Analyzing different numerical linearization methods for the dynamic model of a turbofan engine

Abstract

State equations of aircraft engine dynamics usually required for controller design, are not available in closed form, so the dynamic models are commonly linearized numerically. Development of model-based controllers for aeroengine in the recent years necessitates the use of accurate linear models. However, there is no comprehensive study about the accuracy of the linear models obtained from nonlinear engine models. In this paper, the accuracy of different numerical linearization methods for linearizing the dynamic model of a turbofan engine is investigated. For this objective, a thermodynamic model of a two-spool turbofan engine is considered and three various numerical linearization methods are defined. The first method is based on the perturbation technique, including ordinary and central difference perturbation. The second one is a system identification method and the third one is tuning the elements of the matrices of the linear state-space model using genetic algorithm. The accuracy analysis of the presented procedures is performed for both single-input and double-input cases. In the single-input case, the fuel mass flow rate and in the double-input, in addition to the fuel, the bleed air taken from between the two compressors are considered as control variables. Finally, by defining different error criterions, the accuracy of the linearization methods is evaluated. The results show that the linear model obtained from system identification and central difference perturbation methods have higher percentage of compliances compared to the others.