Reports: AC9
48144-AC9 Determining Sets of Parameters to Be Estimated for Nonlinear Model Predictive Control
The use of nonlinear models in process control and monitoring applications in the process industries has become increasingly popular in recent years. This is due to several factors, the most important of them being that highly accurate models can now be solved with modern dynamic simulators and powerful optimization algorithms in real time, and also that tighter environmental regulations and increasing productivity requirements necessitate the use of nonlinear models for some applications. As a variety of software packages for controller design can now be purchased from control vendors, the quality of a particular controller is often more affected by the accuracy of the model that the controller is based upon than by the software implementation of the control algorithm.
A common solution for improving accuracy of a process model is to estimate some of the model parameters from process data. However, the question of which model parameters should be estimated from data is often not systematically addressed and instead parameter set selection is performed based upon experience with the process. This practice can be problematic as determining a good set of parameters for estimation becomes less intuitive as more sophisticated models containing dozens or even hundreds of parameters are used, of which only a handful can be estimated from process data. An additional problem results from nonlinearity of the process. While techniques for parameter set selection exist for linear systems, they cannot take into account that the set of parameters to be estimated may depend upon operating conditions or even upon the nominal values of the parameters to be estimated.
The objective of the conducted work is to systematically address the issue of determining a set of parameters to be estimated. The procedure is specifically geared towards nonlinear systems as changing operating conditions, but also uncertainty in the nominal values of the parameters may change the importance of a chosen parameter set.
The work that has so far been conducted as part of this grant makes three contributions: (1) integrating parameter set selection and experimental design, (2) deriving a computationally-efficient procedure for performing parameter set selection of nonlinear uncertain systems, and (3) determining the number of parameters that should be estimated as part of the parameter set selection procedure.
The first objective of this work has dealt with integrating parameter set selection and experimental design. We formulated an optimization problem where the solution returns both the optimal experimental design and the parameters to be estimated. The problem is of the form of a MINLP and can be computationally expensive to solve. We investigated approaches that decompose the optimization problem such that it becomes tractable for problems of a size of interest to us. This portion of the work has been conducted by Yunfei Chu who is a PhD student in my group and has resulted in one journal and one conference paper.
The second objective of the conducted work was motivated by the complexity of the optimization problem resulting from the previous objective. The approaches used computes the sensitivity vector of individual parameters over time and then uses the angles between sensitivity vectors for hierarchical clustering. This technique is computationally efficient and is able to significantly reduce the size of the optimization problem that needs to be solved. We have illustrated the benefits of this technique by applying it to a chemical reaction network that included over 110 parameters. A problem of this size is intractable using conventional approaches, however, the only a few minutes of computation time on a standard desktop computer are needed using our approach. Thus portion of the work has also been conducted by Yunfei Chu and resulted in one journal and one conference paper.
The third objective of the conducted work deals with determining the number of clusters that should be chosen for performing parameter clustering. We have developed a technique that determines the number of clusters based upon the model structure as well as the uncertainty description of the parameters. It has been shown using statistical techniques that using the developed approach does not only result in improved accuracy over different number of clusters chosen for parameter set selection, but also that the model accuracy is higher than if all parameters were estimated. This work was also for the most part conducted by Yunfei Chu and resulted in one journal paper. Additionally, three undergraduate students (Keith Weatherford, Jacob Heartsfield, and Zuleika Oguendo-Diaz) and Mitch Serpas, a new PhD student in my group, have also contributed to this work and their work has been partially supported by this grant.
Summarizing, the grant PRF# 48144-AC9 partially supported two PhD students, includes contributions from three undergraduate students, and resulted in 3 journal papers and 2 conference papers that acknowledge ACS-PRF support.
