The auxiliary power unit (APU), which is a compact gas turbine engine, is employed to provide a stable compressed air supply to the aircraft. This compressed air is introduced into the various aircraft components via the pneumatic servo system, thereby ensuring the normal operation of the aircraft’s systems. The objective of this study is to examine the impact of parameter variation on the transmission characteristics of an APU pneumatic servo system, with a particular focus on the aerodynamic moment associated with the operating process of a butterfly valve. To this end, a mathematical model of the pneumatic servo system has been developed. The accuracy of the mathematical model was verified by means of numerical simulation and comparative analysis of experiments. The simulation model was established in the Matlab/Simulink environment. Furthermore, the effects of throttling area ratio, fixed throttling hole diameter, rodless chamber volume of actuator cylinder and gas supply temperature on the transmission characteristics of the system were discussed in greater detail. The findings of the research indicate that the throttle area ratio is insufficiently sized, which results in a deterioration of the system’s linearity. Conversely, an excessively large throttle area ratio leads to a reduction in the controllable range of the load axis and is therefore detrimental to the servo mechanism of the flow control. An increase in the diameter of the fixed throttling hole or a decrease in the volume of the rodless cavity of the actuator cylinder facilitates a rapid change in flow rate within the rodless cavity and an increase in the response speed of the load-rotating shaft of the servomechanism. An increase in the temperature of the gas supply from 30 °C to 230 °C results in a reduction in the response time of the system by a mere 0.2 s, which has a negligible impact on the transmission characteristics of the system.