N. Z. Safiullin

The problem of designing of mathematical models for up-to-date technical and technological systems is now getting very important because of processes of control and testing of these systems have to meet constantly rising demands. From the analysis of methods of problem solving for the identification of dynamic systems it follows that even in linear terms identification problem for such systems is nontrivial. While identification of nonlinear dynamic systems the difficulties increase immeasurably because of multidimensionality of pulse transfer functions (characteristics) [1,3,4]. The purpose of the article is to develop the method for simplification of algorithms of stochastic analysis, testing and identification of nonlinear slow-responding devises using a choice of proper signals and the analyzable Volterra model structure. The analytical method of transformation of signals having arbitrary forms in nonlinear slow-responding devices with weakly and strongly expressed oscillatory properties is developed. The method of solving of the problem of parametrical identification for nonlinear slow-responding devices on the basis of analytical system of elementary signals decomposition of real input signals is offered. Analytical representation of input and output signals applications of parametrical Volterra model and reduction of the unknown parameters number of pulse characteristics enabled us to integrate repeated integrals analytically, to solve parameters optimization problem for the model using a computer and to reduce the machine time. Mathematical model of the video amplifier is designed. The mean-square departure of the difference between real output signal and the signal of its nonlinear Volterra model of the 4-th order was not more than 0.1%.