Comparative Study of Simplified Models of the Planar Inverted Pendulum: Dynamics and Control.
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| Title: | Comparative Study of Simplified Models of the Planar Inverted Pendulum: Dynamics and Control. |
|---|---|
| Authors: | Alvarez, Paul1 (AUTHOR) palvarez@unitru.edu.pe, Vaiana, Nicolò1 (AUTHOR) nicolo.vaiana@unina.it |
| Source: | Modelling & Simulation in Engineering. 7/1/2026, Vol. 2026, p1-20. 20p. |
| Subjects: | Inverted pendulum (Control theory), Dynamic models, Computer simulation, Model validation, Bond graphs, Reduced-order models, Nonlinear control theory |
| Abstract: | The inverted pendulum is one of the most studied systems in automatic control, serving as a testbed for new control strategies. One of its variants is the planar inverted pendulum, which consists of a pendulum articulated to a mobile base that moves in a horizontal plane. Although this system has been widely studied, the models employed are simplified and a formulation that captures its full dynamics is still lacking. Moreover, the impact of these simplifications has not yet been assessed. In this research, using the bond graph methodology, a complete and energetically coherent dynamic model of the planar inverted pendulum is developed. No previous work provides a dynamic model with this level of detail. This model was validated by comparing it with a Simulink reference model. Eight simplified models were built and compared using open‐loop and closed‐loop simulations with a hybrid nonlinear control strategy. The results show that most simplified models exhibit closed‐loop responses that closely match those of the full dynamics model, whereas under open‐loop conditions significant discrepancies arise in some cases. The study also demonstrates that controllers designed using simplified models can achieve performance comparable to that obtained with a controller designed from the full dynamics model. These findings provide strong support for the widespread use of simplified models for controller design, analysis, and simulation of the planar inverted pendulum and similar systems. [ABSTRACT FROM AUTHOR] |
| Copyright of Modelling & Simulation in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 195000167 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Comparative Study of Simplified Models of the Planar Inverted Pendulum: Dynamics and Control. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Alvarez%2C+Paul%22">Alvarez, Paul</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> palvarez@unitru.edu.pe</i><br /><searchLink fieldCode="AR" term="%22Vaiana%2C+Nicolò%22">Vaiana, Nicolò</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> nicolo.vaiana@unina.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Modelling+%26+Simulation+in+Engineering%22">Modelling & Simulation in Engineering</searchLink>. 7/1/2026, Vol. 2026, p1-20. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Inverted+pendulum+%28Control+theory%29%22">Inverted pendulum (Control theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+models%22">Dynamic models</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Model+validation%22">Model validation</searchLink><br /><searchLink fieldCode="DE" term="%22Bond+graphs%22">Bond graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Reduced-order+models%22">Reduced-order models</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+control+theory%22">Nonlinear control theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The inverted pendulum is one of the most studied systems in automatic control, serving as a testbed for new control strategies. One of its variants is the planar inverted pendulum, which consists of a pendulum articulated to a mobile base that moves in a horizontal plane. Although this system has been widely studied, the models employed are simplified and a formulation that captures its full dynamics is still lacking. Moreover, the impact of these simplifications has not yet been assessed. In this research, using the bond graph methodology, a complete and energetically coherent dynamic model of the planar inverted pendulum is developed. No previous work provides a dynamic model with this level of detail. This model was validated by comparing it with a Simulink reference model. Eight simplified models were built and compared using open‐loop and closed‐loop simulations with a hybrid nonlinear control strategy. The results show that most simplified models exhibit closed‐loop responses that closely match those of the full dynamics model, whereas under open‐loop conditions significant discrepancies arise in some cases. The study also demonstrates that controllers designed using simplified models can achieve performance comparable to that obtained with a controller designed from the full dynamics model. These findings provide strong support for the widespread use of simplified models for controller design, analysis, and simulation of the planar inverted pendulum and similar systems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Modelling & Simulation in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1155/mse/9353684 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 1 Subjects: – SubjectFull: Inverted pendulum (Control theory) Type: general – SubjectFull: Dynamic models Type: general – SubjectFull: Computer simulation Type: general – SubjectFull: Model validation Type: general – SubjectFull: Bond graphs Type: general – SubjectFull: Reduced-order models Type: general – SubjectFull: Nonlinear control theory Type: general Titles: – TitleFull: Comparative Study of Simplified Models of the Planar Inverted Pendulum: Dynamics and Control. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Alvarez, Paul – PersonEntity: Name: NameFull: Vaiana, Nicolò IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: 7/1/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 16875591 Numbering: – Type: volume Value: 2026 Titles: – TitleFull: Modelling & Simulation in Engineering Type: main |
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