In the paper, the problem of multiple controlled synchronization of a pair of unbalanced rotors is considered. To ensure the desired system behavior in the face of uncertainty and variations of the system parameters a novel adaptive control law based on the Implicit Reference Model (IRM) approach taking into account the discrete-time implementation is proposed and studied both by the computer simulations and experiments on the Multiresonance Mechatronic Laboratory Setup (MMLS) SV-2M of the IPME RAS, demonstrating the efficiency of the proposed approach and revealing its application scope.