Analysis of the accuracy of estimating the time constant of a single-spool gas turbine engine in real conditions

Abstract

At present, the concept of an on-board self-tuning model has been formed and successfully developed by many scientific schools, and it provides real-time determination of parameters of the working process of engines, which are not measured. However, the problem of the accuracy of estimating parameters of dynamic models based on real data is clearly insufficiently studied, as a result of which there is a lack of recommendations for the formation of control influences on the engine, periodicity and duration of registration of parameters, as well as verification of the sufficiency of the collected information to obtain a dynamic model with the specified accuracy. The subject of this study is the process of forming dynamic mathematical models (MM) of gas turbine engines using real data for the subsequent use of these models to solve problems related to the control and diagnostics of on-board systems. The goal is to determine the dependence of the estimation errors of the dynamic parameters of mathematical models on the influencing factors under the conditions of real change of these factors over time. Tasks considered in the work: forming the least-squares functional for the assessment task, determining the errors in estimating dynamic coefficients, analysis of influencing factors, and determining dependencies between factors and errors. For this purpose, the methods of the theory of air-jet engines, the theory of linear dynamic systems, and the methods of statistical evaluation are used. The following results were obtained: the ratio was determined, which allowed us to calculate the errors of estimating the constant time of a single-cycle engine or gas generator under real conditions when the fuel consumption changed at a constant rate, after which it stabilized. Scientific and practical innovation: for the first time, a ratio was obtained that determines the errors in estimating the time constant based on the specified values of the measurement errors, the amplitude and time of change in fuel consumption, as well as the frequency and duration of observations. These relations are presented in dimensionless coordinates, which makes them universal and able to be applied to any single-stroke turbojet engine or single-stroke gas generator during a priori or a posteriori analysis of the results, as well as planning experiments and debugging on-board self-tuning algorithms of models. Scientific and practical novelty: A correlation was obtained, which relates the error of the time constant estimate to the amplitude and time of change in fuel consumption, as well as the frequency and durability of the data recording. These relationships are presented in dimensionless coordinates so that they are universal and valid for the design of any single-shaft turbojet engine or single-shaft gas generator under a priori or a posteriori analysis of the results, as well as for planning experiments and improving on-board algorithms for the self-tuning of models. An example of determining the time constant errors of the gas generator rotor of a helicopter turboshaft engine under different operating modes is provided.