This paper describes development of a new control system for active dynamic absorbers using a neural oscillator and position controller. The neural oscillator, which is a nonlinear oscillator, has been studied over the last few decades in the field of biology. The oscillator can be synchronized with an external sinusoidal input whose frequency is within a frequency band determined by the natural frequency of oscillator. In an effort to alleviate the problems associated with the stroke limitation and flexibility, the authors have recently proposed a new control system which is capable of confining the movable region of the mass and following the change of stiffness of the structure. However the proposed system is still coarse, and we are trying to further improve the system. In this paper, we analyze the phase relation between the mass of dynamic absorber and structure to evaluate the performance of energy dissipation. Form viewpoint of effective energy dissipation, the relative velocity of the auxiliary mass and the absolute displacement of the structures should be in-phase. The phase relation of the system including the oscillator synchronized with a structure and position controller was investigated by numerical simulation. As a result of the simulation, it is clear that the proposed system had an appropriate phase relation for vibration control.