Novel Approaches to Nonlinear Optimizing Control under Uncertainty
Final Report Abstract
Model Predictive Control (MPC) has become one of the most popular control techniques in the process industries and beyond mainly because of its ability to deal with multiple-input-multipleoutput plants and with constraints on inputs and states. MPC uses a mathematical model of the process to predict the future behavior of the system and to compute control actions that optimize a chosen performance criterion. Therefore its performance can significantly deteriorate in the presence of deviations of the behaviour of the controlled system from the predictions of the model and unmodelled disturbances. In the last years, the development of robust MPC techniques that can handle model uncertainties and disturbances has been widely discussed, but these were rarely applied in practice due to their conservativeness and/ or their computational complexity. This project investigated the concept of multi-stage nonlinear model predictive control (multi-stage NMPC) as a promising non-conservative robust NMPC control scheme, which is applicable in realtime. The approach is based on the representation of the evolution of the plant-model mismatch or disturbances by a scenario tree. It leads to non-conservative robust control of the plant because it takes into account explicitly that new information (usually provided by online measurements) will become available at future time steps and that the future control inputs can be adapted accordingly, thus acting as recourse variables. Therefore, in the optimization of the next input, not one fixed control sequence but a tree of future control inputs is considered which will be applied according to the evolution of the uncertainty. Different aspects of the proposed multi-stage NMPC scheme were studied in detail in the course of the project. Firstly, the formulation of the approach was analyzed from a control theoretic point of view, including a formulation that guarantees stability and constraint satisfaction. Secondly, an efficient implementation was developed which is necessary to deal with one of the challenges of the concept of multi-stage NMPC: the size of the resulting optimization problems. Thirdly, novel algorithms and modifications were proposed to enhance its performance and capabilities. The method has been demonstrated and evaluated using examples mostly from the field of chemical engineering but also from other domains. Extensive simulation studies, including a casestudy of a polymerization reactor provided by industry, and real experiments have been performed during the project. The results show that multi-stage NMPC is a promising strategy for the optimizing control of uncertain nonlinear systems that are subject to hard constraints. It has been also shown that multi-stage NMPC performs significantly better than standard NMPC and better than other robust NMPC approaches presented in the literature while still being implementable in real-time. One of the surprising findings of the project was the observation that already a simple multi-stage NMPC approach with one or two stages over which the most significant uncertain parameters vary and few values of the parameters leads to very good results in practice. Such robust control policies can be computed in real-time for nonlinear plant models of moderate order by the use of state-of-the art numerical solvers. The promising results that were developed within the project have been recognized by the VAA Dissertation Award, awarded to Sergio Lucia for his PhD thesis which contains most of the results of the project (https://www.vaa.de/presse/artikel/news/vaa-stiftungspreis-verliehen-forschung-effizienter-mitindustrie-verknuepfen/).
Publications
- A new robust NMPC scheme and its application to a semi-batch reactor example. In Proc. of the International Symposium on Advanced Control of Chemical Processes, pages 69-74, Singapore, 2012
S. Lucia, T. Finkler, D. Basak and S. Engell
- Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty. Journal of Process Control 23 (9), 1306-1319, 2013
S. Lucia, T. Finkler and S. Engell
(See online at https://doi.org/10.1016/j.jprocont.2013.08.008) - Economic Multi-stage Output Nonlinear Model Predictive Control. In Proc. of the 2014 IEEE Multi-conference on Systems and Control, pages 1837-1842, Antibes, France, 2014
S. Subramanian, S. Lucia and S. Engell
(See online at https://doi.org/10.1109/CCA.2014.6981580) - Handling Uncertainty in Economic Nonlinear Model Predictive Control: a Comparative Case Study. Journal of Process Control 24 (8), 1247-1259, 2014
S. Lucia, J. Andersson, H. Brandt, M. Diehl and S. Engell
(See online at https://doi.org/10.1016/j.jprocont.2014.05.008) - Multi-stage Nonlinear Model Predictive Control with Verified Robust Constraint Satisfaction. In Proc. of the 54th IEEE Conference on Decision and Control, pages 2816-2821, Los Angeles, USA, 2014
S. Lucia; R. Paulen and S. Engell
(See online at https://doi.org/10.1109/CDC.2014.7039821) - Robust multi-stage nonlinear model predictive control. Dissertation, Fakultät für Bio- und Chemieingenieurwesen, Technische Universität Dortmund, 2014. Shaker-Verlag, Aachen, 2015, ISBN: 978-3-8440-3609-1
S. Lucia
