The article demonstrates the feasibility of quantized positioning and moving scanning x-ray interferometers by feedback of traveling fringes. Two new features, feedback and equilibrium quantization, combine to yield accurate positioning and movement by successive transitions between equilibrium positions. In contrast with feedforward positioning and movement, piezoelectric linearity and stability are not subjected to strict conditions. In preliminary experiments, the performances of an x-ray interferometer were greatly improved and servo-movements up to 0.4 mu m were achieved and tracked with picometer resolution. (C) 1997 American Institute of Physics.