Abstract
Self-optimizing control focuses on minimizing the steady-state loss for processes in the presence of disturbances by holding selected controlled variables at constant set-points. The loss can further be reduced by controlling linear measurement combinations that have been obtained with the purpose of minimizing either the worst-case loss or the average loss. Since self-optimizing control mainly focuses on the steady-state operation, little emphasis has been put on the dynamic behaviour of the resulting closed-loop system. The general approach is to first compute the optimal controlled variables and then design their respective controllers. However, the optimal measurement combinations, can often (especially if many measurements are used) result in very dynamically complex systems, that makes designing the feedback controllers difficult. In this work, PI controllers and measurement combinations are simultaneously obtained with the aim to find an optimal trade-off between minimizing the steady-state loss and the transient response for the resulting closed-loop system. A solution can be found by solving a bilinear matrix inequality (BMI), which becomes a linear matrix inequality (LMI) by specifying a stabilizing state feedback gain. The optimization problem can also be combined with the sparsity promoting weighted l1-norm, which penalizes the number measurements used and thus, attempts to find an optimal measurement subset. The proposed method requires solving a BMI, for which an iterative LMI approach can be used to find a local optimum, which often seems to give good results, as illustrated on two case studies, consisting of a binary and a Kaibel distillation column.
Highlights
The ever-increasing competitive pressure in the global markets results in the need for continuously improving the performance of chemical processes
Chemical process plants are typically operated with the aid of a multilayer hierarchical control structure, consisting of several layers that address different time scales [1,2]
The economic optimization is usually located in an upper layer and uses real-time optimization (RTO) [3] to compute and send the optimal set-points to the lower layers
Summary
The ever-increasing competitive pressure in the global markets results in the need for continuously improving the performance of chemical processes. If there are large deviations from the optimal operation, caused by, e.g., external disturbances, it would result in an economic loss and could violate some of the operating constraints Both the steady-state (economic) objective and the dynamic performance of the process should be considered when designing the control system. It is economically optimal to operate the plant as close as possible to its active constraints, it is usually necessary to employ some “back off” to avoid dynamic and steady-state problems. The SOC variables should preferably, when subjected to disturbances, drive the process to the new optimal operating point while minimizing deviations in the active constraints (i.e., reducing the “back off”) or in other variables with large economic impact.
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