Adaptive tracking of multisinusoidal signal for linear system with input delay and external disturbances

Abstract

The problem of adaptive tracking of the output variable of a linear stationary plant behind a multiharmonic signal under conditions of control delay and external disturbances is considered. The state vector of the object is not available for direct measurements. The reference and disturbance signal parameters (amplitudes, phases, and harmonic frequencies) are a priori unknown, and a new algorithm is proposed to improve the performance of frequency estimation of a multisinusoidal signal. Examples are given that confirm the relevance of the proposed approach.

Stability analysis of nonstationary mechanical systems with time delay via averaging method

“…Here x(t), ẋ(t) ∈ R n are vectors of generalized coordinates and velocities, respectively, A is a constant symmetric and positive definite matrix of inertial characteristics of the system, B is a constant symmetric and positive definite matrix of dissipative forces, matrix functions C(t) and D(t) are continuous and bounded for t ∈ [0, +∞), h is a positive parameter, τ is a constant positive delay. The term D(t)x(t − τ ) can be interpreted as a result of application of a control with delay in the feedback law [Fridman, 2014;Andreev and Peregudova, 2021;Khac, Vlasov and Pyrkin, 2022].…”