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MLD-MPC Approach for Three-Tank Hybrid Benchmark Problem

Hanen Yaakoubi1, Hegazy Rezk2, Mujahed Al-Dhaifallah3,4,*, Joseph Haggège1

1 Research Laboratory in Automatic Control (LARA), National Engineering School of Tunis (ENIT), University of Tunis El Manar, Tunis, 1002, Tunisia
2 Department of Electrical Engineering, College of Engineering in Wadi Alddawasir, Prince Sattam bin Abdulaziz University, Wadi Alddawasir, 11911, Saudi Arabia
3 Control and Instrumentation Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia
4 Interdisciplinary Research Center (IRC) for Renewable Energy and Power Systems, King Fahd University of Petroleum & Minerals, Dhahran, 31261, Saudi Arabia

* Corresponding Author: Mujahed Al-Dhaifallah. Email:

Computers, Materials & Continua 2023, 75(2), 3657-3675.


The present paper aims at validating a Model Predictive Control (MPC), based on the Mixed Logical Dynamical (MLD) model, for Hybrid Dynamic Systems (HDSs) that explicitly involve continuous dynamics and discrete events. The proposed benchmark system is a three-tank process, which is a typical case study of HDSs. The MLD-MPC controller is applied to the level control of the considered tank system. The study is initially focused on the MLD approach that allows consideration of the interacting continuous dynamics with discrete events and includes the operating constraints. This feature of MLD modeling is very advantageous when an MPC controller synthesis for the HDSs is designed. Once the MLD model of the system is well-posed, then the MPC law synthesis can be developed based on the Mixed Integer Programming (MIP) optimization problem. For solving this MIP problem, a Branch and Bound (B&B) algorithm is proposed to determine the optimal control inputs. Then, a comparative study is carried out to illustrate the effectiveness of the proposed hybrid controller for the HDSs compared to the standard MPC approach. Performances results show that the MLD-MPC approach outperforms the standard MPC one that doesn’t consider the hybrid aspect of the system. The paper also shows a behavioral test of the MLD-MPC controller against disturbances deemed as liquid leaks from the system. The results are very satisfactory and show that the tracking error is minimal less than 0.1% in nominal conditions and less than 0.6% in the presence of disturbances. Such results confirm the success of the MLD-MPC approach for the control of the HDSs.


Cite This Article

H. Yaakoubi, H. Rezk, M. Al-Dhaifallah, J. Haggège, H. Yaakoubi et al., "Mld-mpc approach for three-tank hybrid benchmark problem," Computers, Materials & Continua, vol. 75, no.2, pp. 3657–3675, 2023.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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