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In this paper, the characteristics of forces in active control systems connected to adjacent levels of a building are analyzed. The following characteristics arc observed: ( 1 ) active control can provide significantly superior supplemental damping to a building, but causes a small frequency shift; (2) the linear quadratic regulator (LQR)-based control force is composed of an elastic restoring force component and a damping force component, where the damping force is almost identical to the total control force, however, the elastic restoring force is very small; and (3) the active control forces prevent mection most of the time during the entire control process. These three characteristics imply that active control systems connected to adjacent levels of a building behave like passive damping devices with adjustable parameters, namely damping characteristics in an active control, which is the mechanism used by semi-active control devices to reach similar performance as active control systems. Two indices are defined to quantify the damping characteristics of control forces in active control systems. These two indices can also be used to quantify the capacity of semi-active control to achieve the performance of active control. Based on the above observations, two principles arc founded for optimization of parameters of semi-active control devices and passive dampers. The first is that the maximum output force of a semi-active or passive device to bc designed is identical to an active device, called "design principle". The other is the response equivalent principle, which states that the response of a building with semi-active or passive devices is the same as with active devices when the same maximum output force is applied. The design procedure for semi-active control devices and passive dampers is described in detail. Finally, numerical simulations of two benchmark problems is conducted to demonstrate the damping characteristics of active control and investigate the capacity of semi-active control to achieve the same performance as active control.