Optimal Finite-Precision Controller and Filter Implementations Using Floating-Point Arithmetic

Whidborne, James F.; Gu, Da‐Wei

doi:10.3182/20020721-6-es-1901.00383

Cited by 4 publications

(14 citation statements)

References 12 publications

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“…It is useful to compare the proposed measure with the previous results, especially the most recent one given by [11]. For a complex-valued matrix Ý ℄, define the Frobenius norm…”

Section: Propositionmentioning

confidence: 99%

“…Under an assumption that the exponent bits are unlimited, the computationally tractable weighted closed-loop eigenvalue sensitivity index addressed in [11] is given by §´ µ …”

Section: Propositionmentioning

confidence: 99%

“…The example taken from [2] was used to illustrate the proposed design procedure for obtaining optimal FWL floating-point controller realizations and to compare it with the method given in [11]. The discrete-time plant was given by…”

Section: A Numerical Examplementioning

confidence: 99%

“…An "optimal" controller realization problem was given in [11] based on the weighted closed-loop eigenvalue sensitivity index (32). We will use the index "s", rather then "opt", to denote the solution of this "optimal" realization problem.…”

Section: A Numerical Examplementioning

confidence: 99%

“…There has been little work studying explicitly the closed-loop stability issue of FWL floating-point digital controller implementations. An exception is the work [11], in which a weighted closed-loop eigenvalue sensitivity index was defined for floating-point digital controller realizations. This FWL measure, however, only considers the mantissa part of floating-point arithmetic, under an assumption that the exponent bits are unlimited.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimal floating-point realizations of finite-precision digital controllers

Chen

Whidborne³

et al.

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

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The paper investigates the closed-loop stability issue of finite-precision realizations for digital controllers implemented in floating-point arithmetic. Unlike the existing methods which only address the effect of the mantissa bits in floating-point format to the sensitivity of closed-loop stability, the sensitivity of closed-loop stability is analyzed with respect to both the mantissa and exponent bits of floating-point format. A computationally tractable finite word length (FWL) closed-loop stability measure is defined, and the optimal controller realization problem is posed as searching for a floating-point realization that maximizes the proposed measure. A numerical optimization approach is adopted to solve for the resulting optimization problem. Simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced FWL closed-loop stability performance.

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“…It is useful to compare the proposed measure with the previous results, especially the most recent one given by [11]. For a complex-valued matrix Ý ℄, define the Frobenius norm…”

Section: Propositionmentioning

confidence: 99%

“…Under an assumption that the exponent bits are unlimited, the computationally tractable weighted closed-loop eigenvalue sensitivity index addressed in [11] is given by §´ µ …”

Section: Propositionmentioning

confidence: 99%

Section: A Numerical Examplementioning

confidence: 99%

Section: A Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal floating-point realizations of finite-precision digital controllers

Chen

Whidborne³

et al.

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

View full text Add to dashboard Cite

show abstract

Optimal realizations of floating-point implemented digital controllers with finite word length considerations

Chen

Whidborne

et al. 2004

International Journal of Control

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The closed-loop stability issue of finite word length (FWL) realizations is investigated for digital controllers implemented in floating-point arithmetic. Unlike the existing methods which only address the effect of the mantissa bits in floatingpoint implementation to the sensitivity of closed-loop stability, the sensitivity of closed-loop stability is analysed with respect to both the mantissa and exponent bits of floating-point implementation. A computationally tractable FWL closed-loop stability measure is then defined, and the method of computing the value of this measure is given. The optimal controller realization problem is posed as searching for a floating-point realization that maximizes the proposed FWL closed-loop stability measure, and a numerical optimization technique is adopted to solve for the resulting optimization problem. Simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced FWL closed-loop stability performance.

show abstract

Polynomial operator-based digital controller structures of high stability performance and computation efficiency

Hao

ICARCV 2004 8th Control, Automation, Robotics and Vision Conference, 2004.

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Optimal Finite-Precision Controller and Filter Implementations Using Floating-Point Arithmetic

Cited by 4 publications

References 12 publications

Optimal floating-point realizations of finite-precision digital controllers

Optimal floating-point realizations of finite-precision digital controllers

Optimal realizations of floating-point implemented digital controllers with finite word length considerations

Polynomial operator-based digital controller structures of high stability performance and computation efficiency

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