285353 Online Model-Based Experimental Design
In chemical processes, unknown model parameters have to be calibrated to data from dynamic experiments by solving nonlinear constrained parameter estimation problems minimizing a weighted sum of squares of the deviations between data and model responses subject to the model equations. For nonlinear models it further depends on the values of the parameter estimate. To obtain a parameter estimate with maximum reliability, an experimental design is computed minimizing a functional of the variance-covariance matrix subject to the model equations and constraints to experimental cost and operability. This results in intricate nonlinear non-standard constrained optimal control problems. Moreover, in order to cope with the problem of large uncertainties in the initial parameter values, we follow the idea of an adaptive experiment design. This idea is implemented via online estimation of parameter values as well as the generation of these optimal input actions. In other words, in each sampling instant, where measurements data are taken, current estimates of the parameters as well as the currently planned experiment design are then repeatedly updated.
In this work, an experimental verification of the developed approach will also be presented. The experimental results correspond to an ion-exchange high performance liquid chromatography column (HPLC) for protein separation, where transport and adsorption parameters and parameters for the calibration of a concentration sensor are determined. The Basis of the HPLC system is given by a Smartline Pump with Manager (Knauer GmbH, Berlin, Germany), which is used for the generation of time dependent feed concentrations, which are then supplied to the chromatography column. The HPLC system is fully automated by a commercial process control system Freelance 800F ABB (Ladenburg, Germany) and interfaced with the numeric programming environment Matlab®, where algorithms for parameter subset selection, parameter estimation, and the generation of optimal input designs are implemented.
Acknowledgement: The authors would like to thank the Knauer GmbH, Berlin-Germany for their support regarding the experimental case study.