Abstract: Water-cooled proton exchange membrane fuel cell air supply system contains multi-parameter and multi-variable control features. This paper establishes a 1-D proton exchange membrane fuel cell stack model,introduces a linear quadratic optimal control strategy based on Kalman filter and a second-order sliding mode nonlinear control strategy based on extended state observer,and optimizes control parameters by genetic algorithm. The simulation results show that both control algorithms have better control effects and can adjust the oxygen excessive ratio to the set value under different load currents quickly and accurately. Compared with the traditional PID control strategy,the adjustment time is reduced by about 30% and air compressor consumption power is reduced by about 10%.