Extremum seeking control applied to a semi-batch reaction operation

Date

2014-08

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Abstract

Batch and semi-batch systems are by nature more complex when considering strategies for regulation, as compared to continuous systems. Batch and semi-batch systems are used widely in the production of pharmaceutical drugs, specialty chemicals, and agricultural products (herbicides and fungicides). Extremum Seeking Control (ESC) is a control approach that may be very promising to regulate non-continuous systems. ESC achieves its target objective without relying on explicit model of the system. The goal of this study was to determine if an extremum seeking controller can be designed to regulate a semi-batch reactor that not only carries out multiple reactions with undesirable by-products, but also has constraints including productivity, toxicity and solubility at the designed conditions. The extremum seeking controller was tested in the face of disturbances and noise to assess closed-loop controller performance. With the identification of a viable feed pattern the ESC was tuned to achieve a target. The chemical reaction that occurs in the batch reactor is the acetoacetylation of pyrrole with diketene to produce 2-acetoacetyl pyrrole (PAA). For the reaction to be economically feasible it must convert at least 58% of the pyrrole to PAA. Dehydroacetic acid (DHA) is a byproduct that must have a final concentration under 0.15 mol l-1 to avoid solubility problems. Diketene is a toxic compound that must have a final concentration below 0.025 mol l-1. A mathematical model of the chemical reaction system was formulated. After simulating the reaction system under open-loop conditions, four different feed patterns of diketene into the system were designed to keep the system within the constraints. The first pattern involved step-changes in the diketene feed rate. The second used a Gaussian curve. The third and fourth, were bimodal curves: one featuring low peaks followed by high peaks, and the other the reverse. The main objective of this study was accomplished with the finding that it is possible to design an ESC to control a semi-batch reactor. Out of the four selected feed patterns, the high-how bimodal feed was more successful in keeping the system within the constraints. Further scenarios were tested to select an ESC and filter configuration that would perform successfully with the four feed patterns, in the face of disturbances. It was concluded that the classical ESC configuration with a high- and low-pass filters produced satisfactory closed-loop performance.

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Keywords

Semi-batch operations, Feedback control, High-pass/low-pass filter design, Robustness

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