Future spacecraft will have stringent performance requirements that need advanced vibration suppression systems. Examples of these spacecraft are an extended space station, Mission-to-Planet-Earth platforms, and military platforms. Operating conditions for these large space structures (LSSs), e.g., retargeting slew maneuvers and spacecraft docking, can induce unacceptable structural vibrations that take many minutes to naturally dampen out. Increased damping must be added to the structures. This added damping can be a passive mechanism, an active vibration control system, or a combination of passive and active systems. In this investigation, we consider how to satisfy the settling time requirement of a typical LSS. We attempt to determine the amount of vibration suppression or damping necessary to meet the stringent settling time requirement of a typical LSS and then to design, analyze, and experimentally verify an active control system to meet the damping requirement. We also study the effect of passive damping on the active damping system of an LSS to get an idea of what an optimal mix of both passive and active vibration suppression might depend on.