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Mathematical modeling of the gas turbine engine control systems

## Mathematical modeling of the gas turbine engine control systems

To match this engine models with models of ACS and other elements of the SU system simplified model equations must be supplemented by the transition from the physical parameters of formulas to the given trip.

The standard formula to bring, if necessary, adjusted in the parameters Tx, Re and the other on the basis of experimental data and calculations using models of the higher level to take account of violations of the conditions of similarity. To determine the members of the model of functional relationships and identify patterns can be used a rolling motor model or experimental data. Errors in the calculation of the established modes of engine operation in the application of this model are 3%. .5%, And transients - 5%. 10%.

Linear motor model

Methods of preparing linear engine models are well designed. The basis for these models are models of a higher level.

linear motor model system of equations is obtained by linearization of systems of nonlinear equations, for example, a rolling mathematical model. In particular, the linear mathematical model of two-shaft turbofan as follows:

For each test mode operation of the engine and flight mode must have separate mathematical models of the type which can generally vary as the coefficients, and structure of the equations.

The required level of description of the various elements of the ACS determined by the degree of influence of various factors on the regulatory process and the purpose of the problem being solved. Mathematical models of three types are used in the gas turbine engine control problems:

(1) element-wise, designed to carry out calculations using a computer. In such models, the design and circuit parameters of the regulators are directly considered as parameters. In this case, various factors can be correctly taken into account, such as friction in structural elements, forces on actuators, changes in the shape of flow sections of holes in hydromechanical devices, time and level quantization of signals, delay in issuing decisions, the effect of noise and faults in the electronic part and others;

(2) approximate non-linear, fully reproducing engine control programs in the entire range of operating modes and simplified describing the dynamic properties and static characteristics of the regulators. The models are intended for research "in large" and can be used in assessing the effectiveness of control methods on semi-gated stands;

(3) linear models with typical equivalent nonlinear static characteristics (dead zones, saturation regions, hysteresis, etc.) used to study the characteristics of stability and quality control with small deviations from the steady state. Such models are obtained by linearizing nonlinear models or approximation of dynamic experiment data (frequency characteristics, transients).

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21.08.2019

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