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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.06906 |
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| _version_ | 1866909248498171904 |
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| author | Holroyd, Oscar A. Cimpeanu, Radu Gomes, Susana N. |
| author_facet | Holroyd, Oscar A. Cimpeanu, Radu Gomes, Susana N. |
| contents | We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the system state is challenging in physical settings, so methods able to take this into account are important. The Navier-Stokes equations modelling the flow are a complex, highly nonlinear set of PDEs, so standard control theoretical results are not applicable. Instead, we chain together a hierarchy of increasingly idealised approximations, developing a control strategy for the simplified model which is shown to be successfully applied to simulations of the full system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilisation of falling liquid films with restricted observations Holroyd, Oscar A. Cimpeanu, Radu Gomes, Susana N. Optimization and Control Fluid Dynamics 93B52, 76A20, 49N10, 93C41 We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the system state is challenging in physical settings, so methods able to take this into account are important. The Navier-Stokes equations modelling the flow are a complex, highly nonlinear set of PDEs, so standard control theoretical results are not applicable. Instead, we chain together a hierarchy of increasingly idealised approximations, developing a control strategy for the simplified model which is shown to be successfully applied to simulations of the full system. |
| title | Stabilisation of falling liquid films with restricted observations |
| topic | Optimization and Control Fluid Dynamics 93B52, 76A20, 49N10, 93C41 |
| url | https://arxiv.org/abs/2407.06906 |