This letter deals with nonlinear repetitive control (RC), a technique used to reject periodic disturbances with a known and constant period. Since RC systems are defined over a state space of infinite dimension, the main theoretical problem that makes nonlinear case not trivial resides in the lack of adequate mathematical tools to study well-posedness of the closed-loop system and regularity of the solutions. Here, the stability analysis relies on recent results about the boundary control of infinite-dimensional port-Hamiltonian systems via nonlinear regulators, and the major contribution is the definition of a class of nonlinear plants for which a RC scheme is, at first, well-posed, and then exponentially stable. Moreover, an explicit proof of perfect local asymptotic tracking and disturbance rejection for exponentially stable RC systems is provided.

Stability Analysis of Nonlinear Repetitive Control Schemes

Califano, Federico
;
BIN, MICHELANGELO;Macchelli, Alessandro;Melchiorri, Claudio
2018

Abstract

This letter deals with nonlinear repetitive control (RC), a technique used to reject periodic disturbances with a known and constant period. Since RC systems are defined over a state space of infinite dimension, the main theoretical problem that makes nonlinear case not trivial resides in the lack of adequate mathematical tools to study well-posedness of the closed-loop system and regularity of the solutions. Here, the stability analysis relies on recent results about the boundary control of infinite-dimensional port-Hamiltonian systems via nonlinear regulators, and the major contribution is the definition of a class of nonlinear plants for which a RC scheme is, at first, well-posed, and then exponentially stable. Moreover, an explicit proof of perfect local asymptotic tracking and disturbance rejection for exponentially stable RC systems is provided.
2018
Califano, Federico; Bin, Michelangelo; Macchelli, Alessandro; Melchiorri, Claudio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/655669
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