An analytical approach to real-time linearization of a gas turbine engine model

Abstract

A recent development in the design of control system for a jet engine is to use a suitable, fast and accurate model running on board. Development of linear models is particularly important as most engine control designs are based on linear control theory. Engine control performance can be significantly improved by increasing the accuracy of the developed model. Current state-of-the-art is to use piecewise linear models at selected equilibrium conditions for the development of set point controllers, followed by scheduling of resulting controller gains as a function of one or more of the system states. However, arriving at an effective gain scheduler that can accommodate fast transients covering a wide range of operating points can become quite complex and involved, thus resulting in a sacrifice on controller performance for its simplicity.

This thesis presents a methodology for developing a control oriented analytical linear model of a jet engine at both equilibrium and off-equilibrium conditions. This scheme requires a nonlinear engine model to run onboard in real time. The off-equilibrium analytical linear model provides improved accuracy and flexibility over the commonly used piecewise linear models developed using numerical perturbations. 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 typically 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 off-equilibrium conditions for a 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 fidelity of linear model is examined by validating against a detailed nonlinear engine model using time domain response, the normalized additive uncertainty and the nu-gap metric. The effects of each simplifying assumptions, which are crucial to the linear model development, on the fidelity of the linear model are analyzed in detail. A case study is performed to investigate the case when the current state (including both slow and fast states) of the system is not readily available from the nonlinear simulation model. Also, a simple model based control is used to illustrate benefits of using the proposed modeling approach.