frequency Tracking System for Sensing Resonator

We propose a novel cascade control system to suppress the relative frequency noise between laser frequency and resonance frequency for improving the stability of resonance frequency tracking of sensing resonator. The phase locking loop (PLL) of the cascade control with optical single sideband (OSSB) modulator is designed to provide a standard reference of the laser frequency for reducing the relative frequency noise in tracking system. And, we precisely extract the closed-loop error signal of the resonance frequency tracking with Pound-Drever-Hall (PDH) modulation technology. Then, we theoretically analyze the dynamic model of cascade control system considering relative frequency noise and optical nonlinearity. The algorithm of cascade control system is designed to further improve the stability of resonance frequency tracking for sensing resonator with a prescribed H_∞ performance. The experimental result shows that the relative frequency noise level is suppressed 30dB. Moreover, the Allan deviation analysis shows that the stability of resonance frequency tracking of sensing resonator compared with the free spectral range (FSR) is improved to 1.493×10^-9. The experimental results validate the effectiveness of our proposed cascade control system to improve the tracking precision of resonance frequency for sensing resonator.