Progress in the development of a position sensor for LISA drag-free control

We report on progress in the development of free-falling moving test-masses for LISA and for the related technology demonstration mission. We present simple formulae to evaluate the performance of the device as a function of the various design parameters, and we compare them with preliminary experim ental results from a test prototype we are developing. Quantitative agreeme nt is found. Finally, we present a control law, along with a performance si mulation, for low-frequency electrostatic suspension of the test-mass with minimal perturbation of the motion within the measuring frequency band.