Stability of pneumatic cabin pressure regulating system with complex nonlinear characteristics is considered. The mathematical model of each component is obtained and given in detail. The governing equations of the considered system consist of 8 differential equations. In the circumstance, commonly used methods of nonlinear system analysis are not applicable. Therefore a new method is proposed to construct phase plane trajectories numerically. The calculation steps are given in detail. And convergence region of numerical calculation and limits on step size is defined. The method is applied constructing phase plane trajectories for considered cabin pressure regulating system. Phase plane analysis shows that there exists a limit cycle, which is responsible for pressure pulsating in aircraft cabin. After parameters adjustment, excellent stability characteristics are acquired. And the validity of this method is confirmed by the simulation.

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To overcome the shortcomings of traditional method for modeling pop action pressure relief valves (PAPRVs), a new method for modeling PAPRVs as a bistable element is proposed. The effects of the model’s main parameters on a valve’s behavior are simulated and analyzed. Through simulations, the atypical behaviors of PAPRV previously found by other researchers do arise and can be explained based on the simulation data. Then, according to this new method, a model was built for a special pressure relief valve, and the simulation data agree well with the experimental results. These results demonstrate the validity of the modeling method.