On the design of equation-free controllers for dissipative PDEs via DEIM

Manda Yang, Antonios Armaou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We propose an equation free control method to control dissipative distributed parameter systems, in which the dynamics of the system are unknown while the effect of the control action is. A static observer is used to estimate the state using proper orthogonal decomposition (POD) so that a complete profile of the system can be estimated when a limited number of point sensors are available. Sensor locations are determined by interpolation indices in discrete empirical interpolation method (DEIM). By using both velocity and state sensors an explicit form of the complete equation become superfluous, needing to only have a description of the actuator effect. The proposed method is successfully employed in a diffusion-reaction process with Dirichlet and Neumann boundary conditions. Feedback linearization is combined with the proposed method to regulate the system. Computational results demonstrate that this method can regulate a dissipative distributed parameter system without explicitly requiring a model of it and is robust to disturbances.

Original languageEnglish (US)
Title of host publication2017 American Control Conference, ACC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3789-3796
Number of pages8
ISBN (Electronic)9781509059928
DOIs
StatePublished - Jun 29 2017
Event2017 American Control Conference, ACC 2017 - Seattle, United States
Duration: May 24 2017May 26 2017

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2017 American Control Conference, ACC 2017
CountryUnited States
CitySeattle
Period5/24/175/26/17

Fingerprint

Interpolation
Controllers
Sensors
Feedback linearization
Distributed parameter control systems
Actuators
Boundary conditions
Decomposition

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Yang, M., & Armaou, A. (2017). On the design of equation-free controllers for dissipative PDEs via DEIM. In 2017 American Control Conference, ACC 2017 (pp. 3789-3796). [7963535] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2017.7963535
Yang, Manda ; Armaou, Antonios. / On the design of equation-free controllers for dissipative PDEs via DEIM. 2017 American Control Conference, ACC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 3789-3796 (Proceedings of the American Control Conference).
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Yang, M & Armaou, A 2017, On the design of equation-free controllers for dissipative PDEs via DEIM. in 2017 American Control Conference, ACC 2017., 7963535, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 3789-3796, 2017 American Control Conference, ACC 2017, Seattle, United States, 5/24/17. https://doi.org/10.23919/ACC.2017.7963535

On the design of equation-free controllers for dissipative PDEs via DEIM. / Yang, Manda; Armaou, Antonios.

2017 American Control Conference, ACC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 3789-3796 7963535 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Yang M, Armaou A. On the design of equation-free controllers for dissipative PDEs via DEIM. In 2017 American Control Conference, ACC 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 3789-3796. 7963535. (Proceedings of the American Control Conference). https://doi.org/10.23919/ACC.2017.7963535