For the suspension control of active magnetic bearing (AMB) flywheel rotor in the flywheel energy storage system, a multi-objective optimal control strategy based on multi-dimensional visualization was proposed. Firstly, the AMB-flywheel rotor system was simplified into a planar rotor model, and the analytical solutions of equivalent stiffness, equivalent damping, maximum amplitude and sensitivity function of the planar rotor control system were derived. On this basis, the optimization model of the AMB-flywheel rotor system was established, in the optimization model, the vibration and robustness of the control system were taken as the optimization objectives, and the system stability, "natural" stiffness and "natural" damping, bearing air gap, and robustness boundary of magnetic bearing were considered as the constraints. Subsequently, the multi-dimensional visualization algorithm was used to solve the optimization model, obtaining the optimal feasible regions of PID (proportional-integral-derivative) control parameters. Finally, the control method proposed was verified by system simulations and experiments, and the results show that the control system proposed can achieve stable suspension of the flywheel rotor system in the speed range of 0 ~ 15 000 r/min, with the characteristics of low vibration and strong robustness.