Analysis of the accuracy of actuation electronics in the laser interferometer space antenna pathfinder

M. Armano et al.
The Laser Interferometer Space Antenna Pathfinder (LPF) main observable, labeled Δg, is the differential force per unit mass acting on the two test masses under free fall conditions after the contribution of all non-gravitational forces has been compensated. At low frequencies, the differential force is compensated by an applied electrostatic actuation force, which then must be subtracted from the measured acceleration to obtain Δg. Any inaccuracy in the actuation force contaminates the residual acceleration. This study investigates the accuracy of the electrostatic actuation system and its impact on the LPF main observable. It is shown that the inaccuracy is mainly caused by the rounding errors in the waveform processing and also by the random error caused by the analog to digital converter random noise in the control loop. Both errors are one order of magnitude smaller than the resolution of the commanded voltages. We developed a simulator based on the LPF design to compute the close-to-reality actuation voltages and, consequently, the resulting actuation forces. The simulator is applied during post-processing the LPF data.
This work was supported by ETH Research Grant No. ETH-05 16-2, and it has been made possible by the LISA Pathfinder mission, which is part of the space-science program of the European Space Agency. The French contribution has been supported by the CNES (Accord Specific de Projet Grant No. CNES 1316634/CNRS 103747), the CNRS, the Observatoire de Paris, and University Paris-Diderot. E. Plagnol and H. Inchauspé would also like to acknowledge the financial support of the UnivEarthS Labex program at Sorbonne Paris Cité (Grant Nos. ANR-10-LABX-0023 and ANR-11-IDEX-0005-02). The Albert-Einstein-Institut acknowledges the support of the German Space Agency, DLR. The work is supported by the Federal Ministry for Economic Affairs and Energy based on a resolution of the German Bundestag (Grant Nos. FKZ 50OQ0501 and FKZ 50OQ1601). The Italian contribution has been supported by the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare. The Spanish contribution has been supported by Contract Nos. AYA2010-15709 (MICINN), ESP2013-47637-P, ESP2015-67234-P, and ESP2017-90084-P (MINECO). Support from AGAUR (Generalitat de Catalunya) contract 2017-SGR-1469 is also acknowledged. M. Nofrarias acknowledges support from Fundacion General CSIC (Programa ComFuturo). F. Rivas acknowledges an FPI contract from MINECO. The Swiss contribution acknowledges the support of the Swiss Space Office (SSO) via the PRODEX Programme of the ESA. L. Ferraioli is supported by the Swiss National Science Foundation. The UK groups wish to acknowledge support from the United Kingdom Space Agency (UKSA), the University of Glasgow, the University of Birmingham, Imperial College, and the Scottish Universities Physics Alliance (SUPA). J. I. Thorpe and J. Slutsky acknowledge the support of the U.S. National Aeronautics and Space Administration (NASA). N. Korsakova would like to thank the support from the CNES Fellowship. The LISA Pathfinder collaboration would like to acknowledge Professor Pierre Binetruy (deceased 30 March 2017) and Professor José Alberto Lobo (deceased 30 September 2012) for their contribution to the LISA Pathfinder science.