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. - In: IEEE CONTROL SYSTEMS LETTERS. - ISSN 2475-1456. - STAMPA. - 2:4(2018), pp. 773-778. [10.1109/LCSYS.2018.2849617]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.