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Keywords:

  • extremum seeking;
  • adaptive learning;
  • tubular reactor;
  • distributed feed;
  • persistence of excitation

Abstract

An adaptive extremum seeking control scheme for a class of nonlinear distributed parameter systems is presented. It addresses the real-time optimization of a parallel chemical reaction system in an isothermal tubular reactor with uniform distributed feed described by a set of hyperbolic partial differential equations. Only limited knowledge of the kinetics is assumed. An adaptive learning technique is introduced to design an extremum seeking algorithm that drives the system states to a set point that maximizes the value of an objective function. Lyapunov's stability theorem is used in the design of the extremum seeking controller structure and the development of the parameter learning laws. © 2006 American Institute of Chemical Engineers AIChE J, 2006