EQUIVALENT FORMS OF MATHEMATICAL MODELS OF PROCESSES OF CONTROLLED CHANGE OF THE STATE OF POWER AND ENERGY INSTALLATIONS
DOI:
https://doi.org/10.32782/mathematical-modelling/2022-5-2-4Keywords:
mathematical model; power and energy installations; equivalent transformations; status monitor; integral equationsAbstract
The state of power and energy installations is determined by a change in a multidimensional set of output variables and external disturbances, which are interconnected by complex relationships corresponding to intensive processes of energy transformation and material flows. Not all such processes have known physical laws of transformation, and therefore theoretical and empirical mathematical models are used. The peculiarities of the processes of the controlled state change of power and energy installations require the computer implementation of such mathematical models in real time, since an important set of output variables cannot be directly measured, or require complex technical solutions for such measurements. In particular, for power and energy installations built on the basis of gas turbine engines, thrust, gas temperature in front of the turbine, available power, etc. cannot be directly measured. The output variables, the obtaining of which requires complex and expensive technical solutions, include, in particular, the torque for turboshaft gas turbine engines. But such variables are used in modern effective regulation programs and need to be obtained in real time, which can be achieved only by applying appropriate mathematical models in the form of virtual measuring channels. The requirements for such mathematical models usually consist in their adequacy and the possibility of computer implementation. Regarding adequacy, it is understood that the errors of virtual measuring channels should be commensurate with the errors of physically implemented ones. Regarding the computer implementation, the time of receiving output data through such channels should not exceed the run time, that is, the time of issuing a control action to the control object. Therefore, research aimed at building new classes of mathematical models of changes in the state of power and energy installations and their equivalent transformations is of great practical importance. On the other hand, classical and widely used mathematical models of the state space of power and energy installations have significant limitations regarding their computer implementation. Therefore, such studies are also of theoretical importance for establishing the fundamental properties of control systems, namely, stability, controllability, and observability.
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