This experimental study demonstrates the efficiency of simple control strategies to damp a 3-stage tensegrity tower structure. The tower is mounted on a moving support which is excited with a limited bandwidth random signal (filtered white noise) by a shaker. Our goal is to minimize the transmissibility between base acceleration and top plate acceleration using piezoelectric displacement actuators and force sensors collocated at the bottom stage of vertical strings. Two types of controllers have been designed, namely, local integral force feedback control and acceleration feedback control. It can be shown that both controllers can effectively damp the first 2 bending modes by about 20 dB, and the acceleration feedback controller performs even better as it can also reduce the amplitude of the next 2 bending modes by about 5-10 dB.