Improved eigenvalue sensitivity for finite-precision digital controller realisations via orthogonal Hermitian transform.
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| Title: | Improved eigenvalue sensitivity for finite-precision digital controller realisations via orthogonal Hermitian transform. |
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| Authors: | Yu, W.-S.1, Ko, H.-J.1 |
| Source: | IEE Proceedings -- Control Theory & Applications. Jul2003, Vol. 150 Issue 4, p365. 11p. |
| Subjects: | Digital control systems, Finite element method data processing, Hermitian forms, Eigenvalues |
| Abstract: | An improved eigenvalue sensitivity is presented for digital controller realisations via the orthogonal Hermitian transform, subject to finite word length (FWL) effects. This approach can preserve the stability of the closed-loop system when the designed stabilising digital controllers are actually implemented with FWL by using the mode of fixed-point arithmetic. A performance index defined by eigenvalue sensitivity of the closed-loop system is evaluated by the mixed matrix-2/ Frobenius norms, so that the eigenvalues of the closed-loop system, from infinite precision after using an FWL implemented digital controller, become limited precision, the influence suffered is minimal. Then, the optimal similarity transformation for the controller is obtained via the orthogonal Hermitian transform. Thus, a minimum bit number used for implementing the stabilising digital controllers can be obtained from the performance index and the optimal similarity transformation under certain stability criteria. The main contributions are that this approach provides an analytical closed-form solution for the optimal transformation and leads to the implementation of the stabilising controllers with a lower bit number when using this optimal one. Finally, a numerical example is used to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR] |
| Copyright of IEE Proceedings -- Control Theory & Applications is the property of Institution of Engineering & Technology 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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| Items | – Name: Title Label: Title Group: Ti Data: Improved eigenvalue sensitivity for finite-precision digital controller realisations via orthogonal Hermitian transform. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yu%2C+W%2E-S%2E%22">Yu, W.-S.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Ko%2C+H%2E-J%2E%22">Ko, H.-J.</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IEE+Proceedings+--+Control+Theory+%26+Applications%22">IEE Proceedings -- Control Theory & Applications</searchLink>. Jul2003, Vol. 150 Issue 4, p365. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Digital+control+systems%22">Digital control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method+data+processing%22">Finite element method data processing</searchLink><br /><searchLink fieldCode="DE" term="%22Hermitian+forms%22">Hermitian forms</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: An improved eigenvalue sensitivity is presented for digital controller realisations via the orthogonal Hermitian transform, subject to finite word length (FWL) effects. This approach can preserve the stability of the closed-loop system when the designed stabilising digital controllers are actually implemented with FWL by using the mode of fixed-point arithmetic. A performance index defined by eigenvalue sensitivity of the closed-loop system is evaluated by the mixed matrix-2/ Frobenius norms, so that the eigenvalues of the closed-loop system, from infinite precision after using an FWL implemented digital controller, become limited precision, the influence suffered is minimal. Then, the optimal similarity transformation for the controller is obtained via the orthogonal Hermitian transform. Thus, a minimum bit number used for implementing the stabilising digital controllers can be obtained from the performance index and the optimal similarity transformation under certain stability criteria. The main contributions are that this approach provides an analytical closed-form solution for the optimal transformation and leads to the implementation of the stabilising controllers with a lower bit number when using this optimal one. Finally, a numerical example is used to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IEE Proceedings -- Control Theory & Applications is the property of Institution of Engineering & Technology 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: 10.1049/ip-cta:20030634 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 365 Subjects: – SubjectFull: Digital control systems Type: general – SubjectFull: Finite element method data processing Type: general – SubjectFull: Hermitian forms Type: general – SubjectFull: Eigenvalues Type: general Titles: – TitleFull: Improved eigenvalue sensitivity for finite-precision digital controller realisations via orthogonal Hermitian transform. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yu, W.-S. – PersonEntity: Name: NameFull: Ko, H.-J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2003 Type: published Y: 2003 Identifiers: – Type: issn-print Value: 13502379 Numbering: – Type: volume Value: 150 – Type: issue Value: 4 Titles: – TitleFull: IEE Proceedings -- Control Theory & Applications Type: main |
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