Shape adjustment of cable mesh reflector antennas considering modeling uncertainties

Cable mesh antennas are the most important implement to construct large space antennas nowadays. Reflector surface of cable mesh antennas has to be carefully adjusted to achieve required accuracy, which is an effective way to compensate manufacturing and assembly errors or other imperfections. In this paper shape adjustment of cable mesh antennas is addressed. The required displacement of the reflector surface is determined with respect to a modified paraboloid whose axial vertex offset is also considered as a variable. Then the adjustment problem is solved by minimizing the RMS error with respect to the desired paraboloid using minimal norm least squares method. To deal with the modeling uncertainties, the adjustment is achieved by solving a simple worst-case optimization problem instead of directly using the least squares method. A numerical example demonstrates the worst-case method is of good convergence and accuracy, and is robust to perturbations.