Depth-Optimal Distribution of Drilling Meterage Under Uncertainty

Gorbiychuk, Mikhail; Lazoriv, O. T.; Zaiachuk, Yaroslav

doi:10.1007/s10559-020-00242-9

Cited by 1 publication

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“…Work [14] proves that the operation of calculating the sum of fuzzy numbers and multiplying a fuzzy number by an explicit number is carried out using the following formula:…”

Section: Calculating the Characteristic Polynomial And Trans Fer Function Of An Open System Taking Into Consideration The Fuzziness Of Itmentioning

confidence: 99%

Determining the effect of fuzziness in the parameters of a linear dynamic system on its stability

Horbiychuk

Lazoriv

Feshanych

2021

EEJET

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This paper considers a relevant issue related to the influence exerted by the fuzziness in linear dynamic system parameters on its stability. It is known that the properties of automated control systems can change under the influence of parametric disturbances. To describe the change in such properties of the system, the concept of roughness is used. It should be noted that taking into consideration the fuzziness in the parameters of mathematical models could make it possible at the design stage to assess all the risks that may arise as a result of an uncontrolled change in the parameters of dynamic systems during their operation. To prevent negative consequences due to variance in the parameters of mathematical models, automated control systems are designed on the basis of the requirement for ensuring a certain margin of stability of the system in terms of its amplitude and phase. At the same time, it remains an open question whether such a system would satisfy the conditions of roughness. Parameters of the mathematical model of a system are considered as fuzzy quantities that have a triangular membership function. This function is inconvenient for practical use, so it is approximated by the Gaussian function. That has made it possible to obtain formulas for calculating the characteristic polynomial and the transfer function of the open system, taking into consideration the fuzziness of their parameters. When investigating the system according to Mikhailov’s criterion, it was established that the dynamic system retains stability in the case when the parameters of the characteristic equation are considered as fuzzy quantities. It has been determined that the quality of the system significantly deteriorated in terms of its stability that could make it enter a non-steady state. When using the Nyquist criterion, it was established that taking into consideration the fuzziness in the parameters of the transfer function did not affect the stability of the closed system but there was a noticeable decrease in the system stability reserve both in terms of phase and amplitude. The relative decrease in the margin of stability for amplitude was 16 %, and for phase ‒ 17.4 %.

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“…Work [14] proves that the operation of calculating the sum of fuzzy numbers and multiplying a fuzzy number by an explicit number is carried out using the following formula:…”

Section: Calculating the Characteristic Polynomial And Trans Fer Function Of An Open System Taking Into Consideration The Fuzziness Of Itmentioning

confidence: 99%

Determining the effect of fuzziness in the parameters of a linear dynamic system on its stability

Horbiychuk

Lazoriv

Feshanych

2021

EEJET

View full text Add to dashboard Cite

show abstract

Depth-Optimal Distribution of Drilling Meterage Under Uncertainty

Cited by 1 publication

References 1 publication

Determining the effect of fuzziness in the parameters of a linear dynamic system on its stability

Determining the effect of fuzziness in the parameters of a linear dynamic system on its stability

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