Dynamics of nonlinear systems of controlled machine units with discrete parameters is analyzed. The objectives of the investigation are to study possible vibrations in such discrete dynamical systems, as well as to find ways how to decrease the harmful effect of vibrations on the normal functioning of the systems. The used mathematical model is a system of ordinary differential equations of the fifth order with a cubic nonlinearity. For the investigations averaging method is first applied to such advanced model, that allows to determine conditions of stability of both one-frequency stationary modes and biharmonic ones. Amplitudes of the vibrations, as well as the approach to equilibrium on fast time scales, are obtained. Dependence of stationary modes on the different parameters of the system is analyzed. Using feedback, one can optimize functioning of the machine units with discrete parameters. The results may be applied in industry for the design of new improved technical systems.