Optimization of Low-Level Controllers and High-Level Polymer Grade Changes

Abstract: Two design problems at different levels in the control hierarchy are considered; optimization of robust low-level controllers with constrained control signal activity and optimization of economical high-level polyethylene grade changes. As for the first design problem, a constraint on control signal activity due to measurement noise is presented and used when optimizing and comparing PI/PID controllers with measurement filters of different orders. The results show increased performance when roll-off is present in the feedback loop and that similarities exist between PID and high-order Youla-parametrized controllers. Robustness margins separating the dead-time uncertainty from other process uncertainties are presented. Methods to compute the margins, posed as optimization problems based on Nyquist diagram interpretations, are given. PID and predictive PI (PPI) controllers with measurement filters are optimized and compared using the presented control signal activity constraint and robustness margins. The two controllers show similar performance on industrially representative processes, with a few exceptions where the PID controller outperforms the PPI controller. Concerning the second design problem mentioned above, a cost function for optimization of economical polyethylene grade changes is proposed. It considers inflow costs, on- and off-grade polymer production revenues and polymer quality variable intervals to define on-grade production as well as economical incentives for on-target production. Using the JModelica.org platform, several stationary operating points and dynamic grade changes are optimized with regards to economy. The optimizations are based on Modelica models of both a gas-phase polyethylene reactor and the polyethylene plant PE3 at Borealis AB. The results show that economically optimal grade changes can be divided into three phases with distinguishing features, and that the synchronization of control flows and the usage of recycle area off-gas flows are important. A Modelica library for the plant PE3 at Borealis AB, including three reactors and three distillation columns, is presented.