A study of model adaptation in iterative real-time optimization of processes with uncertainties

Abstract

In real-time optimization, plant-model mismatch can be handled by adding bias and gradient correction terms to the model-based optimization problem in order to meet the first-order necessary conditions of optimality. However, since these correction terms do not ensure the satisfaction of the second-order condition of optimality upon convergence, the model that is used in the optimization can be inadequate. In the framework of iterative modifier-adaptation, this paper proposes to only use effective model parameter updates to ensure and to speed up the convergence to the process optimum. Additionally, this paper shows that model adequacy can and should be enforced explicitly in model parameter adaptation. By means of a simulation study of maximizing the product yield in a fed-batch reactor, we demonstrate that the proposed model adaptation procedure computes model parameters which make the iterative real-time optimization with modifier-adaptation converge faster and more reliably to the plant optimum.