Period-adding and chaos in fluidized bed catalytic reactors

A conventional Proportional-Integral-Derivative (PID) controller is considered for the stabilization of a non-isothermal fluidized bed catalytic reactor with consecutive exothermic reactions, modeled using the two-phase theory of fluidization. The investigation, although in a restricted region of the parameter space, has uncovered a good part of the rich dynamic characteristics of the controlled unit, including sequences of burst patterns that undergo transition from simple to complex oscillatory behavior. The alternation between the period-doubling sequence and the saddle-node bifurcation creates the chaotic regime while the generation and persistence of complex bursting are associated with the period-adding bifurcation.