Real Time Analytical Linearization of Turbofan Engine Model

Abstract

This paper presents a methodology for developing a control oriented analytical linear model of a turbofan engine at both equilibrium and nonequilibrium conditions. This scheme provides improved accuracy over the commonly used linearization method based on numerical perturbation and piecewise linear interpolation. Linear coefficients are obtained by evaluating at current conditions analytical expressions, which result from differentiation of simplified nonlinear expressions. Residualization of the fast dynamics states are utilized since the fast dynamics are outside of the primary control bandwidth. Analytical expressions based on the physics of the aerothermodynamic processes of a gas turbine engine facilitate a systematic approach to the analysis and synthesis of model based controllers. In addition, the use of analytical expressions reduces the computational effort, enabling linearization in real time at both equilibrium and nonequilibrium conditions to enable more accurate capture of system dynamics during aggressive transient maneuvers. The methodology is formulated and applied to a separate flow twin spool turbofan engine model in the numerical propulsion system simulation (NPSS) platform. The derived linear model is validated against the full nonlinear engine model.