Real-Time Hybrid Simulation (RTHS) is a powerful and cost-effective dynamic experimental technique. In civil engineering, RTHS has the advantage of investigating the dynamic behavior of full-scale and complex structures by testing only the critical components. To implement a stable and accurate RTHS, the time delay in the experiment loop needs to be compensated. This delay is mostly introduced by servo-hydraulic actuator dynamics and can be reduced by applying appropriate compensators. Several existing compensators have demonstrated effective performance in reducing the actuator time delay. But most of them have been applied only in cases where the structure under investigation is subjected to inputs with relatively low-frequency content such as earthquake motion. To make RTHS an attractive technique for engineering applications with broader excitation frequency, a discrete-time feedforward compensator is developed via various optimization techniques to enhance the performance of RTHS. The effectiveness of the proposed compensator is demonstrated through both numerical and experimental studies. The proposed compensators are successfully applied to RTHS tests to study the seismic behavior of a linear-elastic reinforced concrete building equipped with a new type of tuned mass damper, known as the Disruptive Tuned Mass (DTM) damper designed by the National Aeronautics and Space Administration (NASA). The obtained results show that the proposed compensator reduces the time delay adequately and leads to a successful RTHS test. Results also suggest that the DTM damper can successfully reduce the response of the building subjected to the seismic loads. In addition, the dynamic properties of the DTM damper are fully investigated and a mathematical model is suggested for it.