Algorithms of adaptive tracking of unknown multisinusoidal signals in linear systems with arbitrary input delay

Abstract

SummaryThe problem of adaptive tracking control is addressed for the class of linear time‐invariant plants with known parameters and arbitrary known input delay. The reference signal is a priori unknown and is represented by a sum of biased harmonics with unknown amplitudes, frequencies, and phases. Asymptotic tracking is provided by predictive adjustable control with parameters generated by one of three designed adaptation algorithms. The first algorithm is based on a gradient scheme and ensures zero steady‐state tracking error with all signals bounded. The other two algorithms additionally involve the scheme with fast parametric convergence improving the closed‐loop system performance. In all the algorithms, the problem of delay compensation is resolved by special augmentation of tracking error. The adjustable control law proposed do not require identification of the reference signal parameters.