Mathematical modeling of dynamic processes in systems with distributed parameters
Journal Title: Комп’ютерне моделювання: аналіз, управління, оптимізація - Year 2017, Vol 2, Issue 2
Abstract
In this paper, a discrete method is developed and generalized for the study of transient processes in systems with distributed parameters described by telegraph equations, at any point at any time. In this connection, in this paper, we consider the estimation of the error obtained with this assumption. We note that when we expand the expressions for , from a real system with distributed parameters we pass to a balanced system, and the coefficient Ò, depending on the specifics of particular objects, in particular, the main pipelines, gets different values. The conducted research shows that the higher the value Ò is, the more the function value deviates in the steady state from the value corresponding to the steady state of the unbalanced link. Proceeding from the foregoing, we can conclude that the expansion in a series of expressions for the coefficient is valid only for small values of Ò. In the work of prof. Y.B. Kadimov, by approximating an infinite series of Bessel series of functions of the first kind of zero order, when passing from the transform to the original (at x=0), a solution of the telegraph equation in the form of lattice functions is obtained. It makes possible to calculate transient processes in electric drives and automatic control systems, including links with distributed parameters, with allowance for losses, with an error not exceeding 5%. However, in a number of practical tasks when solving the problem of the dynamics of objects with distributed parameters, it becomes necessary to investigate the transient processes of the initial system at any point at any time. Proceeding from the foregoing, in this paper, we propose a numerical method for calculating transient processes at any point of systems, with distributed parameters described by telegraph equations. The proposed method for calculating transient processes in systems with distributed parameters is discrete.
Authors and Affiliations
В. Г. Мусаев
Keywords
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