Using sampled-data dynamic controller to stabilize rotating pulses

Abstract

We consider the stabilization of a rotating temperature pulse moving in a continuous asymptotic model of many connected chemical reactors organized in a loop with continuously switching of the feed point synchronously with the motion of the pulse solution. We use the switch velocity as control parameter and design it to follow the pulse: the switch velocity is formed at every step on-line using the discrepancy between the temperature at the front of the pulse and a set point. The resulting feedback controller, which can be regarded as a dynamic sampled-date controller, is designed using root-locus technique. Convergence conditions of the control law are obtained in terms of the zero structure (finite zeros, infinite zeros) of the related lumped model. The theoretical results are applied to keep a moving solution in the typical loop reactor in which a single exothermic reaction occurs and is confirmed by numerical simulations.