Constructive non-iterative explicit models of turbofan engines with introduced poles

Nonlinear implicit constraint equations and differential dynamic functions are the most accurate descriptions of open-loop model of turbofan engines. However, it´s time-consuming to iterate the implicit constraint equations during time-domain simulation. In some literatures, those implicit constraint equations between components are replaced by explicit dynamic functions of volumes between components. However, there is no evidence to support the feasibility of the replacement, and solution of the volume dynamic model can diverge during large step simulation. In this article, the replacement is made by adding some differential terms to the implicit constraint equations. It´s proved by the theory of secondary poles that the solution of the constructed new non-iterative dynamic model can converge to the solution of the original model if dynamic coefficients of new differential terms are much larger than then that of original differential terms. Since volume dynamic modeling methods are categorized into the proposed method, the feasibility condition of the proposed method also applies to volume dynamic modeling methods. We therefore proposed virtual volume dynamic modeling method to avoid step size limitation of simulation. Second, high-order linear space-state model of rotor speed dynamics and virtual volume dynamics are extracted from the constructed explicit dynamic functions. Third, low-order linear space-state model of rotor speed is reduced from the constructed high-order model by frequency decomposition method.