For several future imaging and communications spacecraft, a challenging area of technology development is the fine acquisition, tracking, and pointing (ATP) control of the spacecraft and its payload. For example, some spacecraft with large aperture(s) in the range of 10~30 m diameter requires a few arc-seconds accuracy, 10~15 nano-radians jitter, and a fast slewing rate to acquire the target. Furthermore these stringent requirements are at risk of great structure and control interactions. This paper we will focus on the control of optical beam jitter. A Laser Jitter Control (LJC) testbed has been constructed to test jitter algorithms. The testbed consists of two fast steering mirrors (FSM), three position sensing modules (PSM), one diode laser, and several beam splitters and mirrors, all on an isolated Newport optical bench. Jitter is injected with one FSM and the other FSM is used to control it. The jitter spectrum, representing the on-orbit spacecraft and beam jitter environment, contains not only narrow band noise due to rotating devices such as gyroscopes and reaction wheels but also broadband noise. The performance of a Wiener Filter-adaptive algorithm with ideal reference signal is established as the baseline for comparison of adaptive control methods in suppressing both broadband and narrowband disturbances. Specifically, the Least Mean Squares (LMS) approach and the Gradient Adaptive Lattice (GAL) approach are investigated during these experiments.