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A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes

A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes
A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes
The closed-loop stability issue of finite-precision realizations is investigated for digital controllers implemented in three different arithmetic formats, namely fixed-point, floating-point and block-floating-point schemes. It is shown that the controller coefficient perturbations resulting from using different finite word length (FWL) representation schemes possess quite different properties. A unified FWL closed-loop stability measure is derived which is applicable to all the three arithmetic schemes. Unlike the existing works which only take into account the precision of a representation scheme with an assumption of an unlimited dynamic range, both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable FWL closed-loop stability measure is then introduced and the method of computing the value of this measure for a given controller realization is given. For each arithmetic scheme, the optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach is adopted to solve for the resulting optimal realization problem. The proposed design procedure provides a unified framework for true optimal controller implementation that requires a minimum bit length with maximum robustness to the FWL effect. Numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes.
0018-9286
816-822
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Chen, S.
9310a111-f79a-48b8-98c7-383ca93cbb80
Whidborne, J.F.
9b1b6066-a72e-46e3-966c-9bc2cca6e6da
Chu, J.
08744087-3532-4f12-9d8a-5c8e5d79be0e
Wu, J.
5a0119e5-a760-4ff5-90b9-ec69926ce501
Chen, S.
9310a111-f79a-48b8-98c7-383ca93cbb80
Whidborne, J.F.
9b1b6066-a72e-46e3-966c-9bc2cca6e6da
Chu, J.
08744087-3532-4f12-9d8a-5c8e5d79be0e

Wu, J., Chen, S., Whidborne, J.F. and Chu, J. (2003) A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes. IEEE Transactions on Automatic Control, 48 (5), 816-822.

Record type: Article

Abstract

The closed-loop stability issue of finite-precision realizations is investigated for digital controllers implemented in three different arithmetic formats, namely fixed-point, floating-point and block-floating-point schemes. It is shown that the controller coefficient perturbations resulting from using different finite word length (FWL) representation schemes possess quite different properties. A unified FWL closed-loop stability measure is derived which is applicable to all the three arithmetic schemes. Unlike the existing works which only take into account the precision of a representation scheme with an assumption of an unlimited dynamic range, both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable FWL closed-loop stability measure is then introduced and the method of computing the value of this measure for a given controller realization is given. For each arithmetic scheme, the optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach is adopted to solve for the resulting optimal realization problem. The proposed design procedure provides a unified framework for true optimal controller implementation that requires a minimum bit length with maximum robustness to the FWL effect. Numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes.

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More information

Published date: May 2003
Additional Information: submitted for publication in Jan. 2002
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 257441
URI: http://eprints.soton.ac.uk/id/eprint/257441
ISSN: 0018-9286
PURE UUID: 59246a90-fd50-4418-b3f1-3cf931eed817

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Date deposited: 16 May 2003
Last modified: 20 Jan 2022 17:34

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Contributors

Author: J. Wu
Author: S. Chen
Author: J.F. Whidborne
Author: J. Chu

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