Emulating scaled drag-free control dynamics on a ground simulator testbed

As a key technique for gravitational wave detection, drag-free control presents significant challenges for ground experimental validation. This work addresses the problem of experimentally emulating the scaled drag-free control on a ground simulator composed of an air-bearing testbed and two inverted pendulums. In this paper, the dynamics models are deduced and simplified. The dynamics similarity conditions are determined through the use of the Pi theorem. And the concepts of the equivalent stiffness and equivalent mass of the inverted pendulum are proposed to establish the similar dynamics equations. Subsequently, scaling laws are derived to design the simulator testbed. Basic scaling laws are introduced to evaluate the scaled control index. Besides, an underactuated closed-loop control strategy employing redundant adjustable thrusters is devised for the ground experiment. Finally, the precise tracking control of the air-bearing testbed relative to two pendulums is realized on the ground drag-free simulator, emulating the scaled displacement control mode with two test masses. And the scaled control indexes corresponding to space mission are validated in the resulting drag-free simulation system. The effectiveness of the proposed approach is confirmed by the scaling equivalence experiments of drag-free control with two test masses.