Grasping an unknown object is difficult for robot hands. When the characteristics of the object are unknown, knowing how to plan the speed at and width to which the fingers are narrowed is difficult. In this paper, we propose a method to realize the three functions of simultaneous finger contact, impact reduction, and contact force control, which enable effective grasping of an unknown object. We accomplish this by using a control framework called multiple impedance control, which was proposed in a previous study. The advantage of this control is that multiple functions can be realized without switching control laws. The previous study achieved two functions, impact reduction and contact force control, with a two layers of impedance control which was applied independently to individual fingers. In this paper, a new idea of virtual dynamics that treats multiple fingers comprehensively is introduced, which enables the function of simultaneous contact without compromising the other two functions. This research provides a method to achieve delicate grasping by using proximity sensors. For the effectiveness of the proposed method, please refer to https://youtu.be/q0OrJBal4yA.