Delayed feedback control of rapid directional solidification

The possibility for feedback control of morphological instability of a melt–crystal interface during rapid directional solidification of a binary melt is investigated. The control method is based on heating the melt near the solid–liquid interface, with heating parameters depending on the morphology of the solidification front. A linear stability analysis of the corresponding mathematical problem is performed. It is shown that the chosen feedback control approach can substantially increase the threshold of the morphological instability when the control time delay is relatively small. This increase is proportional to the control amplitude. The simultaneous increase of both the control amplitude and the time delay, however, can yield feedback-induced destabilization.