Analysis of synchronization in a supermarket refrigeration system: Benchmark for Hybrid System Control

Li Zheng, Lars Finn Sloth Larsen, Roozbeh Izadi-Zamanabadi, Rafal Wisniewski

Research output: Contribution to journalJournal articleResearchpeer-review

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.

Original languageEnglish
JournalKybernetes
Volume12
Pages (from-to)154-162
Number of pages9
ISSN0368-492X
Publication statusPublished - 2024

Keywords

  • kontrol
  • Stability
  • Hybrid systems
  • Stochastic approximation
  • Limit cycles
  • Synchronization

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