Synchronization of temperature oscillations in heated plates with hysteretic on–off control

The synchronized behavior of two coupled, top heated, square plates with on–off control based on plate temperature is analyzed in this work. Each plate is represented by a two dimensional heat equation, and thermal communication between the plates is modeled by a thermal resistance; each plate also has an internal point at which the temperature is monitored for control. The problem is nonlinear, and numerical simulations are used to determine the long-time dynamic response of the system. As a first step the self-oscillation frequency of a single uncoupled controlled plate is determined as function of the deadband width of the controller. Then the dynamics of the coupled plates is analyzed, and the effect of the thermal resistance and the deadband width on synchronization of temperature oscillations is studied. Like in other complex systems with synchronization, a detuning window is found over which there is synchronization and beyond which the plates have different oscillation frequencies.