Minimum-Time Control for the Test Mass Release Phase of Drag-Free Spacecraft

The capture control of test mass by means of the electrostatic suspensions is crucial for drag-free spacecraft. The test mass must be released to the cage center of the inertial sensor accurately and quickly. This paper proposes a minimum-time capture control method for the test mass release phase of drag-free spacecraft. An analytical solution of optimal control is derived based on Pontryagin’s minimum principle and the linearized dynamics model of the test mass during the release phase. The parameters of the analytical solution are initially guessed with an approximate linear solution of the test mass dynamics model and are slightly modified by using differential correction. Compared with the exact numerical solution by the hp-adaptive pseudospectral method, the analytical solution is proved to be minimum-time. Numerical simulation shows that the proposed control method quickly captures the test mass to the cage center of the inertial sensor. The capture time to stabilization is only half that of the traditional controller.