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This paper discusses dynamic characteristics of proton exchange membrane fuel cell (PEMFC) under rapid fluctuation of power demand. Wavelet neural network is adopted in the identification of the characteristic curve to predict the voltage. The system control scheme of the voltage and power is introduced. The corresponding schemes for voltage and power control are studied. MATLAB is used to simulate the control system. The results reveal that the adopted control schemes can produce expected effects. Corresponding anti-disturbance and robustness simulation are also carried out. The simulation results show that the implemented control schemes have better robustness and adaptability.