Volume 16, Issue 3 (Journal of Control, V.16, N.3 Fall 2022)                   JoC 2022, 16(3): 35-46 | Back to browse issues page


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Bitarafan M, Ramezani A. Hybrid model predictive control of a nonlinear three-tank system based on the proposed compact form of piecewise affine model. JoC 2022; 16 (3) :35-46
URL: http://joc.kntu.ac.ir/article-1-900-en.html
1- Tarbiat Modares University
Abstract:   (3043 Views)
In this paper, a predictive control based on the proposed hybrid model is designed to control the fluid height in a three-tank system with nonlinear dynamics whose operating mode depends on the instantaneous amount of system states. The use of nonlinear hybrid model in predictive control leads to a problem of mixed integer nonlinear programming (MINLP) which is very complex and time consuming to solve. One way to solve this problem is to approximate nonlinear equations with linear or piecewise affine (PWA) expressions. The linear approximation often has a large error in calculating the operating modes and the system states. The PWA approximation produces less error than the linear approximation, but its computational load is much higher. In this study, with the aim of reducing the computational load, a closed form model has been obtained for the equations of the three-tank system in each of the modes. The resulting system is an PWA, each mode being described by an PWA expression. Predictive control of this system is a mixed integer linear programming problem that can be solved by conventional solvers. To evaluate the performance of the proposed method and the possibility of using it online, the optimal control input sequence is calculated using MOSEK commercial solver in MPT toolbox, and at any sampling time only the first member of the sequence is applied to the precise modeled three-tank system in the Simulink/Stateflow environment. The simulation results indicate that the proposed controller performs the tracking efficiently and the constraints on the system states are also satisfied.
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Type of Article: Research paper | Subject: Special
Received: 2021/09/18 | Accepted: 2022/05/11 | ePublished ahead of print: 2022/05/23

References
1. [1] Andersen ED and Andersen KD (2000) The mosek interior point optimizer for linear programming: an implementation of the homogeneous algorithm. In: High performance optimization. Springer, pp. 197-232. [DOI:10.1007/978-1-4757-3216-0_8]
2. [2] Bemporad A, Mignone D and Morari M (1999) Moving horizon estimation for hybrid systems and fault detection. In: Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251), volume 4. IEEE, pp. 2471-2475.
3. [3] Bemporad A and Morari M (1999) Control of systems integrating logic, dynamics, and constraints. Automatica 35(3): 407-427. [DOI:10.1016/S0005-1098(98)00178-2]
4. [4] Blanke M, Kinnaert M, Lunze J, Staroswiecki M and Schr¨oder J (2006) Diagnosis and fault-tolerant control, volume 2. Springer.
5. [5] B¨ohme TJ and Frank B (2017) Hybrid systems, optimal control and hybrid vehicles. Cham, CH: Springer International. [DOI:10.1007/978-3-319-51317-1]
6. [6] Camacho EF and Alba CB (2013) Model predictive control. Springer science & business media.
7. [7] Camacho EF, Ram'ırez DR, Lim'on D, De La Pe˜na DM and Alamo T (2010) Model predictive control techniques for hybrid systems. Annual reviews in control 34(1): 21-31. [DOI:10.1016/j.arcontrol.2010.02.002]
8. [8] Farias AO, Queiroz GAC, Bessa IV, Medeiros RLP, Cordeiro LC and Palhares RM (2018) Sim3tanks: a benchmark model simulator for process control and monitoring. IEEE Access 6: 62234-62254. [DOI:10.1109/ACCESS.2018.2874752]
9. [9] Geyer T (2005) Low complexity model predictive control in power electronics and power systems. Cuvillier Verlag.
10. [10] Hariprasad K and Bhartiya S (2016) A computationally efficient robust tube based mpc for linear switched systems. Nonlinear Analysis: Hybrid Systems 19: 60-76. [DOI:10.1016/j.nahs.2015.07.002]
11. [11] Heemels WP, De Schutter B and Bemporad A (2001) Equivalence of hybrid dynamical models. Automatica 37(7): 1085-1091. [DOI:10.1016/S0005-1098(01)00059-0]
12. [12] Heiming B and Lunze J (1999) Definition of the three-tank benchmark problem for controller reconfiguration. In: 1999 European Control Conference (ECC). IEEE, pp. 4030-4034. [DOI:10.23919/ECC.1999.7099963]
13. [13] Ingole, D., Drgoˇna, J., and Kvasnica, M. (2017) Offset-free hybrid model predictive control of bispectral index in anesthesia. In: 2017 21st International Conference on Process Control (PC), IEEE, pp. 422-427. [DOI:10.1109/PC.2017.7976251]
14. [14] Kvasnica M, Grieder P and Baoti'c M (2004a) Multi-Parametric Toolbox (MPT). URL http://control.ee.ethz.ch/˜MPT/. [DOI:10.1007/978-3-540-24743-2_30]
15. [15] Kvasnica M, Grieder P, Baoti'c M and Morari M (2004b) Multiparametric toolbox (MPT). In: International workshop on hybrid systems: Computation and control. Springer, pp. 448-462. [DOI:10.1007/978-3-540-24743-2_30]
16. [16] Lazar M (2006) Model predictive control of hybrid systems: stability and robustness. PhD Thesis, Eindhoven: Technische Universiteit Eindhoven DOI: 10.6100/IR612103.
17. [17] Lunze J and Lamnabhi-Lagarrigue F (2009) Handbook of hybrid systems control: theory, tools, applications. Cambridge University Press. [DOI:10.1017/CBO9780511807930]
18. [18] Mattone R and De Luca A (2006) Nonlinear fault detection and isolation in a three-tank heating system. IEEE Transactions on Control Systems Technology 14(6): 1158-1166. [DOI:10.1109/TCST.2006.880221]
19. [19] Mignone D (2002) Control and estimation of hybrid systems with mathematical optimization. PhD Thesis, ETH Zurich.
20. [20] Nandola NN and Bhartiya S (2008) A multiple model approach for predictive control of nonlinear hybrid systems. Journal of process control 18(2): 131-148. [DOI:10.1016/j.jprocont.2007.07.003]
21. [21] Sarailoo M, Rezaie B and Rahmani Z (2014) Fuzzy predictive control of three-tank system based on a modeling framework of hybrid systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 228(6): 369-384. [DOI:10.1177/0959651814524948]
22. [22] Sathishkumar K, Kirubakaran V and Radhakrishnan T (2018) Real time modeling and control of three tank hybrid system, Chemical Product and Process Modeling 13(1). [DOI:10.1515/cppm-2017-0016]
23. [23] Siavash, M., Sheikholeslam, F., Askari, J., & Hajshirmohammadi, S. (2015). Asynchronous control and stabilization of linear switched systems with unstabilizable subsystems by average dwell time approach, Journal of Control, vol. 9, no. 2, pp. 59-69.
24. [24] Sontag E (1981) Nonlinear regulation: The piecewise linear approach. IEEE Transactions on automatic control 26(2): 346-358. [DOI:10.1109/TAC.1981.1102596]
25. [25] Sz˝ucs A, Kvasnica M and Fikar M (2012) Optimal piecewise affine approximations of nonlinear functions obtained from measurements. IFAC Proceedings Volumes 45(9): 160-165. [DOI:10.3182/20120606-3-NL-3011.00061]
26. [26] Thomas J, Dumur D, Buisson J and Gu'eguen H (2006) Model predictive control for hybrid systems under a state partition based mld approach (spmld). In: Informatics in Control, Automation and Robotics I. Springer, pp. 217-224. [DOI:10.1007/1-4020-4543-3_26]
27. [27] Torrisi FD and Bemporad A (2004) Hysdel-a tool for generating computational hybrid models for analysis and synthesis problems. IEEE transactions on control systems technology 12(2): 235-249. [DOI:10.1109/TCST.2004.824309]
28. [28] Yang H, Jiang B and Cocquempot V (2010) Fault tolerant control and hybrid systems. In: Fault Tolerant Control Design for Hybrid Systems. Springer, pp. 1-9. [DOI:10.1007/978-3-642-10681-1_1]

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