Assessment and Future Directions of Nonlinear Model Predictive ...

Experiences with Nonlinear MPC in Polymer Manufacturing 395to maximize conversion. It is extremely important that this secondary objectiveis not weighted against the melt index and gloss targets as the conversionoptimization is only important when the gloss and melt index are within theirlimits. Explicit ranking guarantees this. Without ranking it would be possiblethat under certain circumstances that the controller may calculate that slightlyviolating limits was less costly than maximizing peak temperatures and thiswould be unacceptable.6.4 Move PlanThere are severe requirements for the MV move plan. It needs to be executing reliablyat least once a minute, for some applications less than a minute. Typicalcontroller sizes vary between 5 × 5and30× 30 for each tier of the cascaded structure,with a control horizon that may be several hours, particularly on gas phaseprocesses. Typically all the controllers in a cascaded architecture will run on thesame box. A feasible path algorithm is necessary so that sub-optimal solutions canbe used in the (very unlikely) event that cycle time is insufficient to converge. Inpractice we typically see times of a few seconds for solving these types of problemduring transitions, much less for in-grade operation. The practical means to solvethese problems include intelligent blocking of moves and coincident points alongthe CV horizons. The general form of the move plan objective is:Φ = Φ CV T rajectoryP enalty + Φ MV TrajectoryPenalty CV ConstraintHandling+ ΦMV MoveSuppresion+ΦThe first two terms penalize deviation from the CV and MV trajectories, respectively,that join the current point to the calculated steady state target. Thesetrajectories can be tuned online and provide a handle for controlling the aggressivenessof the controller on a per-CV and per-MV basis.One of the important practical requirements for doing polymer transitions,especially in the case of a UNIPOL gas phase process for which the qualitieshave very slow dynamics, is for the control law to support overshoot strategies asdescribed earlier in this paper. This type of strategy is implemented by aggressiveCV trajectories, high CV trajectory penalties, low MV trajectory penalties, andlow MV move suppression.CV constraints are handled by means of L1 penalty treatment as described in [3]and [7]. In L1 penalty treatment, as opposed to L2 penalty treatment, constraintsare exactly satisfied if there is a feasible solution, and the constrained system hasstability characteristics identical to the corresponding unconstrained case.The objective is optimized using a Multi-step Newton-type algorithm as describedin [2] and [4].Another practical issue occurs when the calculated steady state solution liesoutside the operating limits - particularly in the presence of large disturbances.In these situations it is undesirable for the controller to aggressively pursue thisinfeasible steady state solution and the control law must be aware of these typesof situation and act appropriately.