Analysis of the accuracy of actuation electronics for the laser interferometer space antenna

Electrostatic actuation of a free-floating test-mass was tested in the Laser Interferometer Space Antenna (LISA) Pathfinder mission, and it will be integrated into the LISA. We have investigated the LISA Pathfinder actuation accuracy with respect to the precision of fractional digits in the field programmable gate array (FPGA) code of actuation electronics. The LISA Pathfinder data showed that the rounding errors in the FPGA code result in an erroneous force that contaminated the main mission observable, and this error was compensated in the post-processing of the LISA Pathfinder data. To avoid a similar issue for the LISA, the LISA actuation accuracy can be improved by increasing the number of fractional digits in the FPGA code. However, this is restricted by some hardware limitations. In this paper, we investigate the necessary enlargement of the FPGA to fulfill the LISA acceleration requirements and propose a design optimization for LISA actuation electronics.