Robustness Analysis and Controller Design of Arm-locking System in Space-based Gravitational Wave Detectors

TL;DR

This paper develops a parametric stability analysis framework and a robust controller for arm-locking systems in space-based gravitational-wave detectors, improving stability and noise suppression under parameter variations.

Contribution

It introduces a combined D-subdivision and Semi-Discretization stability analysis method and designs a robust controller to enhance arm-locking system stability.

Findings

The proposed method accurately maps stability regions.

The robust controller maintains stability under parameter perturbations.

Simulations confirm effective laser noise suppression.

Abstract

Arm-locking frequency stabilization is a key technique for suppressing laser frequency noise in space-based gravitational-wave detectors. The robustness of the arm-locking control loop is crucial for maintaining laser frequency stability, which directly impacts the accuracy of gravitational-wave measurements. In this work, a parametric stability analysis framework is developed by combining the D-subdivision theory with the Semi-Discretization method to map the stability regions of arm-locking systems in the parameter space and identify their critical stability boundaries. Based on the frequency-domain characteristics, a robust arm-locking controller is designed to enhance loop stability under parameter perturbations. Theoretical analysis and time-domain simulations confirm that the proposed controller maintains closed-loop stability and realize suppression of laser frequency noise against parameter perturbation.