Wisniewski, Rafal1; Leth, John-Josef4; Rasmussen, Jakob Gulddahl6
1 Aalborg University Space Center, The Technical Faculty of IT and Design, Aalborg University, VBN2 Automation & Control, The Technical Faculty of IT and Design, Aalborg University, VBN3 Department of Electronic Systems, The Technical Faculty of IT and Design, Aalborg University, VBN4 Aalborg U Robotics, The Faculty of Humanities, Aalborg University, VBN5 The Faculty of Engineering and Science (TECH), Aalborg University, VBN6 Department of Mathematical Sciences, The Faculty of Engineering and Science, Aalborg University, VBN
In a supermarket refrigeration, the temperature in a display case, surprisingly, influences the temperature in other display cases. This leads to a synchronous operation of all display cases, 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 Poincaré map to determine whether this periodic trajectory is asymptotically stable. To illustrate, this procedure is applied for a refrigeration system with two display-cases.
Journal of Control Theory and Applications, 2014, Vol 12, Issue 2, p. 154-162