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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Main Authors: Hossam S. Abbas, Pablo S. G. Cisneros, Georg Mannel, Philipp Rostalski, Herbert Werner
Format: Article
Language:English
Published: IEEE 2021-01-01
Series:IEEE Access
Subjects:
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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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 L&#x00FC;beck, L&#x00FC;beck, GermanyInstitute of Control Systems, Hamburg University of Technology, Hamburg, GermanyInstitute for Electrical Engineering in Medicine, University of L&#x00FC;beck, L&#x00FC;beck, GermanyInstitute for Electrical Engineering in Medicine, University of L&#x00FC;beck, L&#x00FC;beck, 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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