Abstract
This paper considers the multiscale optimal control of crystal growth. The optimal control is realized for the crystal pulling arm modeled by the standard rigid body dynamics, while the underlying dynamics of the diffusion of heat in the crystal growth region is given by parabolic partial differential equations (PDEs) with time varying spatial domain. The underlying transport-reaction system is developed from the first principles and the associated dynamics is analyzed in appropriate functional state space setting. The complete description of the evolutionary parabolic domain time varying PDE is provided and explored within the coupled master-slave control setting. Numerical simulations demonstrate an optimal pulling evolution rate and its effects on the temperature profile in the crystal with the time varying domain.
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