A stability analysis based on dissipativity of linear and nonlinear repetitive control

Federico Califano; Alessandro Macchelli

doi:10.1016/j.ifacol.2019.08.008

A stability analysis based on dissipativity of linear and nonlinear repetitive control

Federico Califano, Alessandro Macchelli

Research output: Contribution to journal › Conference article › Academic › peer-review

7 Citations (Scopus)

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Abstract

This paper deals with repetitive control (RC). More specifically, a parametrised version of the repetitive compensator, i.e. of the infinite-dimensional controller employed in RC schemes, modelled as a boundary control system (BCS) in port-Hamiltonian form is presented. Well-posedness and stability of such control scheme are rigorously addressed thanks to novel tools based on dissipativity theory and originally developed for the stabilisation of BCS. Here, the linear and the nonlinear cases are tackled, and in both the cases the classes of plants for which RC schemes are exponentially stable are determined. Moreover, and explicit motivation of perfect asymptotic tracking and disturbance rejection for exponentially stable RC systems without relying on the internal model theory is provided. To show the validity of the analysis, simulations are reported.

Original language	English
Pages (from-to)	40-45
Number of pages	6
Journal	IFAC-papersonline
Volume	52
Issue number	2
DOIs	https://doi.org/10.1016/j.ifacol.2019.08.008
Publication status	Published - 1 Jun 2019
Event	3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2019 - Oaxaca, Mexico Duration: 20 May 2019 → 24 May 2019 Conference number: 3

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title = "A stability analysis based on dissipativity of linear and nonlinear repetitive control",

abstract = "This paper deals with repetitive control (RC). More specifically, a parametrised version of the repetitive compensator, i.e. of the infinite-dimensional controller employed in RC schemes, modelled as a boundary control system (BCS) in port-Hamiltonian form is presented. Well-posedness and stability of such control scheme are rigorously addressed thanks to novel tools based on dissipativity theory and originally developed for the stabilisation of BCS. Here, the linear and the nonlinear cases are tackled, and in both the cases the classes of plants for which RC schemes are exponentially stable are determined. Moreover, and explicit motivation of perfect asymptotic tracking and disturbance rejection for exponentially stable RC systems without relying on the internal model theory is provided. To show the validity of the analysis, simulations are reported.",

author = "Federico Califano and Alessandro Macchelli",

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note = "3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2019, CPDE 2019 ; Conference date: 20-05-2019 Through 24-05-2019",

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T1 - A stability analysis based on dissipativity of linear and nonlinear repetitive control

AU - Califano, Federico

AU - Macchelli, Alessandro

N1 - Conference code: 3

PY - 2019/6/1

Y1 - 2019/6/1

N2 - This paper deals with repetitive control (RC). More specifically, a parametrised version of the repetitive compensator, i.e. of the infinite-dimensional controller employed in RC schemes, modelled as a boundary control system (BCS) in port-Hamiltonian form is presented. Well-posedness and stability of such control scheme are rigorously addressed thanks to novel tools based on dissipativity theory and originally developed for the stabilisation of BCS. Here, the linear and the nonlinear cases are tackled, and in both the cases the classes of plants for which RC schemes are exponentially stable are determined. Moreover, and explicit motivation of perfect asymptotic tracking and disturbance rejection for exponentially stable RC systems without relying on the internal model theory is provided. To show the validity of the analysis, simulations are reported.

AB - This paper deals with repetitive control (RC). More specifically, a parametrised version of the repetitive compensator, i.e. of the infinite-dimensional controller employed in RC schemes, modelled as a boundary control system (BCS) in port-Hamiltonian form is presented. Well-posedness and stability of such control scheme are rigorously addressed thanks to novel tools based on dissipativity theory and originally developed for the stabilisation of BCS. Here, the linear and the nonlinear cases are tackled, and in both the cases the classes of plants for which RC schemes are exponentially stable are determined. Moreover, and explicit motivation of perfect asymptotic tracking and disturbance rejection for exponentially stable RC systems without relying on the internal model theory is provided. To show the validity of the analysis, simulations are reported.

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VL - 52

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JO - IFAC-papersonline

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T2 - 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2019

Y2 - 20 May 2019 through 24 May 2019

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A stability analysis based on dissipativity of linear and nonlinear repetitive control

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