   ## 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-by-element, designed for 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 the flow sections of holes in hydromechanical devices, quantization in time and signal level, delay in issuing decisions, the effect of interference and failures in the electronic part, and others;

(2) approximate nonlinear, fully reproducing motor control programs in the entire range of operating modes and simplifying the dynamic properties and static characteristics of regulators. The models are designed for research "in large" and can be used to assess the effectiveness of control methods on semi-natural stands;

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

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