Elsevier

Control Engineering Practice

Volume 9, Issue 2, February 2001, Pages 135-148
Control Engineering Practice

Application of system identification techniques to aircraft gas turbine engines

https://doi.org/10.1016/S0967-0661(00)00091-5Get rights and content

Abstract

A variety of system identification techniques are applied to the modelling of aircraft gas turbine dynamics. The motivation behind the study is to improve the efficiency and cost-effectiveness of system identification techniques currently used in the industry. Three system identification approaches are outlined in this paper. They are based upon: multisine testing and frequency-domain identification, time-varying models estimated using extended least squares with optimal smoothing, and multiobjective genetic programming to select model structure.

Introduction

The modelling of gas turbines is a topic of great importance, given their widespread use in aero, marine and industrial applications. Three system identification techniques are employed in this paper, with specific application to an aero gas turbine engine. The techniques span the statistical and systems approaches described by Ljung (1996) in a recent survey of system identification. The motivation behind this work was to reduce test times while improving and quantifying model accuracy. The project involved three university teams, in collaboration with a leading gas turbine manufacturer.

Aircraft gas turbines are subjected to rigorous tests immediately after manufacture, in order to ensure reliable operation and give confidence in design predictions. One such test is a dynamic verification test, conducted on a static test-bed such as that shown in Fig. 1. The dynamic models obtained can then be used for simulation and as a basis for control system design. Engine dynamics arise from complex, interacting phenomena: gas-flow behaviour in the compressor and turbine (affected by air inlet as well as engine conditions), shaft inertias and losses, fuel-flow transport delay, fuel dispersal and combustion, and the thermal behaviour of the engine and its surroundings.

Identification of aircraft gas turbine dynamics has historically relied on the use of “wobble” tests, in which the engine is excited by single sines of different frequencies. The gain and phase shift are then calculated at each frequency, generating Bode plots which are easy to interpret and familiar to control engineers. Low-amplitude sinewave tests can be made insensitive to the nonlinearities in the engine response and to noise. However, they have severe drawbacks, the primary one being the expense associated with very long test durations to allow the decay of initial transients at each frequency.

Moreover, the presence of nonlinearities necessitates taking a frequency response at each of several operating conditions spanning the range of engine speeds from ground idle to full power. There are at least two sources of nonlinearity in the engine response. The first of these is the nonlinear variation of the engine dynamics with operating power and condition (Saravanamuttoo, 1992). Secondly, the dynamics change with the thermal state of the engine; for instance they differ between a fast and slow acceleration, due to effects such as changes in blade-tip clearances (Pilidis & Maccallum, 1986). Some such effects can be treated as slow linear modes but the frequency responses give very limited insight into the slow thermal dynamics of the engine.

Finally, the current wobble-test procedure, although believed to give accurate estimation of the small-signal, steady-state engine behaviour, provides little indication of the accuracy of the results.

The work described here is intended to improve the speed and quality of engine testing and to allow better exploitation of test-bed results. The overall aim is to gain insight into alternatives to traditional testing and identification methods for multi-shaft aircraft gas turbine engines. This case study utilised a large set of engine records from a twin-shaft Rolls Royce Spey engine, logged by the Defence Evaluation and Research Agency (DERA) Pyestock, according to test schedules specified by the university teams.

This paper concentrates on the dynamic relationship between the measured input fuel flow and the high-pressure (HP) and low-pressure (LP) shaft speeds, denoted by NH and NL. The engine speed control was operated in open-loop and a perturbed fuel-demand signal was fed to the fuel-feed system, which regulates the fuel flow to the engine by means of a stepper valve, as shown in Fig. 2. The fuel flow was measured downstream of the fuel-feed system, using a turbine flow meter, in order to exclude the fuel-feed dynamics from the engine model.

Any alternative gas turbine identification technique must allow the user to assess the accuracy of the resulting models and must not yield lower accuracy than the current procedure. The intention is to improve on the “wobble” test technique currently used at Rolls Royce through:

  • Reduction in the time (and hence cost) of engine testing.

  • Improved accuracy of the estimated engine models and an assessment of the model uncertainty.

  • Greater insight into the slow engine dynamics.

  • Better understanding of the nonlinear behaviour.

The combination of shorter, and thus cheaper, test runs and better coverage of engine behaviour is a strong incentive to look for more efficient test signal designs and model-estimation procedures. The three system identification approaches addressed in this paper are:

  • multisine test signals and frequency-domain identification techniques, for improved linear modelling;

  • extended least squares with optimal-smoothing, for finding time-varying linear models;

  • multiobjective genetic programming, for the selection and identification of a nonlinear model structure.

After a description of each approach and associated results, conclusions will be drawn about the scope and merits of the various techniques.

Section snippets

Multisine signals and frequency-domain identification

Previous work by Evans, Rees and Jones (1995) and Evans, Rees and Hill (1998) illustrated how multisine test signals and frequency-domain techniques could be used to accurately estimate parametric and nonparametric models of a gas turbine engine. That work focused on the study of the engine dynamics at a single operating point. In this section, the same techniques are used to estimate s-domain models of the engine dynamics at a range of points, with the aim of verifying the linearised

Extended least-squares with optimal smoothing

Traditional single sine engine testing deals with nonlinearity only by generating small-signal models about a range of steady-state operating points. It does not cover effects far from equilibrium, which may be prominent in large transients such as slam accelerations (rapid, full throttle opening). Small-signal models for short-term response also give little insight into the slow thermal dynamics of the engine. Although such models are valuable for verifying engine performance near steady

Nonlinear system identification using multiobjective genetic programming

Genetic programming (GP) is an evolutionary paradigm where the computer structures which undergo adaptation are themselves represented as computer programs (Koza, 1992). Koza immediately recognised that symbolic regression was as an obvious application domain, where mathematical expressions and their numeric coefficients may be obtained to provide a good fit to a set of data points. Rodrı́guez-Vázquez and Fleming (1997) describe how GP can be used to search for a suitable nonlinear model

Conclusions

The three techniques outlined in this paper were all applied to real engine test data. They provide significant insights into alternative identification strategies. The aims, to improve the efficiency of gas turbine dynamic testing and to see how far the identification approaches can give insight into complex engine behaviour, have largely been realised. The conclusions from each of the techniques will be summarised in turn.

The contribution based on the use of multisine signals and

Acknowledgements

This work was conducted with the support of Rolls Royce plc. and the UK Defence Evaluation and Research Agency (DERA). The data used throughout this study were supplied by DERA Pyestock and the authors would like to thank all the staff involved. The authors acknowledge partial support for this work from NATO Linkage Grant HTECH.JG.970611 and the contribution made by Dr. Valentin Arkov, Ufa State University, Russia, to the overall programme of work. Katya Rodrı́guez Vázquez gratefully

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