Additional damping ratio (ADR) is an important performance parameter in the design of energy dissipation system. The ratio of the hysteretic energy dissipation of the damper to the total strain energy of the damping system is used as the quantitative ADR in the traditional method, and the bilinear model is usually used to calculate the hysteretic energy dissipation of the buckling-restrained brace (BRB). The accuracy of the above calculation methods is low. The explicit analytical expression of the hysteretic energy of Bouc-Wen model which can accurately characterize the hysteretic performance of the damper is derived by integral method, and time-varying ADR calculation methods based on the strain energy method and the modal damping energy dissipation method are proposed. In order to accurately achieve the damping ratio of the damping system, the inter-story displacement angle and damping ratio of the damping system are taken as the control objectives, and the layout scheme and damping force of the damper are taken as the design variables. The design method of damping ratio-displacement double objective is proposed. The iterative design and analysis of a RC frame damping system are carried out. The reasonable length of time interval for calculating time-varying hysteretic energy is determined, and different calculation methods of time-varying ADR are compared. The results show that the ADR based on the strain energy method is larger, which is not conducive to the structural safety. It is suggested to use the average value of modal damping energy dissipation method to characterize ADR. The double objective design method is reasonable, and the performance requirements are more detailed and accurate.