The idea of a tendon vibration control system for the flexible space structure has been proposed, and to verify the feasibility of this concept for a cantilever beam-like flexible space structure, a hardware model was constructed in the laboratory. this paper discusses the hardware experiment of the tendon control system for a clamped-free flexible stainless-steel beam hung in the vertical direction. Since the test structure has very low damping, a low-order modal controller becomes unstable due to the truncated modes in the controller design called residual modes. This phenomenon is called spillover. In order to avoid the spillover instability, two different approaches to the control system design are examined both by numerical simulations and by hardware experiments. First, the DVFB(Direct Velocity Feedback Control) which adds damping to all the vibration modes like a passive damper, is applied. Next, a state feedback controller based on a reduced-order model which is called the HAC(High Authority Control), is applied and results in a spillover instability, Finally, a hierarchical controller called LAC/HAC(Low Authority Control/High Authority Control) considering of the DVFB(LAC) for damping augmentation of the truncated modes, and HAC is applied. As the result, the closed-loop system becomes stable and high performance is achieved.