Robust Direct Adaptive Regulation of Unknown Disturbances in the Vicinity of Low-Damped Complex Zeros--Application to AVC

Abstract

Adaptive feedback control approaches have been widely used to address the issue of rejecting multiple narrow band disturbances with unknown and time varying characteristics (frequency, phase and amplitude), in Active Vibration Control (AVC) and Active Noise Control (ANC). These approaches are based directly or indirectly on the use of the Internal Model Principle and the Youla-Kučera parametrization combined with an adaptive law. All the algorithms associated with these approaches make the assumption that the plant zeros are different from the poles of the disturbance model in order to achieve disturbance compensation. However in practice the problem is more intricate since it is not clear what happens if the plant has very low damped complex zeros (often encountered in mechanical structures) and the frequency of the disturbance is close to the anti-resonance frequency (the resonance frequency of the plant zeros). In this paper we evaluate comparatively in simulation and in real time on a benchmark test bed, two different approaches to deal with the low damped complex zeros of the plant. An evaluation of the combination of the two approaches is also presented.

Reference tracking control and attenuation of unknown periodic disturbances in the presence of noise for unknown minimum‐phase LTI plants

“…where y(k) = y p (k) + n s (k) is the measured output, 1 , 2 ∈ ℝ n c , 3 , c 0 ∈ ℝ are the controller parameters, (z) = [z n c −1 , z n c −2 , … , z , 1] ⊤ for n c ≥ 1, (z) = 0 for n c = 0, and Λ(z) = Λ 0 (z)Z m (z) is an arbitrary monic Hurwitz polynomial of degree n c that contains Z m (z) as a factor, ie, Λ 0 (z) is any monic Hurwitz polynomial of degree n c − deg(Z m ); for simplicity,…”

“…Consider the closed-loop system (1), (4), and (7). Suppose that Assumptions 1 and 2 are satisfied and the input and output disturbances are dominantly (quasi) periodic of the form (3). If n c ≥ deg(R p D s ) − 1 and…”

“…[1][2][3][4][5][6] Most of the successful efforts proposed up to now assume that the modeled part of the plant is stable and perfectly known; however, for plants with large parametric uncertainties, online identification of the plant parameters is necessary to achieve the control objective. [1][2][3][4][5][6] Most of the successful efforts proposed up to now assume that the modeled part of the plant is stable and perfectly known; however, for plants with large parametric uncertainties, online identification of the plant parameters is necessary to achieve the control objective.…”

“…Due to its broad applications in high-performance systems, suppression of unknown periodic disturbances acting on dynamical systems has been the subject of considerable research over the past years. [1][2][3][4][5][6] Most of the successful efforts proposed up to now assume that the modeled part of the plant is stable and perfectly known; however, for plants with large parametric uncertainties, online identification of the plant parameters is necessary to achieve the control objective. That is, the controller must be able to identify the parameters of both plant model and disturbance model.…”

“…( §2 3). and can be expressed as a system of algebraic linear equations as Tx = b, where T is a matrix containing the coefficients of the known polynomials A(z) and B(z) and is of dimension(n c + deg(R p ) − deg(Z p )) × (2n c − deg(Z p ) + 1 − deg(D s )),vector b contains the coefficients of the known polynomial C(z), and x is a vector containing the unknown coefficients ofL(z) and P(z).…”