(528a) Hierarchical Nonlinear Model Predictive Control of Two Time Scale Systems

Authors: 
Baldea, M., The University of Texas at Austin
Daoutidis, P., University of Minnesota
Nagy, Z. K., Loughborough University


The widespread implementation of Nonlinear Model Predictive Control (NMPC) strategies for large, integrated chemical process systems has been hindered by the often overwhelming size of the process models and by their multiple time scale nature and consequent stiffness. These traits dramatically increase the solution time of the associated nonlinear dynamic optimization problems and make online implementation a difficult task. Several efforts have been directed at alleviating the challenges posed by the aforementioned online optimization. Advances in numerical methods have allowed for faster and more efficient online solutions ([1],[2]). In a different vein, a ?divide and conquer? approach to partitioning the plant model has yielded distributed/ decentralized (N)MPC schemes ([3, 4, 5]).

In the present paper, we explore a different avenue for facilitating the implementation of NMPC in plants that feature a two-time scale behavior as a consequence of the strong feedback interactions generated by process integration. We rely on prior results [6] to show that the dynamic behavior of such plants is captured by a system of singularly perturbed ODEs that is in nonstandard form, with a control-dependent equilibrium manifold. We then introduce a framework for simultaneous model reduction and controller synthesis, relying on a composite control approach that consists of linear feedback control for the fast dynamics and a NMPC for the slow dynamics (synthesized using the corresponding reduced-order model). We characterize the stability and optimality properties of the proposed control framework and establish a set of guidelines for implementation in chemical process plants. We argue that the proposed control framework reduces online computation times and, finally, illustrate the developed concepts with a simulation case study.

References

[1] M. Diehl, H.G. Bock, J.P. Schl¨oder, R. Findeisen, Z. Nagy, and F. Allg¨ower. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. J. Proc. Contr., 12(4):577?585, 2002.

[2] L.T. Biegler and V.M. Zavala. Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization. Comput. Chem. Eng., 33(3):575?582, 2009.

[3] T. Keviczky, F. Borrelli, and G.J. Balas. Decentralized receding horizon control for large scale dynamically decoupled systems. Automatica, 42(12):2105? 2115, 2006.

[4] J.B. Rawlings and B.T. Stewart. Coordinating multiple optimization-based controllers: New opportunities and challenges. J. Proc. Contr., 18(9):839?845, 2008.

[5] J. Liu, D.M. de la Pe?na, and P.D. Christofides. Distributed model predictive control of nonlinear process systems. AIChE J., 55(5):1171?1184, 2009.

[6] A. Kumar and P. Daoutidis. Dynamics and control of process networks with recycle. J. Proc. Contr., 12:475?484, 2002.