FUNDAMENTAL MATRIX OF LINEAR CONTINUOUS SYSTEM IN THE PROBLEM OF ESTIMATING ITS TRANSPORT DELAY

N. A. Dudarenko, N. A. Polinova, A. V. Ushakov


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Abstract

The paper deals with the problem of quantitative estimation for transport delay of linear continuous systems. The main result is received by means of fundamental matrix of linear differential equations solutions specified in the normal Cauchy form for the cases of SISO and MIMO systems. Fundamental matrix has the dual property. It means that the weight function of the system can be formed as a free motion of systems. Last one is generated by the vector of initial system conditions, which coincides with the matrix input of the system being researched. Thus, using the properties of the system- solving for fundamental matrix has given the possibility to solve the problem of estimating transport linear continuous system delay without the use of derivation procedure in hardware environment and without formation of exogenous Dirac delta function. The paper is illustrated by examples. The obtained results make it possible to solve the problem of modeling the pure delay links using consecutive chain of aperiodic links of the first order with the equal time constants. Modeling results have proved the correctness of obtained computations. Knowledge of transport delay can be used when configuring multi- component technological complexes and in the diagnosis of their possible functional degeneration.


Keywords: fundamental matrix, linear continuous system, Dirac delta function, weight function, transport delay

Acknowledgements. The work is supported by the Ministry of Education and Science of the Russian Federation (project 14.Z50.31.0031).

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