A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case Study
This paper presents a systematic approach of formulating a Time-Varying Model Predictive Control (TV-MPC) framework for uncertain and under-actuated mechanical systems. The proposed methodology utilizes the nonlinear decomposed dynamics in conjunction with a special class of orthonormal basis functi...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10258265/ |
| _version_ | 1797668030782636032 |
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| author | Farrukh Waheed Imran Khan Yousufzai Michael Valasek |
| author_facet | Farrukh Waheed Imran Khan Yousufzai Michael Valasek |
| author_sort | Farrukh Waheed |
| collection | DOAJ |
| description | This paper presents a systematic approach of formulating a Time-Varying Model Predictive Control (TV-MPC) framework for uncertain and under-actuated mechanical systems. The proposed methodology utilizes the nonlinear decomposed dynamics in conjunction with a special class of orthonormal basis functions – the Laguerre functions in the model structure. A possible numerical ill-conditioning problem, for large prediction horizons, has been coped with using the idea of exponential data weighting in the cost function, which results in condition number improvement, for the main TV-MPC algorithm. A rotary inverted pendulum is considered as a case study under-actuated system. The content of this research revolves around the TV-MPC treatment for cubic polynomial type reference position tracking problem using the decomposed nonlinear dynamics in the TV-MPC model structure and using Laguerre functions for future control trajectory modeling and motion predictions of the rotary servo arm and the pendulum bar. Finally, the applicability of TV-MPC algorithm is demonstrated with the help of simulation results for the subject benchmark system. |
| first_indexed | 2024-03-11T20:22:09Z |
| format | Article |
| id | doaj.art-3c812f7f0bc24a8a9b4cbbf4b60d762d |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-11T20:22:09Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-3c812f7f0bc24a8a9b4cbbf4b60d762d2023-10-02T23:01:05ZengIEEEIEEE Access2169-35362023-01-011110363610364910.1109/ACCESS.2023.331810810258265A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case StudyFarrukh Waheed0https://orcid.org/0000-0002-2736-3106Imran Khan Yousufzai1https://orcid.org/0000-0001-8499-3078Michael Valasek2Faculty of Mechanical Engineering, Czech Technical University in Prague, Prague, Czech RepublicDepartment of Electrical, Electronics and Computer Systems Engineering, College of Engineering and Technology, University of Sargodha, Sargodha, PakistanFaculty of Mechanical Engineering, Czech Technical University in Prague, Prague, Czech RepublicThis paper presents a systematic approach of formulating a Time-Varying Model Predictive Control (TV-MPC) framework for uncertain and under-actuated mechanical systems. The proposed methodology utilizes the nonlinear decomposed dynamics in conjunction with a special class of orthonormal basis functions – the Laguerre functions in the model structure. A possible numerical ill-conditioning problem, for large prediction horizons, has been coped with using the idea of exponential data weighting in the cost function, which results in condition number improvement, for the main TV-MPC algorithm. A rotary inverted pendulum is considered as a case study under-actuated system. The content of this research revolves around the TV-MPC treatment for cubic polynomial type reference position tracking problem using the decomposed nonlinear dynamics in the TV-MPC model structure and using Laguerre functions for future control trajectory modeling and motion predictions of the rotary servo arm and the pendulum bar. Finally, the applicability of TV-MPC algorithm is demonstrated with the help of simulation results for the subject benchmark system.https://ieeexplore.ieee.org/document/10258265/Time-varying MPC (TV-MPC)orthonormal basis functionsLaguerre functionsnumerical ill-conditioningcubic polynomialsdynamic decomposition |
| spellingShingle | Farrukh Waheed Imran Khan Yousufzai Michael Valasek A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case Study IEEE Access Time-varying MPC (TV-MPC) orthonormal basis functions Laguerre functions numerical ill-conditioning cubic polynomials dynamic decomposition |
| title | A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case Study |
| title_full | A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case Study |
| title_fullStr | A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case Study |
| title_full_unstemmed | A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case Study |
| title_short | A TV-MPC Methodology for Uncertain Under-Actuated Systems: A Rotary Inverted Pendulum Case Study |
| title_sort | tv mpc methodology for uncertain under actuated systems a rotary inverted pendulum case study |
| topic | Time-varying MPC (TV-MPC) orthonormal basis functions Laguerre functions numerical ill-conditioning cubic polynomials dynamic decomposition |
| url | https://ieeexplore.ieee.org/document/10258265/ |
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