Decentralized robust tube-based model predictive control: Application to a four-tank -system

  • F. D.J. Sorcia-Vázquez
  • C. D. García-Beltrán
  • G. Valencia-Palomo
  • J. A. Brizuela-Mendoza
  • J. Y. Rumbo-Morales
Keywords: Model predicted control, Decentralized control, Nonlinear control, Robust control.

Abstract

This paper presents a decentralized model predictive controller for nonlinear systems that considers interaction between control inputs. The controller is based on a centralized robust tube-based nonlinear model predictive controller. The main contribution is a procedure to split the process model into s subsystems in order to construct s robust tube-based controllers ensuring a bounded linearization error. In order to show the applicability and effectiveness of the development, the proposed controller is tested on a coupled-tank system and the results are compared with a centralized nonlinear model predictive controller.

References

Richalet J, Rault A, Testud L, Papon J. Model Predictive Heuristic Control: Application to Industrial Processes. J Optimiz Theory App 1978; 14(5): 413-428. doi: 10.1016/0005-1098(78)90001-8.

Cutler C, Ramaker B. Dynamic matrix control- A computer control algorithm. In: Proceeding of th 86th National Meeting of the American Institute of Chemical Engineers (AIChE). ; 1979; Houston, Texas.

Clarke D, Mohtadi C, Tuffs P. Generalized Predictive Control-Part I. The Basic Algorithm. Automatica 1987; 23(2):
137-148. doi: 10.1016/0005-1098(87)90087-2.

Clarke D, Mohtadi C, Tuffs P. Generalized Predictive Control-Part II. Extension and Interpretation. Automatica 1987;
23(2): 149-160. doi: 10.1016/0005-1098(87)90088-4.

Richalet J. Pratique de la commande prédictive. Hermes, France . 1993.

Marquis P, Broustails J. SMOC, a bridge between state space and model predictive controllers: application to the automation of a hydrotreating unit. In: IFAC Model Based Procces. ; 1988; Atlanta, USA: 37-45.

Lee J, Gelormino M, Morari M. Model Predictive Control of Multi-Rate Sample-Data Systems: A Space-State Approach. Int J Control 1992; 55(1): 53-191. doi: 10.1080/00207179208934231.

Lee J, Morari M, Garcia C. Space State interpretation of model predictive control. Automatica 1994; 30(4): 707-717. doi: 10.1016/0005-1098(94)90159-7.

Morari M. Model predictive control: multivariable control technique of choice in the 1990s?. In: Clarke D., ed. Control and Dynamical SystemsOxford University Press; 1994; London: 22-37.

Kwon W, Byun D. Receding horizon tracking control as a predictive control and its stability properties. Int J Control 1989;50(5): 1807-1825. doi: 10.1080/00207178908953467.

Rawlings J, Muske K. The stability of constrained receding horizon control. IEEE T Automat Contr 1993; 38(10): 1512-1516. doi: 10.1109/9.241565.

Mayne D, Rawlings J, Rao P. Constrained model predictive control: Stability and optimality. Automatica 1993; 36(6):
789-814. doi: 10.1109/9.241565.

Bemporad A, Morari M. Robust model predictive control: A survey. In: Garulli A, Tesi A., eds. Robustness in identification and control, Springer London; 1999; London: 207-226.

Chu T, Chen C. Design and Implementation of Model Predictive Control for a Gyroscopic Inverted Pendulum. Appl Sci-Basel 2017; 7(12): 1-18. doi: 10.3390/app7121272.

Patwardhan A, Rawlings J, Edgar T. Nonlinear Model Predictive Control. Chem Eng Commun 1990; 87(1): 123-141. doi:doi.org/10.1080/00986449008940687.

Morari M, Lee J. Model predictive control: past, present and future. Comput and Chem Eng 1999; 23(4): 667-682. doi:doi.org/10.1016/S0098-1354(98)00301-9.

Langson W, Chryssochoos I, Rakovic S. Robust model predictive control using tubes. Automatica 2004; 40(1): 125-133. doi: 10.1016/j.automatica.2003.08.009.

Mayne D, Seron M, Rakovic S. Robust model predictive control of constrained linear systems with bounded disturbances. Automatica 2005; 41(2): 219-224. doi: doi.org/10.1016/j.automatica.2004.08.019.

Mayne D, Kerrigan E, Falugi P. Tube-based robust nonlinear model predictive control. Int J Robust Nonlin 2011; 21(11):1341-1353. doi: 10.1002/rnc.1758.

Gonzalez R, Fiacchini M, Alamo T, Guzman J, Rodriguez F. Online robuts tube-based MPC for time-varying systems: a practical approach. Int J Control 2011; 84(6): 1157-1170. doi: 10.1080/00207179.2011.594093.

Gonzalez R, Fiacchini M, Guzman J, Alamo T, Rodriguez F. Robust tube-based predictive control for mobile robots in
off-road conditions. Robot Auton Syst 2011; 59(10): 711-726. doi: 10.1016/j.robot.2011.05.006.

Cannon M, Kouvaritakis B, Desmond N. Probabilistic tubes in linear stochastic model predictive control. Sys Control Lett. 2009; 58(10): 741-753. doi: 10.1016/j.sysconle.2009.08.004.

Cannon M, Buerger J, Kouvaritakis B, Rakovic S. Robust tubes in Nonlinear Model Predictive Control. IEEE T Automat
Contr 2011; 56(8): 1942-1947. doi: 10.1109/TAC.2011.2135190.

Limon D, Alvarado I, Alamo T, Camacho F. Robust tube-based MPC for tracking of constrained linear systems with additive disturbances. J Process Contr 2010; 20(3): 248-260. doi: 10.1016/j.jprocont.2009.11.007.

Jia D, Krogh B. Distributed Model Predictive Control. In: IEEE American Control Conference. ; 2001; Arlington, USA:
2767-2771.

Camponogara E, Jia D, Krogh B. Distributed Model Predictive Control. IEEE Control Syst Mag 2002; 22(1): 44-52. doi:
10.1109/37.980246.

Venkat A, Hiskens I, Rawlings J, Wright S. Distributed MPC Strategies with Application to Power System Automatic
Generation Control. IEEE T Contr Syst T 2008; 16(6): 1192-1206. doi: 10.1109/TCST.2008.919414.

Vaccarini M, Longhi S, Katebi M. Unconstrained networked decentralized model predictive control. J Process Contr 2009; 19(2): 328-339. doi: 10.1016/j.jprocont.2008.03.005

Sorcia-Vázquez F, Garcia-Beltran C, Valencia-Palomo G, Gerrero-Ramírez G, Adam-Medina M, Escobar-Jiménez R. Distributed Model Predictive Control Applied to a Four Interconnected Tank Process. Rev Iberoam Autom In 2015; 12(2): 365-375. doi: 10.1016/j.riai.2015.07.002

Zheng Y, Zhou J, Xu Y, Zhang Y, Qian Z. A distributed model predictive control based load frequency control scheme for multi-area interconnected power system using discrete-time Laguerre functions. ISA T 2017; 68: 127-140. doi: 10.1016/j.isatra.2017.03.009

Zhang L, Xie W, Liu J. Robust control of saturating systems with Markovian packet dropouts under distributed MPC. ISA T 2019; 85: 49-59. doi: 10.1016/j.isatra.2018.08.027

Trodden P, Richards A. Distributed model predictive control of linear systems with persistent disturbances. Int J Control 2010; 83(8): 1653-1663. doi: 10.1080/00207179.2010.485280

Trodden P, Richards A. Cooperative Tube-based Distributed MPC for Linear Uncertain Systems Coupled Via Constraints. In: Maestre J, Negenbor R., eds. Distributed Model Predictive Control Made Easy. 69. Springer. 2014 (pp. 57-72).

Riverso S, Ferrari-Trecate G. Tube-based distributed control of linear constrained systems. Automatica 2012; 48(11): 2860- 2865. doi: 10.1016/j.automatica.2012.08.024

Buerger J. Fast Model Predictive Control. PhD thesis. University of Oxford, 2013.
Johansson K. The Quadruple-Tank Process: A Multivariable Laboratory with an Adjustable Zero. IEEE T Contr Syst T
2000; 8(3): 456-465. doi: 10.1109/87.845876.

Rumbo-Morales, J., Lopez-Lopez, G., Alvarado, V., Valdez-Martinez, J., Sorcia-Vázquez, F. and Brizuela-Mendoza, J. 2018. SIMULATION AND CONTROL OF A PRESSURE SWING ADSORPTION PROCESS TO DEHYDRATE ETHANOL. Revista Mexicana de Ingeniería Química. 17, 3 (Jul. 2018), 1051-1081. DOI:https://doi.org/10.24275/uam/izt/dcbi/revmexingquim/2018v17n3/Rumbo.

Rodríguez-Mata, A.; Flores-Colunga, G.; Rangel-Peraza, J.; Lizardi-Jiménez, M.; Amabilis-Sosa, L. ESTIMATION OF STATES IN PHOTOSYNTHETIC SYSTEMS VIA CHAINED OBSERVERS:DESIGN FOR A TERTIARY WASTEWATER TREATMENT BY USING Spirulina Maxima ON PHOTOBIORREACTOR. rmiq 2018, 18, 273-287.

M.A. Hernández-Pérez, B. del Muro-Cuéllar, D. Cortés-Rodríguez e I. Araujo-Vargas. STABILIZATION OF THIRD-ORDER SYSTEMS WITH POSSIBLE COMPLEX CONJUGATE POLES AND TIME DELAY. rmiq Vol. 12, No. 2 (2013) 351-360.
Published
2020-01-11
How to Cite
Sorcia-Vázquez, F., García-Beltrán, C., Valencia-Palomo, G., Brizuela-Mendoza, J., & Rumbo-Morales, J. (2020). Decentralized robust tube-based model predictive control: Application to a four-tank -system. Revista Mexicana De Ingeniería Química, 19(3), 1135-1151. https://doi.org/10.24275/rmiq/Sim778
Section
Simulation and control