A Globally Convergent Estimator of the Parameters of the Classical Model of a Continuous Stirred Tank Reactor

TL;DR

This paper introduces a novel, globally convergent parameter estimator for a continuous stirred tank reactor model, overcoming longstanding challenges posed by exponential nonlinearities in the system dynamics.

Contribution

It presents the first globally exponentially convergent estimator for the reactor model using a new regression equation and a novel Immersion and Invariance-based estimation algorithm.

Findings

Estimator guarantees parameter convergence with weak excitation.

The approach effectively handles exponential nonlinearities in the model.

Provides a practical solution to a long-standing open problem.

Abstract

In this paper we provide the first solution to the challenging problem of designing a globally exponentially convergent estimator for the parameters of the standard model of a continuous stirred tank reactor. Because of the presence of non-separable exponential nonlinearities in the system dynamics that appear in Arrhenius law, none of the existing parameter estimators is able to deal with them in an efficient way and, in spite of many attempts, the problem was open for many years. To establish our result we propose a novel procedure to obtain a suitable nonlinearly parameterized regression equation and introduce a radically new estimation algorithm - derived applying the Immersion and Invariance methodology - that is applicable to these regression equations. A further contribution of the paper is that parameter convergence is guaranteed with weak excitation requirements.