This article presents an analysis of a flexible Jeffcott rotor with an active bearing support. The rotor is coupled with lateral and torsional vibrations and a force from the unbalance vector derived from the Lagrangian method. The active support bearing is controlled by FOPID controller. Changing the rotor vibration is followed by shifting rotor angular speed and achieving the natural frequency. Simulation results demonstrate torsional and lateral vibration of thr rotor at the rotating speed near the natural frequency. Consequently, controlling the lateral vibrations mitigates potential damage and improves safety. FOPID controller introduces a new approach to vibration control of a rotating machine.