Unconstrained and Constrained Model Predictive Control for a Modified Quadruple Tank System

Sazuan Nazrah Mohd. Azam, John Bagterp Jørgensen

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

In this paper, an implementation of Model Predictive Control (MPC) for a Modified Quadruple Tank System (MQTS) is addressed. The MQTS system is a multi-input-multi-output (MIMO) system and has complicated variables interactions. The aim of this work is to demonstrate the implementation of MPC, including the derivations of unconstrained and constrained MPC equations for the particular system. Besides that, we want to evaluate the performance of the MPCs in terms of the behaviour of the system and to verify should the realisations are physically feasible. For the purpose of the study, a linear discrete-time state space model is employed. The model is from an existing dynamics of the system which comprises deterministic and stochastic components. As for the controller, the MPC consists of a state estimator and a constrained regulator. A Kalman filter is incorporated to estimate the current state from the filtered part while the predictions part is used by the constrained regulator, which is an Optimal Control Problem (OCP) to predict the future output trajectory. The objective of the OCP consists of a tracking error term that penalizes deviations of the predicted outputs from the setpoint and a regularization term that penalizes the changes in the inputs (manipulated variables). The resulting OCP is represented as a Quadratic Programming (QP) is solved and the performance of MPC is demonstrated through simulations using MATLAB.
Original languageEnglish
Title of host publicationProceedings of 2018 IEEE Conference on Systems, Process and Control
PublisherIEEE
Publication date2018
Pages147-152
ISBN (Print)9781538663271
DOIs
Publication statusPublished - 2018
Event2018 IEEE Conference on Systems, Process and Control - Hatten Hotel, Melaka, Malaysia
Duration: 14 Dec 201815 Dec 2018

Conference

Conference2018 IEEE Conference on Systems, Process and Control
LocationHatten Hotel
CountryMalaysia
CityMelaka
Period14/12/201815/12/2018

Keywords

  • Mathematical model
  • Stochastic processes
  • Predictive control
  • Regulators
  • Kalman filters
  • Linear programming

Cite this

Mohd. Azam, S. N., & Jørgensen, J. B. (2018). Unconstrained and Constrained Model Predictive Control for a Modified Quadruple Tank System. In Proceedings of 2018 IEEE Conference on Systems, Process and Control (pp. 147-152). IEEE. https://doi.org/10.1109/SPC.2018.8704144
Mohd. Azam, Sazuan Nazrah ; Jørgensen, John Bagterp. / Unconstrained and Constrained Model Predictive Control for a Modified Quadruple Tank System. Proceedings of 2018 IEEE Conference on Systems, Process and Control. IEEE, 2018. pp. 147-152
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Mohd. Azam, SN & Jørgensen, JB 2018, Unconstrained and Constrained Model Predictive Control for a Modified Quadruple Tank System. in Proceedings of 2018 IEEE Conference on Systems, Process and Control. IEEE, pp. 147-152, 2018 IEEE Conference on Systems, Process and Control, Melaka, Malaysia, 14/12/2018. https://doi.org/10.1109/SPC.2018.8704144

Unconstrained and Constrained Model Predictive Control for a Modified Quadruple Tank System. / Mohd. Azam, Sazuan Nazrah; Jørgensen, John Bagterp.

Proceedings of 2018 IEEE Conference on Systems, Process and Control. IEEE, 2018. p. 147-152.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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AB - In this paper, an implementation of Model Predictive Control (MPC) for a Modified Quadruple Tank System (MQTS) is addressed. The MQTS system is a multi-input-multi-output (MIMO) system and has complicated variables interactions. The aim of this work is to demonstrate the implementation of MPC, including the derivations of unconstrained and constrained MPC equations for the particular system. Besides that, we want to evaluate the performance of the MPCs in terms of the behaviour of the system and to verify should the realisations are physically feasible. For the purpose of the study, a linear discrete-time state space model is employed. The model is from an existing dynamics of the system which comprises deterministic and stochastic components. As for the controller, the MPC consists of a state estimator and a constrained regulator. A Kalman filter is incorporated to estimate the current state from the filtered part while the predictions part is used by the constrained regulator, which is an Optimal Control Problem (OCP) to predict the future output trajectory. The objective of the OCP consists of a tracking error term that penalizes deviations of the predicted outputs from the setpoint and a regularization term that penalizes the changes in the inputs (manipulated variables). The resulting OCP is represented as a Quadratic Programming (QP) is solved and the performance of MPC is demonstrated through simulations using MATLAB.

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Mohd. Azam SN, Jørgensen JB. Unconstrained and Constrained Model Predictive Control for a Modified Quadruple Tank System. In Proceedings of 2018 IEEE Conference on Systems, Process and Control. IEEE. 2018. p. 147-152 https://doi.org/10.1109/SPC.2018.8704144