Vadim Onufriev (Tomsk Polytechnical University): Real Interpolation Method: Application for Technical Objects Control

Fri, 11/22/2013

An informal presentation of a doctoral student visiting our department/group. The presentation starts at 2pm and takes place at K14 room. Everyone interested in methods ofor systems identification is welcome.

Abstract of the talk: We consider the problem of identification and obtaining of desired system model. All methods of solving this problem can be classified by type of mathematical model of the plant or, actually, areas in which basic calculations are held. It is able to select an area of dynamic performance on a time-domain and image-domain of the functions. The first of these mathematical models is human-friendly, since they have a clear physical meaning. However, fulfillment of transforms in this area is difficult. In this sense it is more preferable to image area on the basis of Laplace, Fourier, and other tools. For this area various classifications are offered. We use one of them. The first group includes methods of using the entire complex plane with zeros and poles of the function located on it. The second group comprises methods based on a projection of the complex plane on the imaginary axis. This group includes all frequency methods. The third group is based on the projection of the complex plane on its positive real axis. The first two groups of methods operate on a model that contains a complex variable p = b + jw  or jw. We see that in both cases there is an imaginary argument, requiring separation of functions into the real and imaginary parts in operations over them. Refer to the third group. Here the argument is the real variable, p = b, w = 0. From the standpoint of numerical methods the first two groups require separation of functions into the real and imaginary parts.
In fact, that is an extra step from functional positions. In the third case, there is no such step, and therefore the volume of transactions is reduced by more than half.
We present the Real Interpolation method, which belongs to the third group and includes all its advantages. We outline its basis and application.
We also outline that there is a possibilities to use the real variable instead of complex variables in the image-domain. We will consider some numeric examples and in conclusion perspectives of the Real interpolation method will be shown.