Nonlinear Active Disturbance Rejection Controller Design for Drag-Free Satellite with Two Test Massess

Space gravitational wave detection missions require low bandwidth, high accuracy and strong robustness for the drag-free satellite systems, which require laser interference experiments with dual test masses (TMs) inside the satellite. For drag-free control and electrostatic levitation control with dual TMs satellites, linear controllers are difficult to solve the comprehensive problems of high accuracy and stability. In this paper, fractional order active disturbance rejection control (FOADRC) is used as the drag-free controller and electrostatic levitation controller, in which the non-linear controller controls the drag-free system and the active disturbance rejection compensates the system with feedback, achieving the objectives of frequency division control and interference suppression for the drag-free control and electrostatic levitation control. The simulation results show that the relative displacement of the satellite and the test mass (TM) is less than \(1 \times 10^{ - 9}\,{\mathrm{m\,Hz}}^{ - 1/2}\) $1\times {10}^{-9}{\mathrm{m}\mathrm{Hz}}^{-1/2}$ and the residual acceleration is less than \(1 \times 10^{ - 15}\,{\mathrm{m\,s}}^{ - 2}\,{\mathrm{Hz}}^{ - 1/2}\) $1\times {10}^{-15}{\mathrm{m}\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ in the sensitive band of 0.1 mHz–1 Hz gravitational wave detection. The designed controller scheme ensures the system robustness and control accuracy under the ultra-low bandwidth constraint and improves the system-response performance.