Inertial sensors act as inertial references in space gravitational wave detection missions, necessitating that their internal test mass (TM) maintains minimal residual acceleration noise. High-energy particles and cosmic rays in space, along with ion pumps in ground-based torsion pendulum experiments, can cause charge accumulation on the TM surface, leading to increased residual acceleration noise. Consequently, a charge management system was introduced to control the TM’s charge. The complex light path propagation within the electrode housing (EH) makes the TM’s charging and discharging process difficult to theoretically calculate and fully simulate. To address this issue, we propose a simulation method for charging and discharging inertial sensors within ultraviolet (UV) charge management systems. This method innovatively considers the impact of photoelectron emission angle and the TM’s position offset from symmetry on performance. The method also simulates charging and discharging rates over time under conditions of symmetry and preliminarily examines factors affecting the TM’s equilibrium potential. Simulation results indicate that this method effectively models the charge management system’s operation, providing a valuable reference for system design.

In space-based gravitational wave detection missions, inertial sensors act as the inertial reference, requiring the test mass (TM) to maintain exceptionally low residual acceleration noise. High-energy particles, cosmic rays, and ion pumps during ground tests can quickly lead to charge accumulation on the TM surface, necessitating a charge management system to regulate surface charges. To manage the TM surface potential, this paper develops a mathematical model of the charge management system using established ultraviolet (UV) discharge simulation methods. The model describes how photoelectron emission or absorption on the TM surface varies with UV light-emitting diodes (LEDs) power and bias voltage. For the first time, a dual-loop control method is implemented for charge control, highlighting its practical significance. The controller precisely regulates the TM surface potential and residual charges to specified values, achieving a control accuracy of $1.1\times {10}^6$e, meeting the stringent requirements of space-based gravitational wave detection missions. This approach offers a closed-loop charge management solution and provides valuable insights for designing future charge management systems.

Inertial sensors are the key payloads in space gravitational wave detection missions, and they need to ensure that the test mass (TM), which serves as the inertial reference, freely floats in the spacecraft without contact, so that the TM is not disturbed by the satellite platform and the cosmic environment. Space gravitational wave detection missions require that the residual acceleration of the TM should be less than $3\times {10}^{-15}{\mathrm{ms}}^{-2}{\mathrm{Hz}}^{-1/2}$. However, the TM with charges will interact with surrounding conductors and magnetic fields, introducing acceleration noise such as electrostatic force and Lorentz force. Therefore, it is necessary to carry out charge management on the TM, in which the high-precision measurement of charge is crucial. Space gravitational wave detection missions require a residual charge measurement accuracy of $3\times {10}^{-13}\mathrm{C}$ for the TM. In this paper, we design a high-precision inertial sensor charge measurement method based on phase-sensitive demodulation (PSD). By establishing a torsion pendulum rotation model based on the force modulation method, the characteristics of the TM torsion angle signal are analyzed. The PSD is used to extract the amplitude of the specific frequency signal component containing the charge information, and then to calculate the value of the accumulated charges. The method is compared with the Butterworth band-pass filtering method, and the simulation results show that the method has a higher measurement accuracy, shorter settling time, and stronger anti-interference ability, meeting the TM residual charge measurement accuracy index requirement.

In space-based gravitational wave detection missions, the test mass (TM), which serves as the inertial reference, must maintain extremely low residual acceleration noise. During in-orbit operation, Galactic Cosmic Rays (GCRs) and Solar Energetic Particles (SEPs) cause charge accumulation and additional electrostatic forces. Therefore, ultraviolet (UV) light is used to illuminate the interior of the inertial sensor and regulate the TM charge through the ultraviolet photoelectric effect. However, surface contamination, temperature fluctuations, and material aging can degrade the surface Quantum Yield (QY) of the TM. In addition, transient intense charging disturbances induced by SEP events can rapidly alter the charge state of the TM, thereby degrading the long-term performance and operational stability of the Charge Management System (CMS). To address these issues, based on the nonlinear UV discharge model of the CMS, this study investigates the effects of QY degradation and external charging disturbances on the charge-transfer dynamics and control performance of the CMS and proposes an adaptive disturbance-rejection charge control method that integrates a Fuzzy self-tuning PID (FPID) controller with an Extended State Observer (ESO). Simulation results show that the proposed method enables effective charge regulation under different illumination schemes and prescribed QY degradation and external charging conditions and exhibits greater adaptability than conventional PID and fuzzy PID controllers. The findings of this study provide a theoretical reference for the design of charge control systems operating in complex space environments.