(748f) Optimization of Heterogeneous Batch Reactor Under Parameter Uncertainty

Heterogeneous batch processes are widely used in food, agrochemical
and pharmaceutical industries to generate small amounts of high-priced fine
chemicals. The optimal control of this type of processes is typically aimed to
reduce the batch time, increase conversion and product purity, which ultimately
enhance the profitability of the batch process. The optimal control highly
depends on accurate mathematical models. A first principle model is usually
developed based on fundamental physical and chemical mechanisms, carrying a set
of unknown parameters. Parameter estimation and model discrimination are then
conducted by fitting process data. However, due to model mismatch, measurement
errors and even the absence of variable measurements, the parameters are always
estimated with uncertainties. Exerting the optimal control designed at the
nominal parameter values is likely to violate path and end-point constraints.
In this work, we are going to quantify parameter uncertainty from estimation
and formulate the robust optimal control to act against uncertainty and improve
feasibility, while reducing the batch time.

We firstly introduce a dynamic model of a solid-liquid batch
reactor, the parameters of which are estimated by limited experimental and
plant data. The confidence region of estimated parameters is described by a
hyper-ellipsoid or an arbitrary shape based on linear and nonlinear
approximation [1].

The parameter uncertainty can be addressed in different ways.
Two effective methods, multi-scenario approach and back-off approach, are
implemented. In the multi-scenario approach, the optimal control problem is
formulated initially at the estimated parameter set and extreme points in the
confidence region [2]. Subsequently, the optimal control problem is iteratively
augmented with worst case scenarios, where the largest constraint violations
are observed by Monte Carlo (MC) simulations.  In the back-off approach, a small term is
added to the hard constraint to prevent violations in a high probability. The
value of the back-off term can be approximated by MC simulations or
sensitivities [3]. Both methods are implemented to the heterogeneous batch
reactor case study to improve feasibility of the optimal control design.

References

[1] Albuquerque, João S., Lorenz
T. Biegler, and Robert E. Kass.
"Inference in dynamic error‐in‐variable‐measurement
problems." AIChE journal 43.4
(1997): 986-996.

[2] Rooney, W. C. and Biegler,
L. T. (2001), Design for model parameter uncertainty using nonlinear confidence
regions. AIChE J., 47: 1794-1804.

[2] Diehl, Moritz, Hans Georg Bock, and Ekaterina Kostina. "An approximation technique for robust
nonlinear optimization." Mathematical Programming 107.1 (2006):
213-230.