Abstarct: In recent years, the control of beam vibrations has drawn the attention of researcher, and many studies have been conducted in this field. Due to the fact that the studied beams were mostly mextal or composite materials, in this research, the studied beam was considered as functional graded (FG). In this thesis, the active control of non-linear vibration of the functional graded beam is under consideration during periodic loading. Two piezoelectric laxyers are connected to the upper and lower surfaces of the beam to be used as sensors and actuators. Gelerkin method is used to solve the differential equation. To control the vibrations of the beam, the feedback control method and the sliding mode control are used. The time-deflection and time-voltage graphs for the 5 states of the boundary conditions are presented. These conditions are clamped-clamped, simply supported-simply supported, free-free, clamped-free and clamped-simply supported. The results of the mentioned control methods in the absence and presence of uncertainty are compared for all boundary conditions. Also, for different values of the volume fraction, the time-deflection and time-voltage graphs are presented using sliding mode method.