Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations
In this paper, a practical <italic>model predictive control</italic> (MPC) for tracking desired reference trajectories is demonstrated for controlling a class of nonlinear systems subject to constraints, which comprises diverse mechanical applications. Owing to the <italic>linear p...
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IEEE
2021-01-01
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Online Access: | https://ieeexplore.ieee.org/document/9410253/ |
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author | Hossam S. Abbas Pablo S. G. Cisneros Georg Mannel Philipp Rostalski Herbert Werner |
author_facet | Hossam S. Abbas Pablo S. G. Cisneros Georg Mannel Philipp Rostalski Herbert Werner |
author_sort | Hossam S. Abbas |
collection | DOAJ |
description | In this paper, a practical <italic>model predictive control</italic> (MPC) for tracking desired reference trajectories is demonstrated for controlling a class of nonlinear systems subject to constraints, which comprises diverse mechanical applications. Owing to the <italic>linear parameter-varying</italic> (LPV) formulation of the associated nonlinear dynamics, the online MPC optimization problem is solvable as a single <italic>quadratic programming</italic> (QP) problem of complexity similar to that of LTI systems. For offset-free tracking, based on the notion of <italic>admissible reference</italic>, the controller ensures convergence to any admissible reference while its deviation from the desired reference is penalized in the stage cost of the optimization problem. This mechanism provides a safety feature under the physical limitations of the system. To guarantee stability and recursive feasibility, a terminal cost as a tracking error penalty term and a terminal constraint associated with both the terminal state and the admissible reference are included. We use tube-based concept to deal with the uncertainty of the scheduling parameter over the prediction horizon. Therefore, the online optimization problem is solved for only the nominal system corresponding to the current value of the scheduling parameter and subject to tightened constraint sets. The proposed approach has been implemented successfully in real-time onto a robotic manipulator, the experimental results illustrates its efficiency and practicality. |
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id | doaj.art-3c57b8c71d784d7fa5b9400846c5edac |
institution | Directory Open Access Journal |
issn | 2169-3536 |
language | English |
last_indexed | 2024-12-17T23:28:35Z |
publishDate | 2021-01-01 |
publisher | IEEE |
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series | IEEE Access |
spelling | doaj.art-3c57b8c71d784d7fa5b9400846c5edac2022-12-21T21:28:43ZengIEEEIEEE Access2169-35362021-01-019623806239310.1109/ACCESS.2021.30747419410253Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying RepresentationsHossam S. Abbas0https://orcid.org/0000-0002-5264-5906Pablo S. G. Cisneros1https://orcid.org/0000-0001-8559-9945Georg Mannel2Philipp Rostalski3https://orcid.org/0000-0003-0326-168XHerbert Werner4Institute for Electrical Engineering in Medicine, University of Lübeck, Lübeck, GermanyInstitute of Control Systems, Hamburg University of Technology, Hamburg, GermanyInstitute for Electrical Engineering in Medicine, University of Lübeck, Lübeck, GermanyInstitute for Electrical Engineering in Medicine, University of Lübeck, Lübeck, GermanyInstitute of Control Systems, Hamburg University of Technology, Hamburg, GermanyIn this paper, a practical <italic>model predictive control</italic> (MPC) for tracking desired reference trajectories is demonstrated for controlling a class of nonlinear systems subject to constraints, which comprises diverse mechanical applications. Owing to the <italic>linear parameter-varying</italic> (LPV) formulation of the associated nonlinear dynamics, the online MPC optimization problem is solvable as a single <italic>quadratic programming</italic> (QP) problem of complexity similar to that of LTI systems. For offset-free tracking, based on the notion of <italic>admissible reference</italic>, the controller ensures convergence to any admissible reference while its deviation from the desired reference is penalized in the stage cost of the optimization problem. This mechanism provides a safety feature under the physical limitations of the system. To guarantee stability and recursive feasibility, a terminal cost as a tracking error penalty term and a terminal constraint associated with both the terminal state and the admissible reference are included. We use tube-based concept to deal with the uncertainty of the scheduling parameter over the prediction horizon. Therefore, the online optimization problem is solved for only the nominal system corresponding to the current value of the scheduling parameter and subject to tightened constraint sets. The proposed approach has been implemented successfully in real-time onto a robotic manipulator, the experimental results illustrates its efficiency and practicality.https://ieeexplore.ieee.org/document/9410253/Constrained systemslinear parameter-varying systemsmodel predictive controlrobust stabilityrobotic manipulators |
spellingShingle | Hossam S. Abbas Pablo S. G. Cisneros Georg Mannel Philipp Rostalski Herbert Werner Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations IEEE Access Constrained systems linear parameter-varying systems model predictive control robust stability robotic manipulators |
title | Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations |
title_full | Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations |
title_fullStr | Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations |
title_full_unstemmed | Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations |
title_short | Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations |
title_sort | practical model predictive control for a class of nonlinear systems using linear parameter varying representations |
topic | Constrained systems linear parameter-varying systems model predictive control robust stability robotic manipulators |
url | https://ieeexplore.ieee.org/document/9410253/ |
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