A Stability Analysis Based on Dissipativity of Linear and Nonlinear Repetitive Control
Authors
Federico Califano, Alessandro Macchelli
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.
Citation
- Journal: IFAC-PapersOnLine
- Year: 2019
- Volume: 52
- Issue: 2
- Pages: 40–45
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2019.08.008
- Note: 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2019- Oaxaca, Mexico, 20–24 May 2019
BibTeX
@article{Califano_2019,
title={{A Stability Analysis Based on Dissipativity of Linear and Nonlinear Repetitive Control}},
volume={52},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2019.08.008},
number={2},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Califano, Federico and Macchelli, Alessandro},
year={2019},
pages={40--45}
}
References
- Califano, F., Bin, M., Macchelli, A. & Melchiorri, C. Stability Analysis of Nonlinear Repetitive Control Schemes. IEEE Control Systems Letters vol. 2 773–778 (2018) – 10.1109/lcsys.2018.2849617
- Califano, F., Macchelli, A. & Melchiorri, C. Stability analysis of repetitive control: The port-Hamiltonian approach. 2017 IEEE 56th Annual Conference on Decision and Control (CDC) 1894–1899 (2017) doi:10.1109/cdc.2017.8263926 – 10.1109/cdc.2017.8263926
- Curtain, (1995)
- Hara, S., Yamamoto, Y., Omata, T. & Nakano, M. Repetitive control system: a new type servo system for periodic exogenous signals. IEEE Transactions on Automatic Control vol. 33 659–668 (1988) – 10.1109/9.1274
- Le Gorrec, Y., Zwart, H. & Maschke, B. Dirac structures and Boundary Control Systems associated with Skew-Symmetric Differential Operators. SIAM Journal on Control and Optimization vol. 44 1864–1892 (2005) – 10.1137/040611677
- Macchelli, A. Boundary energy shaping of linear distributed port-Hamiltonian systems. European Journal of Control vol. 19 521–528 (2013) – 10.1016/j.ejcon.2013.10.002
- Macchelli, A. & Califano, F. Dissipativity-based boundary control of linear distributed port-Hamiltonian systems. Automatica vol. 95 54–62 (2018) – 10.1016/j.automatica.2018.05.029
- Macchelli, A., Le Gorrec, Y., Ramirez, H. & Zwart, H. On the Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 62 1700–1713 (2017) – 10.1109/tac.2016.2595263
- Ramirez, H., Le Gorrec, Y., Macchelli, A. & Zwart, H. Exponential Stabilization of Boundary Controlled Port-Hamiltonian Systems With Dynamic Feedback. IEEE Transactions on Automatic Control vol. 59 2849–2855 (2014) – 10.1109/tac.2014.2315754
- Ramirez, H., Zwart, H. & Le Gorrec, Y. Stabilization of infinite dimensional port-Hamiltonian systems by nonlinear dynamic boundary control. Automatica vol. 85 61–69 (2017) – 10.1016/j.automatica.2017.07.045
- Villegas, J. A., Zwart, H., Le Gorrec, Y. & Maschke, B. Exponential Stability of a Class of Boundary Control Systems. IEEE Transactions on Automatic Control vol. 54 142–147 (2009) – 10.1109/tac.2008.2007176
- Yamamoto, Learning control and related problems in infinite-dimensional systems. (1993)