Abstract
A time-discrete spatially-continuous electrowetting on dielectric (EWOD) model with contact line pinning is considered as the state system in an optimal control framework. The pinning model is based on a complementarity condition. In addition to the physical variables describing velocity, pressure, and voltage, the solid-liquid-air interface, i.e., the contact line, arises as a geometric variable that evolves in time. Due to the complementarity condition, the resulting optimal control of a free boundary problem is thus a mathematical program with equilibrium constraints (MPEC) in function space. In order to cope with the geometric variable, a finite horizon model predictive control approach is proposed. Dual stationarity conditions are derived by applying a regularization procedure, exploiting techniques from PDE-constrained optimization, and then passing to the limit in the regularization parameters. Moreover, a function-space-based numerical procedure is developed by following the theoretical limit argument used in the derivation of the dual stationarity conditions. The performance of the algorithm is demonstrated by several examples; including barycenter matching and trajectory tracking.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.