This paper presents the results of positive position feedback (PPF) control and linear-quadratic Gaussian (LQG) control for vibration suppression of a flexible structure using piezoceramics. Experiments were conducted on the US Naval Postgraduate School's flexible spacecraft simulator (FSS), which is comprised of a rigid central body and a flexible appendage. The objective of this research is to suppress the vibration of the flexible appendage. Experiments show that both control methods have unique advantages for vibration suppression. PPF control is effective in providing high damping for a particular mode and is easy to implement. LQG control provides damping to all modes; however, it cannot provide high damping for a specific mode. LQG control is very effective in meeting specific requirements, such as minimization of tip motion of a flexible beam, but at a higher implementation cost.