Challenges in real-time process optimization arise from the inability to build and adapt accurate models for complex physico-chemical processes. Two main classes of optimization methods are available for handling model uncertainty. In the absence of measurements, a robust optimization approach is typically used, whereby conservatism is introduced to guarantee feasibility for the entire range of expected variations [1]. When measurements are available, adaptive optimization can help adjust to process changes and disturbances, thereby reducing conservatism [2].
This presentation focuses on the latter class of methods. The measurements can be used in different ways to compensate for model uncertainty. A possible classification can be made as follows [3]: (i) model-adaptation methods that use the measurements to update the parameters of the process model before repeating the optimization; (ii) modifier-adaptation methods that adapt constraint and gradient modifiers; and (iii) input-adaptation methods that convert the optimization problem into a feedback control problem. Here, we argue in favor of modifier-adaptation methods, which use a parameterization and measurements that are tailored to the tracking of the necessary conditions of optimality.
Perhaps the key issue in applying modifier-adaptation methods is tied to the fact that the gradients of the plant outputs with respect to the plant inputs, also called experimental gradients, must be available. An accurate estimate of the experimental gradients is indeed necessary for the iterates to yield a KKT point (relative to the plant) upon convergence. A novel way of estimating the experimental gradients is described in this presentation. It is based on the rather natural idea that the expected level of noise in the gradient estimates, as induced by the measurement noise, can be kept sufficiently small by ensuring a certain distance between the successive operating points. In particular, a number of theoretical results are presented regarding the choice of such a distance.
These developments are illustrated for an experimental three-tank system. It consists of three cylinders interconnected in series by two pipes; two pumps (driven by DC motors) supply the leftmost and rightmost columns with liquid (water). The real-time optimization problem is formulated so as to minimize the overall pumping energy needed to maintain the height of liquid in the columns between given limits.
References
[1] Monnigmann M. and Marquardt W., "Steady-state process optimization with guaranteed robust stability and feasibility," AIChE J 49(12):3110-3126, 2003.
[2] Marlin T. E. and Hrymak A. N., "Real-time operations optimization of continuous process," Proc 5th Int Conf on Chemical Process Control (CPC-5), Tahoe City NV, 1997.
[3] Chachuat B., Srinivasan B. and Bonvin D., "Model parameterizaton tailored to real-time optimization," Proc. 18th Eur Symp on Computer Aided Process Engineering (ESCAPE-18), Lyon, France, 2008.