a typical example of an axially moving cantilever beam is flexible robotic manipulators with prism atic joints. the model governing lateral vibration of such system is time-varying. time-varying systems pose significant challenges in modelling and control. the objective of this research is to control the lateral vibration of an axially moving cantilever beam. in this research, first an analytical model of an axially moving cantilever beam is developed. second, the effect of an end mass is investigated. third, piezoelectric actuators (pzt ) are considered to design a direct velocity feedback controller to suppress the lateral vibration of the system. the presence of higher modes in the system and the spillover instability are investigated. fourth, an active control design based on the gradient algorithm is developed. the controllability, observability and the stability of the system are investigated.