Process Transitions in continuous processes from one to another steady-state are of critical importance in the polymerization industry, which produces several distinct grades of the same product, polypropylene, for example. Optimal such transitions avoid making an off-spec product that neither customer A nor customer B will accept. If a knowledge-driven model of the process is at hand, non-linear model-predictive controllers are used to make this transition optimally.
The examination of this problem was initially addressed in the first of the two publications listed below. There a new version of the DRSM methodology, called DRSM-2, was introduced to model dynamic characteristics over semi-infinite time intervals. An exponential transformation of time achieved this. One of the process examples used in this paper to demonstrate the power of the DRSM-2 data-driven modeling methodology was the transition between steady states of a propylene polymerization process.
In the second paper, two methodological improvements have been introduced, which significantly reduce the required number of experiments and still achieve similar model accuracy. First, a novel design of the experiments combines the previously separate input domains for transitions that increase and decrease a measure of polymer grade. This enables the use of a single DRSM model, instead of the previous two separate ones, and reduces the number of experiments by half. Furthermore, a sequential modeling strategy is proposed, appending experiments to an initial simple design to estimate a more complex DRSM model. As the desired DRSM model complexity is not known a priori, the sequential modeling strategy is critical in achieving the desired model accuracy with the minimum number of experiments. These methodological advances have been tested against one academic and one industrial process simulation.
The methodology has a great promise in developing data-driven dynamic models from historical data, which can then be used in model-predictive control.
References:
Wang, Z. Y. and C. Georgakis (2017), “New Dynamic Response Surface Methodology for Modeling Nonlinear Processes over Semi-infinite Time Horizons” Ind. & Eng. Chem. Res., 56, (38), pp. 10770-82, http://doi.org/10.1021/acs.iecr.7b02381
Wang, Z. Y. and C. Georgakis (2019), “A Dynamic Response Surface Model for Polymer Grade Transitions in Industrial Plants” Ind. & Eng. Chem. Res., 58, (26), pp. 11187-98 , http://doi.org/10.1021/acs.iecr.8b04491