Filtration Duration and Errors in Finite-Frequency Identification

Abstract

The paper is devoted to analysis of filtration errors in finite-frequency identification. We consider a linear control plant subject to action of an external disturbance, which is assumed to be a bounded function. The finite-frequency identification allows us to find estimates of this plant's parameters. It uses special integral filters (Fourier filters), that find estimates of the plant frequency response at specific frequencies. There are known estimates of convergence rate of Fourier filters errors, which we use as a basis to propose a new approach to determine the duration of identification. The proposed method is based on a special linear programming problem, the solution of which gives us two parameters: an estimate of the filter value and a parameter that describes the rate of the filter error convergence. The last one is used for duration determination. We develop corresponding filtration algorithm and give certain consideration to its accuracy. An illustrative example is presented.