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A mathematical model is developed to estimate the pressure response of an insulated electric air compressor. A pressure switch is modeled as a comparator and the electric motor as an amplifier. It is assumed that the compressed air is a perfect gas when applying the isentropic process. In addition, the effect of a step, ramp and sinusoidal functions of disturbance signals on the air pressure has been studied. A good agreement was obtained when comparing the predicted results with the measured values obtained from the experimental test that was done using a (1.32 kW, 23 litter and 8 bar) electric reciprocating air compressor. In addition, the same behavior of the predicted results was obtained when compared with results of a previously published article. It was found that the time constant of this control system is directly proportional with the value of the spring constant that is inserted inside the pressure switch and with the volume of air storage vessel, and it is inversely proportional with the gain of the amplifier and with the effective cross-sectional area of the pressure switch diaphragm and it is independent of the value of operating pressure set point. In addition, when the value of disturbance signal is positive, it will increase the output pressure response and when it is negative, it will decrease it .

Experimental Investigation and Mathematical Modelling of Pressure Transfer Function for Air Compressor