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Analysis of synchronization in a supermarket refrigeration system

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Abstract

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.

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Authors and Affiliations

  1. Department of Electronic Systems, Aalborg University, Fredrik Bajers Vej 7C, 9220, Aalborg, Denmark

    Rafael Wisniewski & John Leth

  2. Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220, Aalborg, Denmark

    Jakob G. Rasmussen

Authors
  1. Rafael Wisniewski
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  2. John Leth
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  3. Jakob G. Rasmussen
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Corresponding author

Correspondence to Rafael Wisniewski.

Additional information

This work was supported by the Danish Council for Technology and Innovation.

Rafael WISNIEWSKI is a professor in the Section of Automation & Control, Department of Electronic Systems, Aalborg University. He receives his Ph.D. in Electrical Engineering in 1997, and Ph.D. in Mathematics in 2005. In 2007–2008, he was a control specialist at Danfoss A/S. His research interest is in system theory, particularly in hybrid systems.

John LETH received his M.S (2003) and Ph.D. (2007) degrees from the Department of Mathematical Sciences, Aalborg University, Denmark. Currently, he is employed as Assistant Professor at the Department of Electronic Systems, Aalborg University. His research interests include mathematical control theory and (stochastic) hybrid systems.

Jakob Gulddahl RASMUSSEN is an associate professor at the Department of Mathematical Sciences, Aalborg University, Denmark. He received his Ph.D. in Statistics in 2006 also at the Department of Mathematical Sciences. His research interests include spatial statistics and stochastic processes (including stochastic hybrid systems).

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Wisniewski, R., Leth, J. & Rasmussen, J.G. Analysis of synchronization in a supermarket refrigeration system. Control Theory Technol. 12, 154–162 (2014). https://doi.org/10.1007/s11768-014-0077-2

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  • DOI: https://doi.org/10.1007/s11768-014-0077-2

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