Linear quadratic self-tuning control of a liquid-liquid extraction column

An application of a linear quadratic self-tuning control approach to a pulsed liquid-liquid extraction column is described. The control algorithm is derived from the minimization of a quadratic cost function. The resulting Riccati equation is iterated until the closed-loop poles belong to a predefined stability domain included in the unit circle. Based upon the certainty equivalence principle, the adaptive control algorithm involves a parameter identification procedure and a feedback control law which uses the estimated parameters. Several experiments are carried out on a pulsed liquid-liquid extraction column. Such extractors are being increasingly used in several industries because they are not energy-consuming and they lead to high product purity. The column considered has the same dimensions as those currently used in fine chemical processes. The control objective is to optimize the column behaviour. The selected control variables are the pulse frequency and the conductivity measured at the bottom of the column. The experiments have been carried out with a mixture of water and toluene. The physical model developed for the column is too complex to use for control purposes. To represent the complex behaviour of the column, a single-input/single-output discrete-time linear model was adopted. The parameters in the model are estimated on-line with normalized data. The forgetting factor is also adjusted to maintain a constant trace of the estimator gain matrix. The results obtained show the ability of this algorithm to improve the efficiency of the process considered. Finally, some details on practical implementation are provided.