Оцінка стійкості замкнутої системи автоматичного регулювання за допомогою частотних критеріїв
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Файли
Дата
2017
Автори
Майдан, П.С.
Воронін, Г.Ф.
Золотенко, Е.О.
Буряк, А.В.
Maidan, P.S.
Voronin, G.F.
Zolotenko, E.O.
Buryak, A.V.
Назва журналу
Номер ISSN
Назва тому
Видавець
Хмельницький національний університет
Анотація
В роботі представлено результати оцінки стійкості системи автоматичного регулювання (САР) шафи
холодильника за допомогою частотних критеріїв Михайлова та Найквіста. Стійкість системи є необхідною
умовою можливості САР вирішувати поставлені перед нею завдання. Оцінка стійкості системи за даними
критеріями виконується на основі характеристики, тобто побудови годографа. Розглянуто розв’язання
поставленої задачі з використанням різних програмних середовищ, таких як LabVIEW, MathCad, MatLab.
The paper presents the results of the evaluation of the stability of the automatic control system (ACS) of the refrigerator cabin using the frequency criteria of Mikhailov and Nyquist. Stability of the system is a prerequisite for the ability of the ACS to solve its tasks. The evaluation of the stability of the system according to the criteria is performed on the basis of the characteristic, that is, the construction of the hodograph. Solving the problem using a variety of software environments such as LabVIEW, MathCad, MatLab is considered. The availability of mathematical packages enables the use of PCs for the construction of hodographs, including the Mikhailov and Nyukvist hodographs. The MathCAD software package has builtin functions that will allow us to perform the necessary calculations and decompose the equation into real and imaginary parts. In the LabVIEW program environment, the program is a cyclic block with a limited number of iterations (calculated from the Nyquist criterion frequency and step), and separately the numerator and denominator coefficients in the form of a onedimensional array of data, which, in turn, are calculated according to the formulas given in the elements of the calculation. Elements of the calculation are standard subprograms of polynomial calculations, in which numbers are considered in the complex form and after mathematical actions are decomposed into real and imaginary parts, after which according to the coefficients of the actual and imaginary part a graph is drawn on the front panel. In the Matlab software environment, there are necessary builtin functions for calculating the Nyquist criterion, but to find the Mikhailov criteria, the program needs to be written completely from scratch. The analysis of ACS in various ways has shown that the use of software environments such as LabVIEW, MathCad, and Matlab increases the accuracy of system stability determination. However, it requires not only to know the basics of programming to write the necessary fileprograms, but also to have basic knowledge of the theory of automatic control, in order to bring the equation of the transfer function of the ACS to the desired type of program.
The paper presents the results of the evaluation of the stability of the automatic control system (ACS) of the refrigerator cabin using the frequency criteria of Mikhailov and Nyquist. Stability of the system is a prerequisite for the ability of the ACS to solve its tasks. The evaluation of the stability of the system according to the criteria is performed on the basis of the characteristic, that is, the construction of the hodograph. Solving the problem using a variety of software environments such as LabVIEW, MathCad, MatLab is considered. The availability of mathematical packages enables the use of PCs for the construction of hodographs, including the Mikhailov and Nyukvist hodographs. The MathCAD software package has builtin functions that will allow us to perform the necessary calculations and decompose the equation into real and imaginary parts. In the LabVIEW program environment, the program is a cyclic block with a limited number of iterations (calculated from the Nyquist criterion frequency and step), and separately the numerator and denominator coefficients in the form of a onedimensional array of data, which, in turn, are calculated according to the formulas given in the elements of the calculation. Elements of the calculation are standard subprograms of polynomial calculations, in which numbers are considered in the complex form and after mathematical actions are decomposed into real and imaginary parts, after which according to the coefficients of the actual and imaginary part a graph is drawn on the front panel. In the Matlab software environment, there are necessary builtin functions for calculating the Nyquist criterion, but to find the Mikhailov criteria, the program needs to be written completely from scratch. The analysis of ACS in various ways has shown that the use of software environments such as LabVIEW, MathCad, and Matlab increases the accuracy of system stability determination. However, it requires not only to know the basics of programming to write the necessary fileprograms, but also to have basic knowledge of the theory of automatic control, in order to bring the equation of the transfer function of the ACS to the desired type of program.
Опис
Ключові слова
частотні критерії, годограф, Михайлов, Найквіст, LabVIEW, MathCad, MatLab, frequency criteria, hodograph, Mikhailov, Nyquist, LabVIEW, MathCad, MatLab
Бібліографічний опис
Оцінка стійкості замкнутої системи автоматичного регулювання за допомогою частотних критеріїв [Текст] / П. С. Майдан, Г. Ф. Воронін, Е. О. Золотенко, О. В. Буряк // Вісник Хмельницького національного університету. Технічні науки. – 2017. – № 6. – С. 42-50.