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This paper aims at modeling and developing vibration control methods for a flexible piezoelectric beam.A collocated sensor/actuator placement is used.Finite element analysis (FEA) method is adopted to derive the dynamics model of the system.A back propagation neural network (BPNN) based proportional-derivative (PD) algorithm is applied to suppress the vibration.Simulation and experiments are conducted using the FEA model and BPNN-PD control law.Experimental results show good agreement with the simulation results using finite element modeling and the neural network control algorithm.