Sensitivity-based hierarchical distributed model predictive control of nonlinear processes

Abstract Hierarchical distributed model predictive control (HDMPC) is a promising control framework for industrial processes. With the development of efficient solvers for large-scale nonlinear programming (NLP), the implementation of hierarchical distributed control with nonlinear models becomes achievable. However, there is a lack of systematic method that handles the online computational delay in HDMPC which may lead to deterioration of performance or stability. To speed up online computation, an NLP sensitivity-based HDMPC algorithm is proposed in this paper. The implementation strategy is divided into background and online stages. All the local MPC controllers solve their sub-optimization problems iteratively in background based on the predicted future state, and a sensitivity update step is performed online to correct the predicted optimal inputs. The system-wide sensitivity equation is formulated in the upper control level by combining the optimality information of local controllers. The optimality and stability analysis for the proposed method is given. Three case studies are presented to demonstrate the controller performance.

[1]  Yan Zhang,et al.  Nash-optimization enhanced distributed model predictive control applied to the Shell benchmark problem , 2005, Inf. Sci..

[2]  Karl Henrik Johansson,et al.  The quadruple-tank process: a multivariable laboratory process with an adjustable zero , 2000, IEEE Trans. Control. Syst. Technol..

[3]  Victor M. Zavala,et al.  The advanced-step NMPC controller: Optimality, stability and robustness , 2009, Autom..

[4]  David Q. Mayne,et al.  Model predictive control: Recent developments and future promise , 2014, Autom..

[5]  Moritz Diehl,et al.  Distributed Multiple Shooting for Large Scale Nonlinear Systems , 2014 .

[6]  Frank Allgöwer,et al.  Computational Delay in Nonlinear Model Predictive Control , 2004 .

[7]  J. M. Maestre,et al.  Distributed Model Predictive Control: An Overview and Roadmap of Future Research Opportunities , 2014, IEEE Control Systems.

[8]  Dewei Li,et al.  The stability analysis of distributed model predictive control with limited communication , 2010 .

[9]  Stephen J. Wright,et al.  Cooperative distributed model predictive control for nonlinear systems , 2011 .

[10]  L. Biegler,et al.  Fast economic model predictive control based on NLP-sensitivities , 2014 .

[11]  Lorenz T. Biegler,et al.  Advanced-Multi-Step Nonlinear Model Predictive Control , 2013 .

[12]  L. Biegler,et al.  Fast Offset-Free Nonlinear Model Predictive Control Based on Moving Horizon Estimation , 2010 .

[13]  Riccardo Scattolini,et al.  Robustness and robust design of MPC for nonlinear systems , 2007 .

[14]  Riccardo Scattolini,et al.  Architectures for distributed and hierarchical Model Predictive Control - A review , 2009 .

[15]  Lorenz T. Biegler,et al.  On-line implementation of nonlinear MPC: an experimental case study , 2000 .

[16]  Stephen J. Wright,et al.  Cooperative distributed model predictive control , 2010, Syst. Control. Lett..

[17]  Wolfgang Marquardt,et al.  Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization , 2009 .

[18]  Panagiotis D. Christofides,et al.  Distributed model predictive control: A tutorial review and future research directions , 2013, Comput. Chem. Eng..

[19]  Anthony V. Fiacco,et al.  Introduction to Sensitivity and Stability Analysis in Nonlinear Programming , 2012 .

[20]  Xuejin Yang,et al.  Advances in sensitivity-based nonlinear model predictive control and dynamic real-time optimization , 2015 .

[21]  MORITZ DIEHL,et al.  A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control , 2005, SIAM J. Control. Optim..

[22]  Elling W. Jacobsen,et al.  Performance limitations in decentralized control , 2000 .

[23]  L. Biegler,et al.  Nonlinear Programming Properties for Stable and Robust NMPC , 2015 .

[24]  Jairo Espinosa,et al.  A comparative analysis of distributed MPC techniques applied to the HD-MPC four-tank benchmark , 2011 .

[25]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[26]  Stephen J. Wright,et al.  Stability and optimality of distributed model predictive control , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[27]  Daniel Sarabia,et al.  Price-driven Coordination for Distributed NMPC Using a Feedback Control Law , 2014 .

[28]  Michael Athans,et al.  Survey of decentralized control methods for large scale systems , 1978 .

[29]  Tor Arne Johansen,et al.  Distributed MPC of Interconnected Nonlinear Systems by Dynamic Dual Decomposition , 2014 .

[30]  Panagiotis D. Christofides,et al.  Sequential and Iterative Architectures for Distributed Model Predictive Control of Nonlinear Process Systems , 2010 .

[31]  Jie Bao,et al.  Distributed control of chemical process networks , 2015, Int. J. Autom. Comput..

[32]  Panagiotis D. Christofides,et al.  Networked and Distributed Predictive Control , 2011 .

[33]  Panagiotis D. Christofides,et al.  Distributed model predictive control of nonlinear process systems , 2009 .