Constrained iterative learning control of batch transesterification process under uncertainty

Abstract

Biodiesel are fatty acid methyl esters (FAME), which can be produced by the transesterification reaction of vegetable oils with methanol. A batch transesterification process is often associated with model uncertainties and unmeasured disturbances, which may create a detrimental effect on the batch end FAME yield due to plant-model mismatch. Therefore, batch-to-batch iterative learning control (ILC) is necessary to track the desired reference FAME profile under such process variations. This work demonstrates a constrained quadratic programming problem (QPP) based batch-to-batch ILC framework for optimizing the endpoint FAME concentration by controlling the hot water flow profile passing through the reactor jacket under uncertainty. Parametric uncertainties are modeled separately in two case studies, which involve different batch transesterification models differing in the state variables. Case study 1 considers uncertainty in the apparent activation energy and brings out a comparative study between a QPP based ILC and a heuristics based approach. The comparison is shown based on the tracking performance of the ILC in terms of reduction in the batch end tracking error and total root mean square error of the same. Batch-to-batch ILC is superior as it produces faster convergence of the tracking error by saving 6 batches as compared to the heuristics approach. Case study 2 involves the implementation of constrained QPP based ILC algorithm on a proposed 54-state detailed batch transesterification model of canola oil, where uncertainty is modeled as the change in the input triglyceride composition from the base case. The desired reference FAME concentration profile is tracked in 9 batches for fixed uncertainty whereas it takes 15 batches to achieve the stochastic convergence under stochastic disturbance.