Duration of filtration process during finite-frequency identification

A linear control plant subjected to an external disturbance is considered. The disturbance is assumed to be an unknown bounded function. The finite-frequency identification allows us to find estimates of this control plant's parameters. It uses special integral filters (Fourier filters), that find estimates of the plant frequency response at a specific set of frequencies. A system of linear equations is formed from the set of the plant frequency response points. The solution of this system provides desired estimates of the plant parameters. Error dynamics of filtration process is studied. The research is based on known results that describe asymptotic characteristic of the Fourier filters errors in presence of unknown-but-bounded external disturbances. A new approach to determine the filtration duration is proposed, estimation of the filtration accuracy is described. The proposed approach is based on a special linear programming problem, the solution of which gives us an estimate of the filter value and a value of parameter that describes the rate of the filter error convergence. The last one is used for duration determination. The appropriate filtration algorithm is developed. Numerical experiments that prove efficiency of the proposed approach were carried out.