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Journal of Zhejiang University SCIENCE A 2003 Vol.4 No.6 P.651-657

http://doi.org/10.1631/jzus.2003.0651


Optimization of block floating point realizations for digital controllers with finite word length considerations


Author(s):  WU Jun, HU Xie-he, CHEN Sheng, CHU Jian

Affiliation(s):  National Key Laboratory of Industrial Control Technology, Institute of Advanced Process Control, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   jwu@iipc.zju.edu.cn

Key Words:  Digital controller, Finite word length, Block-floating-point, Closed-loop stability, Optimization


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WU Jun, HU Xie-he, CHEN Sheng, CHU Jian. Optimization of block floating point realizations for digital controllers with finite word length considerations[J]. Journal of Zhejiang University Science A, 2003, 4(6): 651-657.

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Abstract: 
The closed-loop stability issue of finite-precision realizations was investigated for digital controllers implemented in block-floating-point format. The controller coefficient perturbation was analyzed resulting from using finite word length (FWL) block-floating-point representation scheme. A block-floating-point FWL closed-loop stability measure was derived which considers both the dynamic range and precision. To facilitate the design of optimal finite-precision controller realizations, a computationally tractable block-floating-point FWL closed-loop stability measure was then introduced and the method of computing the value of this measure for a given controller realization was developed. The optimal controller realization is defined as the solution that maximizes the corresponding measure, and a numerical optimization approach was adopted to solve the resulting optimal realization problem. A numerical example was used to illustrate the design procedure and to compare the optimal controller realization with the initial realization.

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Reference

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[6]Keel, L.H.and Bhattacharryya, S.P., 1997.Robust, fragile, or optimal? IEEE Trans.Automatic Control, 42(8): 1098-1105.

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[8]Whidborne, J.F., Wu, J.and Istepanian, R.S.H., 2000. Finite word length stability issues in an l1 framework.Int.J.Control, 73(2): 166-176.

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