A model-inversion control strategy to attain desired equilibrium points when synthesizing nonlinear resonators
Abstract
The initial conditions of a deterministic nonlinear system affects the attained asymptotic solutions. This is a problem when the nonlinear behaviour is achieved by active control synthesis, and the initial conditions are not accessible for pre-constraining. Meanwhile, the generalized impedance control is recently gaining increasing attention in acoustics, and has been enlarged to achieve nonlinear mechanical responses of Electroacoustic Resonators at low excitation levels. Nevertheless, as the initial conditions of Electroacoustic Resonators are hardly accessible, the equilibrium points actually showcased by the synthetic nonlinear dynamics are not advantageous for noise attenuation in cavities excited by realistic noise sources. In this paper, we propose a control strategy being able to attain the desired equilibrium points, due to the definition of an exosystem characterized by a desired nonlinear impedance and a synthetic external excitation. The exosystem dynamics is integrated in real time and its response is enforced in the actual system (in our case, the Electroacoustic Resonator), by a model-inversion feedforward strategy. The proposed algorithm is implemented in the Electroacoustic Resonator, and is validated both numerically and experimentally. In particular, the experimental testing is conducted both in a quasi-open acoustic environment, and in enclosed cavities for acoustic mode attenuation.
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BibTeX
@misc{morell2026modelinversion,
title = {{A model-inversion control strategy to attain desired equilibrium points when synthesizing nonlinear resonators}},
author = {Maxime Morell and Emanuele De Bono and Emmanuel Gourdon and Manuel Collet and Alireza Ture Savadkoohi and Claude-Henri Lamarque},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30626},
eprint = {2608.30626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30626},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A model-inversion control strategy to attain desired equilibrium points when synthesizing nonlinear resonators
AU - Maxime Morell
AU - Emanuele De Bono
AU - Emmanuel Gourdon
AU - Manuel Collet
AU - Alireza Ture Savadkoohi
AU - Claude-Henri Lamarque
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30626
UR - https://arxiv.org/abs/2608.30626
AB - The initial conditions of a deterministic nonlinear system affects the attained asymptotic solutions. This is a problem when the nonlinear behaviour is achieved by active control synthesis, and the initial conditions are not accessible for pre-constraining. Meanwhile, the generalized impedance control is recently gaining increasing attention in acoustics, and has been enlarged to achieve nonlinear mechanical responses of Electroacoustic Resonators at low excitation levels. Nevertheless, as the initial conditions of Electroacoustic Resonators are hardly accessible, the equilibrium points actually showcased by the synthetic nonlinear dynamics are not advantageous for noise attenuation in cavities excited by realistic noise sources. In this paper, we propose a control strategy being able to attain the desired equilibrium points, due to the definition of an exosystem characterized by a desired nonlinear impedance and a synthetic external excitation. The exosystem dynamics is integrated in real time and its response is enforced in the actual system (in our case, the Electroacoustic Resonator), by a model-inversion feedforward strategy. The proposed algorithm is implemented in the Electroacoustic Resonator, and is validated both numerically and experimentally. In particular, the experimental testing is conducted both in a quasi-open acoustic environment, and in enclosed cavities for acoustic mode attenuation.
ER -