The problem of angular motion stabilization by mechanical systems with nonrigid construction is considered. The control is realized in the class of discrete systems with piecewise constant control actions which can lead to appearance and growth of the elastic oscillations of the object construction. The notion of the influence function of a base control on the elastic oscillations is introduced. Using this function the task of the subsystem formation of the intellectual diagnostics and tuning of the base algorithm is solved. Some results of digital simulation of the suggested method of control by multifrequency large space structure are given