Development of Numerical Method for Obtaining ACS Reference Models by Direct Quality Measures; Вестник Карагандинского государственного индустриального университета (Вестник КГИУ); № 2 (37) - Sidorova A. A. Anastasia Aleksandrovna (2022, 2022)
The paper considers the problem of obtaining transfer functions of automatic control systems (ACS), that are used in the synthesis of ACS regulators as reference desirable models. A promising numerical method, that has an important property allowing to form the desired transfer functions according to the quality parameters of ACS transient response, that have a clear physical representation for the designer, is being studied. However, it has a significant drawback related to the restriction of the order of the desired transfer function. It has been established that the reason for this is that the problem itself is referred to the class of incorrectly formulated problems that leads to poor conditionality of the equation based on the numerical method being studied. Therefore, the method does not allow steadily establishing the desired models above the second order that is confirmed by the computational experiment. However, this result is not completely acceptable for practice, what often requires desired third-order transfer functions. To obtain such models, several possible ways are considered. The obvious variant based on Tikhonov's regularization method did not lead to a positive result due to the peculiarities of the fractional rational form in which the solution is sought. A positive result was obtained by testing a nonlinear programming method, which allows to introduce a desired transfer function coefficients positiveness condition. The paper also suggests other options for obtaining the desired transfer functions of the third order, but they remain only promising, requiring further research.