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Optimal controller and filter realizations using finite-precision, floating-point arithmetic

Optimal controller and filter realizations using finite-precision, floating-point arithmetic
Optimal controller and filter realizations using finite-precision, floating-point arithmetic
The problem of reducing the fragility of digital controllers and filters implemented using finite-precision, floating-point arithmetic is considered. Floating-point arithmetic parameter uncertainty is multiplicative, unlike parameter uncertainty resulting from fixed-point arithmetic. Based on first-order eigenvalue sensitivity analysis, an upper bound on the eigenvalue perturbations is derived. Consequently, open-loop and closed-loop eigenvalue sensitivity measures are proposed. These measures are dependent upon the filter/controller realization. Problems of obtaining the optimal realization with respect to both the open-loop and the closed-loop eigenvalue sensitivity measures are posed. The problem for the open-loop case is completely solved. Solutions for the closed-loop case are obtained using non-linear programming. The problems are illustrated with a numerical example.
0020-7721
405-413
Whidborne, J.F.
9b1b6066-a72e-46e3-966c-9bc2cca6e6da
Gu, D.-W.
0c1f7c32-d483-48eb-84ce-57aaa43b3817
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Chen, S.
9310a111-f79a-48b8-98c7-383ca93cbb80
Whidborne, J.F.
9b1b6066-a72e-46e3-966c-9bc2cca6e6da
Gu, D.-W.
0c1f7c32-d483-48eb-84ce-57aaa43b3817
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Chen, S.
9310a111-f79a-48b8-98c7-383ca93cbb80

Whidborne, J.F., Gu, D.-W., Wu, J. and Chen, S. (2005) Optimal controller and filter realizations using finite-precision, floating-point arithmetic. International Journal of Systems Science, 36 (7), 405-413.

Record type: Article

Abstract

The problem of reducing the fragility of digital controllers and filters implemented using finite-precision, floating-point arithmetic is considered. Floating-point arithmetic parameter uncertainty is multiplicative, unlike parameter uncertainty resulting from fixed-point arithmetic. Based on first-order eigenvalue sensitivity analysis, an upper bound on the eigenvalue perturbations is derived. Consequently, open-loop and closed-loop eigenvalue sensitivity measures are proposed. These measures are dependent upon the filter/controller realization. Problems of obtaining the optimal realization with respect to both the open-loop and the closed-loop eigenvalue sensitivity measures are posed. The problem for the open-loop case is completely solved. Solutions for the closed-loop case are obtained using non-linear programming. The problems are illustrated with a numerical example.

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Published date: June 2005
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 261022
URI: http://eprints.soton.ac.uk/id/eprint/261022
ISSN: 0020-7721
PURE UUID: c8c41034-f170-4121-a8f0-0a5ea66682bd

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Date deposited: 28 Jun 2005
Last modified: 14 Mar 2024 06:46

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Contributors

Author: J.F. Whidborne
Author: D.-W. Gu
Author: J. Wu
Author: S. Chen

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