Abstract: Since the dynamical characteristics of active magnetic bearings (AMBs)-rotor systems are closely related to the structures and the parameters of controllers, it is particularly important to design proper controllers to make the systems work safely, steadily and reliably. Aiming at the AMBs-rigid rotor systems, a design method of a first-order dynamical compensator based on eigenstructure assignment is proposed in this paper. First, the four-degree-of-freedom (4-DOF) AMBs-rigid rotor system is decomposed into two 1-DOF translational sub-systems and two 1-DOF conical sub-systems through modal decoupling method. Then, based on the eigenstructure assignment, the relations between the eigenvalues and the eigenvectors of the closed-loop system using the first-order dynamical compensator, and the parameters of the compensator are obtained. Moreover, the eigenvalues are confined in some specific regions to obtain stability and good dynamical performance, and the objective functions for optimization are constructed to suppress the unbalance displacements and the unbalance control currents of the AMBs-rigid rotor system simultaneously. The AMBs-rigid rotor system under the control of the proposed dynamical compensator has desired dynamical performance, and the effectiveness of the designed compensator is confirmed through numerical simulations and experiments.