(432f) Model-Based Optimizing Control of a Continuous Polymerization Reactor

Model-based Optimizing Control of a Continuous Polymerization Reactor

R. Hashemi, D. Kohlmann, S. Engell

In this contribution we study the application of an economically online optimizing non-linear model predictive controller (NMPC) to a continuous polymerization reactor. The background of this work is the transfer of polymerization reactions from semi-batch to continuous operation. The goal is to run the process at the economically optimal operation point in the presence of disturbances and model inaccuracies. The polymerization is performed in a tubular reactor which is equipped with three side injections of monomer along the reactor axis besides the feed at the entry of the reactor. Model predictive control is an obvious candidate to control such a multi-input system. While the standard implementations of NMPC use cost functions which penalize the deviation of the states or outputs and possibly of the inputs from the targets and the control moves [4], in this work the controller has been formulated to maximize the product throughput while meeting constraints on product quality [1]. The controller employs a discretized dynamic pde model of the process and optimizes the productivity of the plant online. Using the weighted essentially non-oscillatory (WENO) scheme and following the idea of the method of lines, the spatial domain is discretized. WENO scheme is used to handle the steep concentration fronts and temperature profiles that can occur in the reactor when the feeds are changed abruptly without the necessity for a very fine spatial discretization [2]. The resulting set of ODEs is solved by the Matlab solver ode15s.

For the continuous reactor, maximizing the throughput implies to maximize the sum of all feeds of monomer into the reactor. In order to keep the product quality within the specifications, constraints on the monomer content and on the average molecular weight of the polymer at the outlet of the reactor are applied. The resulting optimization problem is solved using the SNOPT algorithm from the TOMLAB package in a sequential appraoch. To gain information about the current state of the process, online quality measurements are required. However, the number of quality sensors is limited because of the high complexity and costs of the suitable measurement devices. For this study two online quality sensors are utilized as input for the controller. Firstly, the monomer concentration is measured by mid IR spectroscopy, which is assumed to be installed in the last section of the reactor. Secondly, an online sensor for the liquid viscosity at the outlet is available, from which the average molecular weight of polymer is derived. This kind of instrumentation has been established in parallel work within the European research project F3 – Flexible Fast Future Factory [3].

As discussed before, the quality specifications of the product enter as constraints in the optimization problem of the NMPC. These can be formulated as hard or soft constraints. Applying the hard constraints has the advantage that the required product specifications are strictly met and no off-spec products are produced. However, this approach results in slow adaptations of the inputs and consequently long settling time of the controlled variables. Moreover, an optimization problem with hard constraints is more difficult to solve. For the soft constraints case, violation of the controlled variables from the predefined bounds are tolerated but penalized in the cost function. This approach results in a relatively shorter settling time of the controlled variables but off-specs are produced. However, by setting suitable bounds for the quality constraints and by stronger penalties for the violation of these bounds, off-spec production is considerably reduced or even prevented.

It will be demonstrated that by the online economic optimization, a gradual transition to a more favorable operating regime is achieved without or with only very small intermediate violations of the product specifications. In base case considered here, the throughput can be increased by more than 60% compared to a reasonable base case. The reduced residence time is compensated by an elevated reaction temperature.

The performance of the controller has been investigated for several cases of model inaccuracies, namely fouling of the reactor which reduces the heat transfer between the reactor and the jacket, a retardation of the start of the reaction due to impurities in the feed and a mismatch in the temperature of the injected monomer due to different ambient temperatures. For all these cases, a moving horizon estimation method is applied to estimate the uncertain parameters and to update the existing model. Moving horizon estimation (MHE) is an optimization-based approach which uses the current and past measurements to estimate the states or parameters [5]. The simulation results show that this method is effective and that the controller can cope with these inaccuracies properly while meeting the quality constraints.

[1] Engell S. (2007). Feedback Control for Optimal Process Operation Journal of Process Control 17(3), 203–219, 2007.

[2] Bouaswaig A.E. and Engell S. (2009). A new numerical solution scheme for tracking sharp moving fronts Proc.19th European Symposium on Computer Aided Process Engineering, 907–912.

[3] Buchholz S. (project coordinator) 2009. F3-Factory project web page, www.f3-factory.com.

[4] Findeisen R., Allgöwer F. and Nagy M.C. (2004). Nonlinear Model Predictive Control: From Theory to Application J. Chin. Inst. Chem. Engrs., 35, No. 3, 299–315, 939–965.

[5] Muske K.R., Rawlings J.B. and Lee J.H. (1993). Receding horizon recursive state estimation Proceedings of the American Control Conference , 900–904.