The paper is devoted to the problem of controlling the rotation speed of unbalanced rotors of a vibration machine. The solution to this problem is important for vibration technologies, such as transportation and mixing of bulk media. Since the characteristics of the rotor drives can vary in the wide range depending on the mode (operating rotation speed), the load on the vibration platforms, and other factors, the requirement for the robustness of the system in relation to the parameters of the setup is of big importance. For this purpose, adaptive control based on the use of an implicit reference model is employed in the work. For the digitalization of the control process, it is also required to transform the control law into discrete form and study the limitations, caused by time sampling. The boundedness of the drive control signal significantly affects the system performance. Therefore a method of digital adaptive control with anti-windup correction is proposed and evaluated in this paper. The results are examined by the simulations and experimentally studied on the mechatronic setup SV-2M, demonstrating the efficiency of the proposed solution.