Method of Restoration of Input Signals of Nonlinear Dynamic Object with Destributed Parameters

Анотація

The article deals with the method of signal restoration at the input of a nonlinear dynamic object with distributed parameters. To describe these objects, a universal mathematical model in the form of a Volterra integro-degree series has been chosen. The problem of signal restoration is reduced to the problem of solving the Volterra polynomial equation of the first kind. The numerical implementation of such models is suggested to be carried out using quadrature methods, in particular, the method of trapezoids. In order to increase the stability of the solution in the presence of noise interference in the input data, it is suggested to use the differential regularization operator, which allows the incorrectly set task to be transformed into a class of correct ones. The possibility of applying such an approach is studied in solving the Volterra polynomial integral equation of the second order type, which describes nonlinear dynamic objects with quadratic nonlinearity. The computational formulas for solving this type of equations are given in the article. The received nonlinear second-order algebraic equations after approximation of the initial equation by integral sums are solved by iterative methods with initial approximation in the form of a pre-calculated radical. The developed algorithms are implemented as software modules in the Matlab, with the help of which a number of computational experiments have been carried out. As an example, non-linear dynamic objects that contain static non-linearity of the second order and dynamic links that are typical for objects with distributed parameters have been chosen. Such links are: a semi-integral link, an attenuation link (semi-delay) and a semi-inertial link. On the basis of applying the equivalent transformations, the macromodels of objects with distributed parameters have been obtained in the form of a polynomial integral Volterra equation of the I kind of the second order with the kernels that describe the above-mentioned components. The results of the computational experiments, presented in the form of graphs, showed that the suggested approach can be effectively used in restoration of signals at the input of nonlinear dynamic objects with distributed parameters.