Multivariable Modelling of Gas Turbine Dynamics

The linear multivariable modelling of an aircraft gas turbine is presented. A frequency-domain identification method is employed to estimate a family of models from engine data at a range of operating points. It is found that the fuel feed to shaft speed dynamics can be represented by second-order models. This matches the results obtained for the reduced-order linearised thermodynamic models derived from the engine physics. A direct comparison can thus be made between the estimated and thermodynamic models, which shows significant discrepancies between them for the engine tested. This work illustrates how modern system identification techniques can be used to verify engine models. The multivariable framework employed means that additional inputs and outputs can be easily incorporated into the model. INTRODUCTION This paper deals with the identification of linear multivariable models of an aircraft gas turbine from engine test data. The identification is conducted in the frequency domain, which allows s-domain multivariable models to be directly estimated. The work is an extension of that previously conducted on the identification of transfer-function models, which was presented at previous ASME gas turbine conferences [1,2] and has been published in a number of recent journal papers [3-5]. The aim of the work presented in this paper is to identify a family of linear multivariable models, estimated at a range of engine operating points, which can be directly compared to the linearised thermodynamic models of the engine. Engine models are required both in the development and operational stages of the life of a gas turbine. Thermodynamic models are derived during the development stage, based on knowledge of the engine physics, and provide important insights into the engine behaviour. Such models are both complex and nonlinear, which can present problems in the design of engine control systems. It is therefore common practice to linearise the thermodynamic models around a series of operating points and then carry out a model-order reduction in order to arrive at models which are more suitable for control system design. Since these models are based on a priori assumptions about the engine physics, it is then important to verify their performance against real engine data. Previous work approached this problem by identifying individual transfer-function models for the fuel flow to HP shaft speed and the fuel flow to LP shaft speed dynamics. Both the numerators and denominators of these models could vary freely. The models identified in the current work are estimated within a multivariable framework, which means that all the transfer functions have a common denominator, the roots of which are the modes of the system. This is a better basis for comparison with the thermodynamic models, since they are also expressed in multivariable form. The estimated and thermodynamic models thus have a common structure, which allows the comparison of like with like. This paper deals with the identification of the dynamics of a Rolls Royce Spey engine, which is a typical military twin-shaft turbofan, with a low by-pass ratio and a variable reheat nozzle. Although no longer in service, it has the same basic architecture, for control purposes, as that of more modern engines such as the EJ200, which is used to power the Eurofighter [6]. A simplified diagram of a Spey engine is shown in Figure 1, where concentric shafts are seen to connect the compressors at the intake end to the turbines at the nozzle end. The gas turbine has two shafts, one connecting the high-pressure (HP)