“Model Predictive Control with Integral Action: A simple MPC algorithm”

Authors: David Di Ruscio,
Affiliation: Telemark University College
Reference: 2013, Vol 34, No 3, pp. 119-129.

Keywords: MIMO systems, model predictive control, optimal controller, integral action, constraints

Abstract: A simple Model Predictive Control (MPC) algorithm of velocity (incremental) form is presented.The proposed MPC controller is insensitive to slowly varying system and measurement trends and thereforehas integral action. The presented algorithm is illustrated by both simulations and practical experimentson a quadruple tank MIMO process.

PDF PDF (809 Kb)        DOI: 10.4173/mic.2013.3.2

DOI forward links to this article:
[1] Christer Dalen and David Di Ruscio (2016), doi:10.4173/mic.2016.1.4
[2] Guibing Zhu, Jialu Du and Yongchao Liu (2016), doi:10.1109/ICIST.2016.7483430
[3] S. Bhat Vinayambika, I. Thirunavukkarasu, S. Shanmuga Priya, D. Zhang, B. Zi, G. Cui and H. Ding (2016), doi:10.1051/matecconf/20167707008
[4] Zeki O. Ilhan, William P. Wehner and Eugenio Schuster (2016), doi:10.1109/CCA.2016.7587899
[5] Kazumune Hashimoto, Shuichi Adachi and Dimos V. Dimarogonas (2017), doi:10.1109/TAC.2016.2537741
[6] J.K. Woodacre, R.J. Bauer and Rishad Irani (2018), doi:10.1016/j.oceaneng.2018.01.030
[7] Michael Schubert, Kshitij Girigoudar and Rik W. De Doncker (2017), doi:10.1109/PEDS.2017.8289146
[8] Vinayambika S Bhat, I. Thirunavukkarasu, S. Shanmuga Priya, C Shreesha, P. Tandon, W. Wisnoe and M.Z. bin Abdullah (2018), doi:10.1051/matecconf/201815306010
[9] Emma D. Wilson, Quentin Clairon, Robin Henderson and C. James Taylor (2018), doi:10.1016/j.arcontrol.2018.05.001
[10] Monika Rybczak (2018), doi:10.1080/00051144.2018.1499427
[11] Eduardo Camacho, Antonio Gallego, Adolfo Sanchez and Manuel Berenguel (2018), doi:10.3390/en12010003
[12] A.J. Sánchez, A.J. Gallego, J.M. Escaño and E.F. Camacho (2019), doi:10.1016/j.solener.2019.03.094
[13] Tarun Varshney, Shekhar Gehlaut and Sanjay Kumar Bansal (2019), doi:10.1088/1757-899X/594/1/012038
[14] C.U. Dogruer (2019), doi:10.1109/ECMR.2019.8870911
[15] Antonio J. Gallego, Adolfo J. Sánchez, M. Berenguel and Eduardo F. Camacho (2020), doi:10.1016/j.jprocont.2019.09.003
[16] Eduardo Camponogara, Helton Scherer, Lorenz Biegler and Ignacio Grossmann (2020), doi:10.1007/s11081-020-09506-x
[17] Zejiang Wang and Junmin Wang (2020), doi:10.1016/j.conengprac.2020.104482
[18] Isah A. Jimoh, Ibrahim B. Kucukdemiral, Geraint Bevan and Patience E. Orukpe (2020), doi:10.1109/MED48518.2020.9183056
[19] Ezequiel Rodriguez, Ramon Leyva, Christopher D. Townsend, Glen G. Farivar, Josep Pou, Margarita Norambuena and Jose Rodriguez (2020), doi:10.1109/IECON43393.2020.9255123
[20] Vinayak Deshpande and Youmin Zhang (2021), doi:10.1109/ICPS49255.2021.9468237
[21] Afonso Botelho, Baltazar Parreira, Paulo N. Rosa and Joao Miranda Lemos (2021), doi:10.1007/978-3-030-75696-3_2
[22] Xiaoda Hu, Hao Yu, Fei Hao and Yueyang Luo (2022), doi:10.1016/j.nahs.2021.101149
[23] Vinayak Deshpande and Youmin Zhang (2021), doi:10.1142/S2737480721400069
[24] Bruno Scaglioni, Luca Previtera, James Martin, Joseph Norton, Keith L. Obstein and Pietro Valdastri (2019), doi:10.1109/LRA.2019.2893418
[25] Shekhar Gehlaut, Tarun Varshney and Sandeep Gupta (2018), doi:10.1109/EPETSG.2018.8659317
[26] Basil Mohammed Al Hadithi, Jose Miguel Adanez, Mayra Comina and Agustin Jimenez (2022), doi:10.1049/cth2.12247
[27] Camilo Garcia-Tenorio and Alain Vande Wouwer (2022), doi:10.1109/CoDIT55151.2022.9803949
[28] Vinayak Deshpande and Youmin Zhang (2022), doi:10.1016/j.ifacol.2022.07.126
[29] Parinit Angadi, Saffron Anas and Sachit Rao (2022), doi:10.1109/CCTA49430.2022.9966140
[30] Ager Paul, Ibrahim Kucukdemiral and Gerain Bevan (2022), doi:10.1109/ICSC57768.2022.9993951
[31] Nour Bargoth, Christer Dalen and David Di Ruscio (2022), doi:10.4173/mic.2022.3.3
[32] Aravind Ingalalli and Sukumar Kamalasadan (2023), doi:10.1109/TSG.2022.3220714
[33] Se Chan Oh, Tae Jun Song, Min Jun Kim and Kwang Seok Oh (2023), doi:10.1007/s12239-023-0068-8
[34] Johannes R. Marx, Robert Damerius and Torsten Jeinsch (2023), doi:10.1109/MED59994.2023.10185819
[35] Jiung Lee, Sehwan Kim and Kwangseok Oh (2023), doi:10.23919/ICCAS59377.2023.10317026
[36] Thuy Vi Tran and Kyeong-Hwa Kim (2023), doi:10.1109/ACCESS.2023.3342192
[37] Aravind Ingalalli and Sukumar Kamalasadan (2024), doi:10.1109/TII.2023.3280308
References:
[1] Athans, M. Falb, P.L. (1966). Optimal Control: An Introduction to the Theory and its Applications, McGraw-Hill.
[2] Balchen, J.G., Fjeld, M., Solheim, O.A. (1970). Reguleringsteknikk Bind 3, Tapir.
[3] Balchen, J.G., Ljungqvist, D., Strand, S. (1992). State-space predictive control, Modeling, Identification and Control, 1.2:77--112 doi:10.4173/mic.1992.2.2
[4] Bellmann, R. (1957). Dynamic Programming, Princeton University Press.
[5] Bitmead, R.R., Gevers, M., Wertz, V. (1990). Adaptive Optimal Control: The Thinking Man´s GPC, Prentice-Hall.
[6] Bristol, E.H. (1966). On a new measure of interactions for multivariable process control, Transactions on Automatic Control, 1.11:113--114 doi:10.1109/TAC.1966.1098266
[7] Camacho, E.F. Bordons, C. (1995). Model Predictive Control in the Process Industry, Springer-Verlag, Berlin.
[8] Clarke, D.W., Mohtadi, C., Tuffs, P.S. (1987). Generalized Predictive Control-Part I, Automatica, 23(2):137--148 doi:10.1016/0005-1098(87)90087-2
[9] DiRuscio, D. (1996). Combined Deterministic and Stochastic System Identification and Realization: DSR - A Subspace Approach Based on Observations, Modeling, Identification and Control, 1.3:193--230 doi:10.4173/mic.1996.3.3
[10] Di Ruscio, D. (2009). Closed and Open Loop Subspace System Identification of the Kalman Filter, Modeling, Identification and Control, 3.2:71--86 doi:10.4173/mic.2009.2.3
[11] García, C.E., Prett, D.M., Morari, M. (1989). Model predictive control: Theory and practice-A survey, Automatica, 25(3):335--348 doi:10.1016/0005-1098(89)90002-2
[12] Gatzke, E.P., Meadows, E.S., Wang, C., Doyle, F. J.I. (2000). Model based control of a four-tank system, Computers and Chemical Engineering, 24(2):1503--1509 doi:10.1016/S0098-1354(00)00555-X
[13] Huang, B. Kadali, R. (2008). Dynamic Modeling, Predictive Control and Performance Monitoring, Springer.
[14] Jazwinski, A.H. (1989). Stochastic processes and filtering theory, Academic Press.
[15] Johansson, K.H. (2000). Interaction bounds in multivariable control systems, Automatica, 38(2):1045--1051 doi:10.1016/S0005-1098(01)00285-0
[16] Maciejowski, J. (2002). Predictive control: with constraints, Pearson Education.
[17] Maeder, U., Borrelli, F., Morari, M. (2009). Linear offset-free Model Predictive Control, Automatica, 4.2:2214--2222 doi:10.1016/j.automatica.2009.06.005
[18] Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P. O.M. (2000). Constrained model predictive control: Stability and optimality, Automatica. 36(2):789--814 doi:10.1016/S0005-1098(99)00214-9
[19] Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F. (1956). The Mathematical Theory of Optimal Processes, English translation: Interscience 1962.
[20] Propoi, A.I. (1963). Use of linear programming methods for synthesizing sampled-data automatic systems, Automation and remote control, 2.7:837--844.
[21] Qin, S.J. Badgwell, T.A. (2003). A survey of industrial model predictive control technology, Control Engineering Practice, 11(11):733--764 doi:10.1016/S0967-0661(02)00186-7
[22] Ruscio, D.D. (2010). On Tuning PI Controllers for Integrating Plus Time Delay Systems, Modeling, Identification and Control, 3.4:145--164 doi:10.4173/mic.2010.4.3
[23] Ruscio, D.D. (2012). Discrete LQ optimal control with integral action: A simple controller on incremental form for MIMO systems, Modeling, Identification and Control, 3.2:35--44 doi:10.4173/mic.2012.2.1
[24] Ruscio, D.D. Foss, B. (1998). On state space model based predictive control, In IFAC Symposiu on Dynamics and Control of process Systems.DYCOPS-5, Corfu, Greece, June.
[25] Widnall, W.S. (1970). The Minimum-time Thrust-Vector Control Law in the Apollo Lunar-Module Autopilot, Automatica, 6(6):661--671 doi:10.1016/0005-1098(70)90039-7


BibTeX:
@article{MIC-2013-3-2,
  title={{Model Predictive Control with Integral Action: A simple MPC algorithm}},
  author={Di Ruscio, David},
  journal={Modeling, Identification and Control},
  volume={34},
  number={3},
  pages={119--129},
  year={2013},
  doi={10.4173/mic.2013.3.2},
  publisher={Norwegian Society of Automatic Control}
};