Drag-free design based on Embedded Model Control for TianQin project

With the ability to detect low-frequency gravitational waves (GWs), space-borne detectors will play an important role in exploring the universe in the future. The TianQin project proposed in China participates in this challenge by aiming to detect millihertz GWs. The TianQin GW detector consists of three spacecraft forming a triangular constellation. Each spacecraft carries a pair of test masses (TM) which, inside shielding cages, are left to free fall along the local geodesic. In this way, a pair of TMs on two separate spacecraft can be each other aligned to become the gravitational references of the GW detector, made by an inter-satellite laser interferometer. Each free-falling TM is limited by parasitic forces to be appropriately bounded. The relevant acceleration bound has been fixed to 10−15 m/s2/Hz within the TianQin measurement bandwidth (MBW) ranging from 0.1mHz to 0.1Hz. In turn, TM to cage fluctuations must be kept below 4nm/Hz to limit the stiffness coupling with the spacecraft displacement caused by non-gravitational disturbances, such as solar radiations and the thruster noise. Suppression of such disturbances calls for a challenging drag-free control technology, since the center of mass (CoM) of a single spacecraft cannot track the separated CoMs of two TMs simultaneously, and consequently tracking must be limited to three degrees of freedom (DoF): two non-orthogonal sensitive axes (one for each TM) and the perpendicular direction to their plane. Control design and simulated tests of this paper will be restricted to the drag-free control along the sensitive axes. The remaining nine DoFs of the two TMs (position and attitude) are controlled by electrostatic suspensions, not to be treated here, but accounted for in the simulated trials. The design of the two-DoF drag-free control relies on a model-based control methodology, the Embedded Model Control (EMC), capable of predicting and suppressing unknown disturbances within the required bandwidth and of decoupling the TM dynamics along the non-orthogonal sensitive axes. The paper starts with the nonlinear model of the TM to cage dynamics, followed by the relevant EMC design, restricted to the sensitive axes. Numerical simulations are employed to validate closed-loop performance and robust stability. Simulated results show that the residual TM to cage fluctuations can be kept below 3nm/Hz, which leaves a margin within the required spectral bound. The EMC methodology discussed in the paper can provide a reference for future developments and implementations.