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- W609548044 abstract "Relevance. The problem of defining the maximum stability degree is an essential and urgent topic of the linear theory of automatic control. The paper considers the maximum stability degree for a class of objects which are considered most often as models. Research objectives. Any three-mass system, that is any masses and rigidity, is considered as a control object. This three-mass system is considered as a single-channel, operated by a regulator 3/3 (polynomial of a degree no more than 3 is the numerator of a transfer function, and a denominator is a polynomial of degree 3). Steering force is applied to the weight closest to the motionless basis; adjustable size is a deviation of the third weight. The paper considers as well the case when the steering force is applied to the weight most remote from the basis, and the adjustable size is a deviation of the first weight. The maximum (limiting) stability degree is investigated. The paper is guided first of all by the following statement proved in earlier and more volume research: for any three mass systems the maximum stability degree is provided by controllers for which the roots of a characteristic polynomial with the greatest material part form quadruple complex pair. Methods. For any fixed object, running controllers 3/3, the characteristic polynomials form some class of polynomials of the ninth degree with the senior factor 1 with two linear communications. In the class of these polynomials the steady polynomial with the maximum stability degree is sought. Then the controller providing this stability is restored by this polynomial. Results. The position of the ninth root depends only on the value of one object parameter. The paper introduces the instruction on calculation of this parameter, the maximum stability degree, a characteristic polynomial and a controller 3/3 providing this stability. The calculations were carried out on the following example: weights and rigidity are equal to a unit. It turned out that in this case the ninth root of a characteristic polynomial is not the most right. Conclusions. The paper can form a basis of a technique of calculating the maximum stability degree and lower-order controllers providing this stability, and for other operated single-channel lower-order systems." @default.
- W609548044 created "2016-06-24" @default.
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- W609548044 date "2014-01-01" @default.
- W609548044 modified "2023-09-24" @default.
- W609548044 title "Наибольшая степень устойчивости трёхмассовой системы с регулятором пониженного порядка" @default.
- W609548044 hasPublicationYear "2014" @default.
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