Stability of MTA, as a linear system, with random excitations of its parameters

Abstract

n general, the dynamics of the functioning of the agricultural machine-tractor aggregate is represented in the form of a deterministic process, which can be described by a system of differential equations. The stability of such a deterministic system is solved by introducing coefficients that also do not have a stochastic component. However, the influence of external factors on the operational characteristics of the machine-tractor aggregate is of a fairly significant probabilistic nature, which must also be taken into account in determining the stability of the MTA. Particular attention in the calculations should be given to the formation of a stochastic component in the form of "white noise", which is formed both by the oscillations of individual elements of the machine and tractor unit, and by harmonious changes in the heights of the unevenness of the supporting bearing surface and the hook load values, which is formed by the resistivity of the agricultural or transport transport-technological), machines. The article is devoted to the stability of the machine-tractor aggregate, considered as a deterministic system, which can be described by equations of a certain order with coefficients whose values have a certain stochastic character. The formation of the stochastic differential equation of the system under the influence of the last random forces in the form of "white noise" is considered. Necessary and sufficient conditions for asymptotic stability in the mean quadratic form are obtained, passing in the absence of noise in the Routh-Hurwitz conditions. It is proved that for asymptotic stability it is necessary and sufficient that there exists a definite-positive quadratic form. Sufficient conditions for the stability of higher-order moments are also presented. As a result of theoretical studies it was established that the obtained conditions for stability in the mean quadratic require the calculation of all determinants, the oldest of which is of order. It turns out that the first determinants are the same as the determinants entering into the Routh-Hurwitz criterion. The last determinant is obtained by replacing in the first line with a string compiled according to a particular rule from the coefficients of the correlation matrix.