In a supermarket refrigeration, the temperature in a display cases. This leads to a synchronous operation of all display cases, case, surprisingly, influences the temperature in other display in which the expansion va...In a supermarket refrigeration, the temperature in a display cases. This leads to a synchronous operation of all display cases, case, surprisingly, influences the temperature in other display in which the expansion valves in the display cases turn on and off at exactly the same time. This behavior increases both the energy consumption and the wear of components. Besides this practical importance, from the theoretical point of view, synchronization, likewise stability, Zeno phenomenon, and chaos, is an interesting dynamical phenomenon. The study of synchronization in the supermarket refrigeration systems is the subject matter of this work. For this purpose, we model it as a hybrid system, for which synchronization corresponds to a periodic trajectory. To examine whether it is stable, we transform the hybrid system to a single dynamical system defined on a torus. Consequently, we apply a Poincare map to determine whether this periodic trajectory is asymptotically stable. To illustrate, this procedure is applied for a refrigeration system with two display-cases.展开更多
文摘In a supermarket refrigeration, the temperature in a display cases. This leads to a synchronous operation of all display cases, case, surprisingly, influences the temperature in other display in which the expansion valves in the display cases turn on and off at exactly the same time. This behavior increases both the energy consumption and the wear of components. Besides this practical importance, from the theoretical point of view, synchronization, likewise stability, Zeno phenomenon, and chaos, is an interesting dynamical phenomenon. The study of synchronization in the supermarket refrigeration systems is the subject matter of this work. For this purpose, we model it as a hybrid system, for which synchronization corresponds to a periodic trajectory. To examine whether it is stable, we transform the hybrid system to a single dynamical system defined on a torus. Consequently, we apply a Poincare map to determine whether this periodic trajectory is asymptotically stable. To illustrate, this procedure is applied for a refrigeration system with two display-cases.
