Track nonlinear energy sinks (track NESs) and single-sided vibro-impact track nonlinear energy sinks (SSVI track NESs) are types of passive structural control dcviccs that can rapidly mitigate the vibration of a primary structure. The smooth motion of the NES mass on a specially designed track provides a continuous nonlinear restoring force. Additionally, the use of an impact surface in the SSVI track NES increases the nonlinearity of the device and further enhances its robustness against changes in stiffness, input energy level, and damping of the device. While previous studies have limited their investigation to NESs on structures of relatively few degree-of-freedoms, in this work, a 32 degree-of-freedom model, based on an actual 32-story high-rise, is used as the primary structure. The mass ratio of the track NES attached to the top of this structure is set as 1%. Numerical optimizations are implemented to determine the properties of the track NES. Response comparison to a conventional tuned mass damper (TMD) shows that the track NES can reduce the structural responses to a similarly low level under both impulsive and seismic excitations. When the stiffness of either the primary structure or the device is shifted, the track NES has a strong advantage of robust performance compared to the TMD. The results also indicate that the SSVI track NES is robust against extensive changes in its viscous damping. Furthermore, the relative displacement of the control mass in the SSVI track NES system is reduced in comparison to the track NES and TMD systems.