Control-Oriented Modeling for Nonlinear MIMO Turbofan Engine Based on Equilibrium Manifold Expansion Model

This paper investigates the control-oriented modeling for turbofan engines. The nonlinear equilibrium manifold expansion (EME) model of the multiple input multiple output (MIMO) turbofan engine is established, which can simulate the variation of high-pressure rotor speed, low-pressure rotor speed and pressure ratio of compressor with fuel flow and throat area of the nozzle. Firstly, the definitions and properties of the equilibrium manifold method are presented. Secondly, the steady-state and dynamic two-step identification method of the MIMO EME model is given, and the effects of scheduling variables and input noise on model accuracy are discussed. By selecting specific path, a small amount of dynamic data is used to identify a complete EME model. Thirdly, modeling and simulation at dynamic off-design conditions show that the EME model has model accuracy close to the nonlinear component-level (NCL) model, but the model structure is simpler and the calculation is faster than that. Finally, the linearization results are obtained based on the properties of the EME model, and the stability of the model is proved through the analysis of the eigenvalues, which all have negative real parts. The EME model constructed in this paper can meet the requirements of real-time simulation and control system design.

A Corrected Equilibrium Manifold Expansion Model for Gas Turbine System Simulation and Control

During recent decades, the equilibrium manifold expansion (EME) model has been considered as a powerful identification tool for complex industrial systems with the aim of system control and simulation. Based on a two-step “dynamic and static” identification method, an approximate nonlinear state-space model is built by using multiple polynomials. However, the existing identification method is only suitable for single-input (SI) systems, but not for multi-input (MI) systems, where EME models cannot guarantee global calculation stability. For solving such a problem, this paper proposes a corrected equilibrium manifold expansion (CEME) model based on gas turbine prior knowledge. The equilibrium manifold is extended in dimension by introducing similarity equations instead of the high dimensional polynomial fitting. The dynamic similarity criterion of similarity theory guarantees the global stability of the CEME model. Finally, the comparative test between the CEME model and the existing MI-EME model is carried out through case studies involving data that are generated by a general turbofan engine simulation. Simulations show superior precision and calculation stability of the proposed model in capturing nonlinear behaviors of the gas turbine engine.

Asymptotic preserving discretization of a Jin–Xin model with implicit equilibrium manifold on a bounded domain

In this paper, we design and analyze a numerical scheme that approximates a Jin–Xin linear system with implicit equilibrium on a bounded domain. This scheme relaxes toward the asymptotic limit of the linear system. The main properties of the limiting scheme are that it does not require to invert the implicit function defining the manifold and that it provides an accurate discretization of the boundary conditions.

Nonlinear System Modeling based on System Equilibrium Manifold

The main objective of the present paper is to provide an approximate method for nonlinear system with a family of equilibrium points (EPs). By investigating the system’s equilibrium manifold (EM) and its expansion form, a class of nonlinear system is modeled analytically. The property of the EM expansion form and the effect of mapping design and parameterizing method to the model have been discussed. Then an approximate nonlinear model for aircraft engine was applied, followed by an identification procedure for aircraft engine. It is shown that the modeling method based on system’s EM can not only comply with the system physical characteristics, but also satisfy the accuracy of modeling requirement. Numerical simulations are given to demonstrate the good precision in capturing the nonlinear behavior of nonlinearities and a simpler structure.