(278a) Nonlinear Model Predictive Control of an Industrial Polymerization Process

Title: Nonlinear Model Predictive Control of an Industrial Polymerization Process

Nonlinear model predictive control (NMPC) is used to maintain and control polymer quality at specified production rates because the polymer quality measures have strong interacting nonlinearities with different temperatures and feed rates. Polymer quality measures that are available from the laboratory infrequently are controlled in closed-loop using a NMPC to set the temperature profile of the reactors. NMPC results in better control of polymer quality measures at different production rates as compared to using the nonlinear process model with reaction kinetics to implement offline targets for reactor temperatures.

Dow's first application of a commercial Nonlinear Model Predictive Control technology that uses the laboratory quality measures in the feedback control loop is presented.

The industrial Nonlinear Model Predictive Control problem has the following challenges

• Long laboratory sampling times for controlled polymer quality attributes (0.5-1 day)
• Varying dead times (2-7 days) and gains (multiplier of 1-20) for controlled polymer quality attributes with respect to reactor temperatures
• Process models need to extend for extremely low feed rates (approximately 35 percent of normal rates)
• Process also occasionally operates with one of the seven reactors bypassed for maintenance
• For the first four reactors, recycle streams can only be manually set for heating or cooling

A Linear Model Predictive Controller (LMPC) will not be able to achieve the process objectives because there are strong nonlinear dependencies for polymer quality attributes with reactor temperatures and feed.

1. Process Description: The industrial polymerization process consists of seven well mixed reactors in series, where the extent of reaction is set by level and temperature in each reactor. The copolymerization of monomer and comonomer is carried out using a catalyst to make a polymer characterized by polymer viscosity, unreacted monomer content and byproduct content. Comonomer composition in the feed is set at a stoichiometric excess value to minimize the unreacted monomer content in the polymer product. The catalyst dissolved in a solvent is also fed separately to the first reactor. The flow rate and composition of the feed streams are measured on-line along with the reactor temperatures and levels. Off-line laboratory measurements are made for the polymer viscosity, unreacted monomer content and byproduct content. Each reactor has a recycle stream, whose temperature is controlled by heating or cooling it. The reactor temperature is controlled by manipulating the recycle stream temperature.
2. Nonlinear Model Predictive Control (NMPC): A validated fundamental kinetic model exists for the process. The model consists of the various reactions taking place in the industrial reactors along with other physical phenomena governing the polymerization process, and has been used historically to maintain polymer quality attributes by evaluating an off-line reactor temperature profile. Aspen Technology Inc.'s Aspen Non-Linear Controller [1] is used as the commercial NMPC controller, thereby requiring development of a bounded-derivative-neural network (BDN) model instead of directly using the fundamental kinetic model. Initial BDN model development was done by using results of numerous fundamental kinetic model cases (approximately 50,000 cases) to cover the operating region of interest. These models were then deployed on-line, and tuned by comparison with real plant data. Over-parameterization of the BDN models was avoided to ensure extrapolation, and suitability for feedback control. The BDN model first derivatives of the controlled variables with respect to reactor temperatures and levels were examined over the operating range to ensure that they were monotonically increasing or decreasing, to match with those from the fundamental kinetic model.
3. Conclusions: The industrial NMPC has been in continuous use since October 2012 to maintain polymer quality at specified production rates. After meeting the polymer quality and feed requirements, the NMPC has been enhanced to minimize the byproduct content. A cascade NMPC scheme was implemented to achieve the process objectives for reactor temperature control and polymer quality specifications that had vastly different settling times, and also to address the computational needs of the associated dynamic optimization problem. Dynamic optimization associated with this nonlinear control problem is computationally very demanding and required the Aspen Technology, Inc.'s software developers to remove program limitations.

References

[1] Turner, P., and J. Guiver, ``Introducing the bounded derivative network—superceding the application of neural networks in control,'' J. Proc. Cont., 15 (4), 407—415 (2005).