(595e) Robust Set-Point Optimization in Close-Loop Control Systems

To guarantee product quality, the common procedure in industrial practice is to select an extremely conservative set-point value. This implicates that the product quality will be unnecessarily much higher than specified and, thus, the operation costs will be much higher than necessary. Moreover, the use of feedback control in order to compensate uncertainties can not ensure compliance of constraints on open-loop variables. Thus, a close-loop control requires on-line measured values of controlled variables. Many variables in the engineering practice can not, though, be measured on-line. These variables often represent the product quality and, thus, their control is desired. To overcome this problem, measurable variables are chosen as controlled variables in order to control the product quality indirectly. Consequently, an optimal set of set-points for the controllers is needed which should be robust against uncertainties.

In this work, we present a novel framework for set-point optimization in close-loop control systems under uncertainty. The developed framework includes a chance-constrained approach where the known properties of some major disturbances can be integrated in the control problem formulation. The uncertainties are described with stochastic distributions, which can be achieved based on historical data. The solution of the chance-constrained control problem has the feature of prediction, robustness and being closed-loop [1].

The proposed framework has been implemented for a pilot plant. Here, a high-pressure column embedded in a coupled two-pressure column system for the separation of an azeotropic mixture is considered. The operating point is defined by the distillate and bottom product specifications, as well as the maximum pressure of the considered high-pressure column. Thus, the implementation of the nominal optimal decisions is realized dividing the optimal operation problem in two decentralized sub-problems. The first problem is concerned with the pressure control problem. In the second one, the reboiler duty and reflux ratio are manipulated in order to operate the product concentrations as close as possible at the product specifications. Furthermore, for the decision of a suitable feed tray we use NLP reformulations with constraint qualification [2]. In order to satisfy the operational constraints the nominal optimal decisions are adjusted cyclical. Closed-loop deviations and model uncertainty are explicitly considered in the problem formulation guaranteeing a feasible and optimal operation. The efficiency and robustness of the developed approaches are demonstrated for different experimental scenarios on the high-pressure column distillation system.

[1] H. Arellano-Garcia; T. Barz; G. Wozny, 2007. Close Loop Stochastic Dynamic Optimization under Probabilistic Output-Constraints. In Assessment and Future Directions of NMPC. Springer, Berlin, 2007.

[2] O. Stein, J. Oldenburg, W. Marquardt, 2004. Continuous reformulations of discrete- continuous optimization problems. Computers & Chemical Engineering, 28 (10), 2004, 1951 ? 1966.