Stability analysis of two-degree-of-freedom control via constructing a linear continuous-time periodic system: Application to rotary inverted pendulum.
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| Title: | Stability analysis of two-degree-of-freedom control via constructing a linear continuous-time periodic system: Application to rotary inverted pendulum. |
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| Authors: | Li, Yue1,2 (AUTHOR), Xin, Xin1,2,3 (AUTHOR) xxin100@seu.edu.cn |
| Source: | Journal of Vibration & Control. May2026, Vol. 32 Issue 9/10, p2267-2277. 11p. |
| Subjects: | Stability theory, Inverted pendulum (Control theory), Feedforward control systems, Dynamical systems, State feedback (Feedback control systems), Feedback control systems, Matrices (Mathematics) |
| Abstract: | In this paper, we introduce a stability analysis approach for systems with two-degree-of-freedom control by converting the linear continuous time-varying system into a periodic one and applying the stability criterion of linear continuous-time periodic (LCP) systems. We illustrate this approach with swing-up task of a rotary inverted pendulum system. It includes three steps. First, we design a periodic orbit by adding a (virtual) swing-down phase. Second, we design a periodic controller which alternates between the swing-up and swing-down controllers in a piecewise manner. In the swing-up phase, the swing-up controller comprises both feedforward and feedback controllers. The feedforward controller and the corresponding nominal trajectory are developed by solving a two-point boundary value problem. The feedback controller is then designed by linearizing around the nominal trajectory and utilizing the LQR state feedback and zero-order hold methods. In the swing-down phase, the swing-down controller is designed using the similar process of the swing-up controller. Third, we directly analyze the stability of the periodic system by applying the stability criterion for LCP systems. The stability of the swing-up phase is naturally ensured by the stability of the periodic system, as the swing-up and swing-down phases together form the periodic cycle. This idea eliminates the numerical calculations of the state transition matrices of LCP systems. Experimental results validate the effectiveness of the proposed periodic controller and the stability of the proposed periodic system. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Vibration & Control is the property of Sage Publications, Ltd. 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193250562 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Stability analysis of two-degree-of-freedom control via constructing a linear continuous-time periodic system: Application to rotary inverted pendulum. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Yue%22">Li, Yue</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xin%2C+Xin%22">Xin, Xin</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> xxin100@seu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Vibration+%26+Control%22">Journal of Vibration & Control</searchLink>. May2026, Vol. 32 Issue 9/10, p2267-2277. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Inverted+pendulum+%28Control+theory%29%22">Inverted pendulum (Control theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Feedforward+control+systems%22">Feedforward control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22State+feedback+%28Feedback+control+systems%29%22">State feedback (Feedback control systems)</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we introduce a stability analysis approach for systems with two-degree-of-freedom control by converting the linear continuous time-varying system into a periodic one and applying the stability criterion of linear continuous-time periodic (LCP) systems. We illustrate this approach with swing-up task of a rotary inverted pendulum system. It includes three steps. First, we design a periodic orbit by adding a (virtual) swing-down phase. Second, we design a periodic controller which alternates between the swing-up and swing-down controllers in a piecewise manner. In the swing-up phase, the swing-up controller comprises both feedforward and feedback controllers. The feedforward controller and the corresponding nominal trajectory are developed by solving a two-point boundary value problem. The feedback controller is then designed by linearizing around the nominal trajectory and utilizing the LQR state feedback and zero-order hold methods. In the swing-down phase, the swing-down controller is designed using the similar process of the swing-up controller. Third, we directly analyze the stability of the periodic system by applying the stability criterion for LCP systems. The stability of the swing-up phase is naturally ensured by the stability of the periodic system, as the swing-up and swing-down phases together form the periodic cycle. This idea eliminates the numerical calculations of the state transition matrices of LCP systems. Experimental results validate the effectiveness of the proposed periodic controller and the stability of the proposed periodic system. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Vibration & Control is the property of Sage Publications, Ltd. 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: 10.1177/10775463251330670 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 2267 Subjects: – SubjectFull: Stability theory Type: general – SubjectFull: Inverted pendulum (Control theory) Type: general – SubjectFull: Feedforward control systems Type: general – SubjectFull: Dynamical systems Type: general – SubjectFull: State feedback (Feedback control systems) Type: general – SubjectFull: Feedback control systems Type: general – SubjectFull: Matrices (Mathematics) Type: general Titles: – TitleFull: Stability analysis of two-degree-of-freedom control via constructing a linear continuous-time periodic system: Application to rotary inverted pendulum. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Yue – PersonEntity: Name: NameFull: Xin, Xin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10775463 Numbering: – Type: volume Value: 32 – Type: issue Value: 9/10 Titles: – TitleFull: Journal of Vibration & Control Type: main |
| ResultId | 1 |
