A Model-Free Extremum Seeking Controller with Application to Tracking a Nonlinear Chemical Reaction

TL;DR

This paper introduces a model-free extremum-seeking control method to track reference trajectories in nonlinear chemical reactions, optimizing the reaction process without relying on explicit system models.

Contribution

The paper develops a novel extremum-seeking control approach for trajectory generation near reference curves in nonlinear systems, specifically applied to chemical reaction optimization.

Findings

Successfully applied to a nonisothermal chemical reaction model

Achieved accurate trajectory tracking in simulations

Demonstrated effectiveness without explicit system models

Abstract

In this paper, we develop the extremum-seeking approach to generate admissible trajectories in a neighborhood of a given reference curve in the state space. The cost function of the problem represents the distance between the current system state and the reference curve, which is parameterized as a function of time. Such reference curves naturally arise as optimal trajectories in isoperimetric optimization problems for nonlinear chemical reactions, where the objective is to maximize the average reaction product over a given period. We apply the proposed extremum seeking control design to a nonisothermal reaction model and illustrate the resulting tracking errors through numerical simulations.