Synchronization Analysis And Control Of The Distributed Hysteresis Control System

The distributed hystersis control system consists of many subsystems,Each subsystem isequipped with a hystersis controller,These controllers are designed and operated independently,but this concept neglects cross-coupling effects. It is hard to deal with the hysteresis in many realsystems.In addition,there is almost no description about synchronization caused bymulti-hysteresis.The supermarket refrigeration system typically has a distributed control structure,which neglects interactions between its subsystems. These interactions from time to time lead to asynchronization operation of the display cases which causes excessive wear on the compressorscompressors and increased energy consumption.The mechanism analysis of synchronization phenomena is studied based on hybrid systemtheory and chaos theory.The paper mainly studies de-synchronization based on parameter tuningand anti-control of chaos.Main contends of the paper are described as follows:The working principle of the distributed hystersis control system and the reasons causingsynchronization in the distributed hystersis control system are introduced; The supermarketrefrigeration system is a typical distributed hystersis control system, the model of the supermarketrefrigeration system aimed to describe the dynamic characteristics of synchronization is discussed,the model is composed of individuals models of the display cases, the compressor rack and thesuction manifold; and under reasonable assumptions, the above nonlinear model is simplified intoa piecewise-affine switched model.The definition, basic characteristics of chaos are introduced; the stability of the system isanalyzed based on the Poincaré map theory; the dynamic characteristics of the system arediscussed based on the bifurcation theory. Wehave found that when the system has a low-periodorbit, there is a tendency to synchronization, when the system has a high-period orbit, even thecomplex chaos-like behavior, it is far away from the synchronization. The above information is afoundation of developing the de-synchronization method by chaotification of the system.The paper takes the supermarket refrigeration system, a typical distributed hystersis controlsystem, as example, and investigates the temperature synchronous phenomenon. The first method is changing the themal load of the surrounding air in the display cases, By adopting differentthermal loads through adjusting air speeds of the air curtains, the system operates in thede-synchronization situation and achieves better performances.The second method analyzes thesynchronization behaviour based on a piecewise-affine switched model and proposes a newde-synchronization scheme by chaotifying the system using delayed feedback control. Boththeoretical analysis and numerical simulation shows the effectiveness of the approach.Allsimulations are based on a simulation model of the supermarket refrigeration system inMatlab/Simulink. Ideas and results in the paper are not limited into the supermarket refrigerationsystem and can be extended to other multi-cooling systems.Meanwhile the ideas proposed in thepaper are likewise useful for analyzing similar complex dynamical systems such as power systems,heating systems, etc., where synchronization of hysteresis controlled subsystems often takes place.