Proportional-integral-derivative (PID) control has been widely adopted for stable and reliable operation of rigid rotors supported by a pair of active magnetic bearing systems. Conventional centralized PID control methods manipulate the feedback gains in prescribed forms until they achieve the desired control performance. In this study, an eigenvalue assignment for decoupled translational and conical modes is proposed in the complex domain to yield a unique PID controller in a closed form, preserving the isotropic bearing characteristics. The eigenvalue assignment necessitates the constraints required for decoupling of the translational and conical whirl motions from the complex equation of motion written in the center of gravity coordinates of the rigid rotor. The complex equation of motion integrates the rigid rotor and electro-magnetic control force models defined in two different coordinate systems by utilizing complex coordinate transformation relations. A flywheel energy storage system is taken as a simulation example in order to demonstrate the validity and effectiveness of the proposed eigenvalue assignment. The simulation results show that the eigenvalue assignment algorithm is superior to conventional control methods at systematically ensuring sufficient stability margins for the lightly-damped and unstable conical modes.