A preliminary study of a deadbeat predictive controller (DPC) on a space truss structure using on/off thrusters was conducted. The laboratory truss experiment for space structure (TESS) was a 54-bay truss designed to validate different active control techniques. Thruster pairs, positioned at the tips of the truss and a first-order multi-pulse-width-modulation (MPWM) technique were used to drive each on/off jet as a pulse amplitude modulated (PAM) device. Two Analog Devices accelerometers having bandwidth limited to 100 Hz were also used as the primary sensors for feedback control. These accelerometers were positioned one at each tip of the truss to measure transversal vibrations in the horizontal plane. It was found that the DPC could assume a compact dynamic output feedback form to measure real plant dynamics and constraints. The results of the study show that the controller is able to effectively dampen TESS vibration to an acceptable magnitude within 10 s.