Optimizing Control of a Tubular Polymerization Reactor: Comparison of Single Shooting and Full Discretization

The goal of this contribution is to study numeric solution techniques for implementing optimizing control of polymerization processes in tubular reactors with multiple side injections of monomer along the reactor. The configuration of the reactor causes long delays between the inputs and the measurements at the reactor outlet and sharp moving fronts when the inflows are changed. Moreover, the polymerization kinetics are strongly nonlinear. The process is described by 1D partial differential equations along the reactor length. This makes the application of optimizing control based on a rigorous process model challenging. The so called weighted essentially non-oscillatory scheme (WENO) is used to discretize the spatial dimension of the plant model. This method avoids the need for a very large number of discretization points and still the model can be simulated sufficiently accurately. The resulting ode model contains 1600 states and comprises five manipulated variables. We implement the optimizing controller using two different approaches: At first single shooting with control vector parametrization is used which is simple to implement and has fewer decision variables. This is compared to full discretization scheme using orthogonal collocation on finite elements which results in a very large but very sparse and structured nonlinear programing problem. The simulation results show that both approaches have a similar performance and drive the system to a significantly more productive steady state.