Solving the problem of incomplete information about an automatic control object based on real-time virtual sensors

Modern automatic control systems use built-in mathematical models for estimation of unmeasured by the direct methods parameters such as $NO_X$ emission in aeroengine low-emission combustion chamber. The two models of $NO_X$ emissions virtual sensor built into the controller are proposed. A stochastic nonlinear mathematical model is based on the Zeldovich equation. It applies the superposition principle of $NO_X$ production in diffusion and homogeneous flames. Probability density distribution functions of the air-fuel mixture concentration in these flames take into account both of a spatial non-uniformity of the mixture composition and a harmonic component of the acoustic waves generated by the heat release. The concept of integral relations models has been developed with the use of numerical modeling of spatial and temporal non-uniformities of the air-fuel mixture concentration (4D-metamodeling) and available experimental data. Another virtual sensor model is based on the neural network predicting $NO_X$ emission in gas turbine combustion chamber. The example of a neural network and results of its training on a real combustion chamber is presented. It is shown that the two or three-layer neural network having 20–30 neurons provides an acceptable error (not exceeding 10 %) of the $NO_X$ emission display and can be used as a virtual emission sensor in an engine control system. The normalized level of $NO_X$ emission per take-off and landing cycle is considered as a target function of the automatic control of low-emission combustion. To estimate the level of $NO_X$ emission a built-in virtual sensor is proposed.