×
Whidborne, James F.; Gu, Da-Wei; Wu, Jun; Chen, Sheng

Optimal controller and filter realizations using finite-precision, floating-point arithmetic. (English) Zbl 1121.93322

Int. J. Syst. Sci. 36, No. 7, 405-413 (2005).
Summary: 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 nonlinear programming. The problems are illustrated with a numerical example.

MSC:

93B50 Synthesis problems
93B40 Computational methods in systems theory (MSC2010)
93E11 Filtering in stochastic control theory

Keywords:

finite-precision arithmetic; finite word length; digital controller; digital filter; eigenvalue sensitivity; floating-point arithmetic; controller fragility
Cite Review PDF
Full Text: DOI Link

References:

[1] Bomar BW, IEEE Trans. Circuits & Syst. II 44 pp pp. 952–955– (1997)
[2] Chen S, IEEE Trans. Autom. Control 44 pp pp. 2149–2153– (1999)
[3] DOI: 10.1080/00207170110067053 · Zbl 1036.93065 · doi:10.1080/00207170110067053
[4] Faris D, Proc. Annual Allerton Conference on Communication Control and Computing 36 pp pp. 600–609– (1998)
[5] DOI: 10.1109/9.40788 · Zbl 0689.93048 · doi:10.1109/9.40788
[6] Gevers M, Parametrizations in Control, Estimations and Filtering Problems: Accuracy Aspects (1993) · doi:10.1007/978-1-4471-2039-1
[7] Golub GH, Matrix Computations (1989)
[8] Horn RA, Matrix Analysis (1985)
[9] Istepanian RH, IEE Proc. Control Theory and Appl. 145 pp pp. 472–478– (1998) · doi:10.1049/ip-cta:19982230
[10] Istepanian RSH, Digital Controller Implementation and Fragility: A Modern Perspective pp pp. 1–12– (2001) · doi:10.1007/978-1-4471-0265-6
[11] DOI: 10.1080/002077200291019 · Zbl 1080.93557 · doi:10.1080/002077200291019
[12] Kalliojärvi K, IEEE Sig. Proc. Letters 1 pp pp. 52–54– (1994) · doi:10.1109/97.295322
[13] DOI: 10.1109/TCT.1971.1083366 · doi:10.1109/TCT.1971.1083366
[14] DOI: 10.1109/TAES.1971.310342 · doi:10.1109/TAES.1971.310342
[15] DOI: 10.1109/9.618239 · Zbl 0900.93075 · doi:10.1109/9.618239
[16] Ko H-J, IEEE Trans. Syst. Man & Cybernetics – B 34 pp pp. 1923–1932– (2004)
[17] DOI: 10.1109/TSP.2004.837439 · Zbl 1370.94157 · doi:10.1109/TSP.2004.837439
[18] Kontro J, Proc 1992 IEEE Int. Symp. Circuits and Syst. pp pp. 1784–1791– (1992)
[19] Ku W, IEEE Trans. Circuits & Syst. 22 pp pp. 927–936– (1975)
[20] DOI: 10.1109/9.728872 · doi:10.1109/9.728872
[21] Li G, IEEE Trans. Circuits & Syst. II 39 pp pp. 365–377– (1992)
[22] DOI: 10.1109/TCT.1971.1083365 · doi:10.1109/TCT.1971.1083365
[23] Liu B, Proc. IEEE 57 pp pp. 1735–1747– (1969)
[24] DOI: 10.1109/TAC.1968.1098902 · doi:10.1109/TAC.1968.1098902
[25] DOI: 10.1109/9.1283 · Zbl 0646.93053 · doi:10.1109/9.1283
[26] Molchanov AP, Proc. 34th IEEE Conf. Decision Contr. pp pp. 4251–4258– (1995)
[27] DOI: 10.1109/TCS.1976.1084254 · Zbl 0342.93066 · doi:10.1109/TCS.1976.1084254
[28] DOI: 10.1016/S0090-5267(96)80039-9 · doi:10.1016/S0090-5267(96)80039-9
[29] Rink RE, IEEE Trans. Autom. Control 24 pp pp. 980–982– (1979)
[30] Rink RE, IEEE Trans. Autom. Control 24 pp pp. 411–421– (1979)
[31] Sandberg IW, Bell Syst. Tech. J. 46 pp pp. 1775–1791– (1967)
[32] Smith LM, IEEE Trans. Circuits & Syst. II 39 pp pp. 90–98– (1992) · doi:10.1109/82.205812
[33] Tsai CM, IEEE Trans. Circuits & Syst. II 44 pp pp. 774–779– (1997)
[34] Vanwingerden AJM, IEEE Trans. Autom. Control 29 pp pp. 385–391– (1984)
[35] Whidborne JF, Proc. 15th IFAC World Congress
[36] DOI: 10.1109/9.905702 · Zbl 1056.93547 · doi:10.1109/9.905702
[37] Wilkinson JH, Rounding Errors in Algebraic Processes (1963)
[38] Wu J, Int. J. Control 72 pp pp. 1331–1342– (1999)
[39] DOI: 10.1109/9.880623 · Zbl 0990.93119 · doi:10.1109/9.880623
[40] DOI: 10.1109/9.935076 · Zbl 1011.93056 · doi:10.1109/9.935076
[41] Wu J, IEEE Trans. Autom. Control 48 pp pp. 816–822– (2003)
[42] Wu J, Int. J. Control 77 pp pp. 427–440– (2004)
[43] Zeng B, IEEE Trans. Circuits & Syst. 38 pp pp. 590–601– (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.