Controlling of Chaos in the Process of Crystallization of Dibasic Lead Phosphite

In this paper three algorithms of control of chaos (destohastization, control with proportional feedback and control with time-delayed feedback) in the process of continuous mass crystallization of dibasic lead phosphite are offered. The first method involves a corrective action in compliance with the required values of the dynamic variables and, therefore, involves a feedback as a necessary component of the system. An algorithm based on the Poincare cross section was developed by Ott, Grebogi, and Yorke, which is referred to as the acronym of their names (the OGY algorithm). For today the OGY-method has quite a number of modifications. The second attractive for scientists method is the time-delayed feedback one. It was offered in 1992 by the Lithuanian physicist K. Pyragas. The main advantage of his idea is the continuity of the method. In other words, when one uses the OGYmethod and its modifications the algorithm starts working when a system gets, for example, to the given area of an unstable fixed point, that takes some time, but when using the Pyragas’ method the algorithm is supposed to be switched on any time when it is necessary due to a feedback principle. The efficiency of Pyragas’ method and its modifications for the physical, chemical and a number of other systems was demonstrated. Another approach to the stabilization of the stochastic behavior of dynamic systems involves external disturbances without feedback. This method of suppression of chaos is referred to as the destochastization method. We show the possibility of using of each method for controlling chaos in the process of continuous mass crystallization of dibasic lead phosphate.