Adaptive rejection of narrow-band disturbances in the presence of plant uncertainties—A dual Youla–Kucera approach

Abstract

The stability of adaptive disturbance rejection schemes using Youla-Kucera (YK) parametrization and the internal model principle (IMP) in the presence of plant model uncertainties is investigated. The problem is approached by using the dual Youla Kucera parametrization for the description of the plant model uncertainties. The known disturbance case is discussed first, emphasizing the need of over parametrization of the Youla Kucera filter used for control in order to both solving the IMP and the stability problems. Then this solution is extended for the case of unknown disturbances leading to the use of a parameter adaptation algorithm with projection. A stability analysis of the adaptive scheme is provided. Simulation results on relevant examples and experimental evaluation on an active noise attenuation system illustrate the possibilities of this approach for handling significant plant-model mismatch.

Recursive algorithms for identification of dual Youla-Kucera parametrized plant models in closed loop

“…There is a growing interest for modeling plant uncertainties using the dual Youla-Kucera plant parametrization [1], [2] when operating in closed loop. Dual Youla-Kucera parametrization appears to be an efficient way for evaluating robustness of adaptive regulation schemes ( [3]). Certainly this representation can be used as well for evaluating the robustness of adaptive feedforward disturbance compensation schemes in the presence of plant uncertainties.…”

“…Certainly this representation can be used as well for evaluating the robustness of adaptive feedforward disturbance compensation schemes in the presence of plant uncertainties. Application in the field of active noise control have been reported ( [3]).…”

Output Error Recursive Algorithms for Identification of Dual Youla-Kucera Models in Closed Loop Operation

“…Dual Youla-Kucera (Y-K) model structure is a useful way of representing plant model uncertainties [2], [3] and evaluate robustness of different control schemes. See for example [4] among other publications. It also offers a way for handling large model uncertainties, provided that this structures can be identified recursively in closed loop operation in view of iterative tuning and adaptive control.…”

Discrete time partial‐state feedback model reference disturbance rejection control

“…This MRAC‐based disturbance rejection scheme can guarantee asymptotic output tracking and the stability of closed‐loop systems in the presence of unmatched disturbances. Before designing the novel adaptive control scheme, we first develop a nominal partial‐state feedback control strategy with respect to systems with known parameters 10,25,26 . Such a strategy provides a controller framework for a unified MRAC scheme.…”

“…Before designing the novel adaptive control scheme, we first develop a nominal partial-state feedback control strategy with respect to systems with known parameters. 10,25,26 Such a strategy provides a controller framework for a unified MRAC scheme. The main issues for the proposed research involve partial-state feedback disturbance rejection controller design, plant-model matching conditions and adaptive design and analysis.…”