All rotating machines, such as electrical AC machines, suffer greatly from vibrations in their rotating parts. Vibrations occur at certain frequencies called critical frequencies that are always characteristic to the machine. Driving a machine at or near the critical frequencies cause two kinds of problems due to the vibrations. First, the air gap between the rotor and the stator must have greater safety margins, which decreases the efficiency of the motor. Otherwise, the motor would suffer a fatal damage from a rotating rotor hitting the stator. Secondly, wear of the structures is significantly increased due to vibrations which causes increased maintenance costs and decreased motor life-time. Active vibration control aims to suppress the vibrations at the critical frequencies by assistance of an additional actuator that is capable of exerting an external force to the rotor. This actuator is implemented with additional windings in the stator such that it has minimal effects on the normal operation of the motor. Active vibration control methods applied in electrical AC machines have previously mainly relied on linear time-invariant (LTI) models of the motor and correspondingly on traditional control methods such as LQ control and convergent control. These methods have produced successful results in active damping of vibrations and significantly decreased the vibrations at the critical frequency of the machine. In this paper, similar methods are studied in the case of a more accurate linear time periodic (LTP) system model of the electrical AC machine. Utilization of a more accurate model enables using more precise control and is therefore expected to give better controller performance. The performance of the developed periodic state feedback control method is compared to the performance given by a constant gain state feedback control. The developed control methods are tested by simulations with a model that is identified from the data measured from a 30kW squirrel-cage induction motor. It is revealed that the proposed control method works successfully but it gives only small improvement of performance in vibrations control. The reason for so moderate improvement of performance is supposed to be due to the small variations in the time-periodic parameters of the system model.