×

An optimal control problem in ultracentrifugation. (English) Zbl 0609.76117

Finite element methods, Proc. China-France Symp., Beijing/China 1982, 157-185 (1983).
[For the entire collection see Zbl 0604.00019.]
We consider the question of optimizing the separative power of a centrifuge and we treat it as an optimal control problem.
We first explain how this problem may be embedded in the framework of optimal control theory. The state of the distributed system is given by the linearized system of equations of motion, the cost function is a functional expressing the separative power of the centrifuge and we take boundary controls representing the temperature field imposed on the boundary of the centrifuge.
Then, applying some variants of classical gradient and conjugate gradient methods, we obtain numerical values for the optimal control, that is for the temperature field maximizing the separative power of the centrifuge (we also present various verifications of these results). These numerical results seem to indicate some interesting and unexpected phenomena concerning the gas flow in the centrifuge.

MSC:

76U05 General theory of rotating fluids
76N15 Gas dynamics (general theory)
65K10 Numerical optimization and variational techniques
49M99 Numerical methods in optimal control

Citations:

Zbl 0604.00019