Assessment and Future Directions of Nonlinear Model Predictive ...

Integration of Economical Optimization and Control 431LF M , RFCκ C sRecycle monomerκ V RTCooling waterRecycle tank holdup V RTRecycletankSolvent concentration C STC0F C,inCatalystτF 4C,inUF R,outτ 4,in F MFresh monomerQLCSeparationReactor outlet F R , outMolecular weight M WQConversionµPolymerκ µdesout R F ,κ F R , outDownstreamProcessingFig. 8. Process schematic with the NCO tracking controllers and triggersin the solution model are implemented using the controllers K as depicted inFigure 8. In this study, PI-type controllers are used employing the nominal inputprofiles as feedforward terms. Advanced controllers could also be used forimproved tracking performance (cf. Section 2.2 and [6]). In the designed controlsuperstructure, depending upon the state of the process, one controller overridesthe other. In the classic process control terminology, this type of control structureis referred to as overriding or signal-select controller [14]. Reliable on-linemeasurements or estimates of the constrained variables are necessary for implementingthe NCO tracking strategy using the superstructure solution model.A considerable amount of uncertainty due to different than nominal initialconditions and reactor solvent concentration is present in practice. The proposedNCO tracking superstructure for optimal grade transition is tested forits performance in the presence of uncertainty using the simulated plant model.The PI controllers are tuned for the nominal case. The simulated NCO trackingprofiles of fresh monomer flowrate F M,in and polymer molecular weight M Ware depicted by dash-dotted lines in Figure 9. The transition time t f for theuncertainty case is considerably larger than that for the nominal case, which iscalculated on-line in simulation by using the solution model. The performanceof the NCO tracking solution is compared to a robust solution and optimizationwith known uncertainty in Table 2. The robust solution (column 2 of Table 2)represents a single strategy computed off-line which is feasible for both the nominaland perturbed cases. Such an approach is often used in industrial practiceto avoid real-time optimization. The NCO tracking approach (column 3 ofTable 2) is computed using the decentralized control structure presented inFigure 9. Finally, the numerical optimal solution (column 4 of Table 2) correspondsto the best possible solution that can be computed using full knowledgeof the uncertainty. Table 2 shows that the robust solution is rather poor. In