Finite-Precision Computing for Digital Control Systems: Current Status and Future Paradigms

  • Robert S. H. Istepanian
  • James F. Whidborne
Part of the Advances in Industrial Control book series (AIC)


This chapter provides an overview of some of the important issues that need to be considered in the implementation of digital controllers. It focusses on the need to consider the precision of the computing device, and reviews some of the work done in the area. A summary is made of some of the advances being made in developing hardware for use in digital control implementation.


Digital Signal Processor Controller Parameter Digital Control Controller Structure Digital Controller 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    G.F. Franklin, J.D. Powell, and M. Workman.Digital Control of Dynamic Systems3rd edition. Addison-Wesley, Menlo Park, CA., 1998.Google Scholar
  2. 2.
    K.A. Aström and B. Wittenmark.Computer Controlled Systems: Theory and Design3rd edition. Prentice-Hall, Upper Saddle River, NJ., 1997.Google Scholar
  3. 3.
    W. Forsythe and R.M. Goodall.Digital Control - Fundamentals Theory and Practice. Macmillan, Basingstoke, U.K., 1991.Google Scholar
  4. 4.
    J.E. Bertram. The effects of quantization in sampled-feedback systems.Trans. AIEE77:177–182, 1958.Google Scholar
  5. 5.
    J.B. Slaughter. Quantization errors in digital control systems.IEEE Trans. Autom. Control9:70–74, 1964.CrossRefGoogle Scholar
  6. 6.
    J.B. Knowles and R. Edwards. Effect of a finite-word-length computer in a sampled-data feedback system.Proc. IEE112(6):1197–1207, 1965.Google Scholar
  7. 7.
    E.E. Curry. The analysis of round-off and truncation errors in a hybrid control system.IEEE Trans. Autom. Control12:601–604, 1967.CrossRefGoogle Scholar
  8. 8.
    P.E. Mantey. Eigenvalue sensitivity and state-variable selection.IEEE Trans. Autom. Control13(3):263–269, 1968.CrossRefGoogle Scholar
  9. 9.
    C.T. Mullis and R.A. Roberts. Synthesis of minimum round off noise fixed-point digital filters.IEEE Trans. Circuits el Syst.23:551–562, 1976.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    S.Y. Hwang. Minimum uncorrelated unit noise in state-space digital filtering.IEEE Trans. Accoustics Speech e9 Sig. Proc.25:273–281, 1977.MATHCrossRefGoogle Scholar
  11. 11.
    P. Morony, A.S. Willsky, and P.K. Houpt. Roundoff noise and scaling in the digital implementation of control compensators.IEEE Trans. Accoustics Speech el Sig. Proc.31(6):1464–1474, 1983.CrossRefGoogle Scholar
  12. 12.
    M.E. Ahmed and P.R. Belanger. Scaling and roundoff in fixed-point implementation of control algorithms.IEEE Trans. Ind. Electr.31(3):228–234, 1984.CrossRefGoogle Scholar
  13. 13.
    M. Steinbuch, G. Schoostra, and H.T. Goh. Closed-loop scaling of fixed-point digital control.IEEE Trans. Control Syst. Technology2:312–317, 1994.CrossRefGoogle Scholar
  14. 14.
    P. Morony, A.S. Willsky, and P.K. Houpt. The digital implementation of control compensators: the coefficient word length issue.IEEE Trans. Autom. Control25:621–630, 1980.CrossRefGoogle Scholar
  15. 15.
    A.J.M. Van Wingerden and W.L. de Koning. The influence of finite word-length on digital optimal-control.IEEE Trans. Autom. Control29(5):385–391, 1984.MATHCrossRefGoogle Scholar
  16. 16.
    P. Morony.Issues in the Implementation of Digital Feedback Compensators.Number 5 in Signal Processing, Optimization, and Control Series. MIT Press, Cambridge, MA, 1983.Google Scholar
  17. 17.
    D. Williamson.Digital Control and Implementation: Finite Wordlength Considerations.Systems and Control Engineering. Prentice Hall, Englewood Cliffs, NJ, 1991.Google Scholar
  18. 18.
    M. Gevers and G. Li.Parametrizations in Control Estimations and Filtering Problems: Accuracy Aspects. Springer-Verlag, Berlin, 1993.MATHCrossRefGoogle Scholar
  19. 19.
    Nagle, H.T. and Carrolf, C. `Hardware realization of sampled data controllers’, Proc. IFAC Symp. Aut. Contr. in Space, Armenia, pp.23–27, Aug.1974.Google Scholar
  20. 20.
    L.H. Keel and S.P. Bhattacharryya. Robust, fragile, or optimal?IEEE Trans. Autom. Control42(8):1098–1105, 1997.MATHCrossRefGoogle Scholar
  21. 21.
    W.M. Haddad and J.R. Corrado. Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations. InProc. 1998 Amer. Contr. Conf.pages 2837–2841, Philadelphia, PA., 1998.Google Scholar
  22. 22.
    L. Thiele. Design of sensitivity and round-off noise optimal state-space discrete systems.Int. J. Circuit Theory Appl.12:39–46, 1984.MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    L. Thiele. On the sensitivity of linear state space systems.IEEE Trans. Circuits 81 Syst.33(5):502–510, 1986.MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    G. Li, B.D.O. Anderson, M. Gevers, and J.E. Perkins. Optimal FWL design of state space digital systems with weighted sensitivity minimization and sparseness consideration.IEEE Trans. Circuits e4 Syst. II39(5):365–377, 1992.MATHCrossRefGoogle Scholar
  25. 25.
    A.G. Madievski, B.D.O. Anderson, and M. Gevers. Optimum realizations of sampled-data controllers for FWL sensitivity minimization.Automatica31(3):367–379, 1995.MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    R.H. Istepanian, G. Li, J. Wu, and J. Chu. Analysis of sensitivity measures of finite-precision digital controller structures with closed-loop stability bounds.IEE Proc. Control Theory and Appl.145(5):472–478, 1998.CrossRefGoogle Scholar
  27. 27.
    G. Li. On the structure of digital controllers with finite word length consideration.IEEE Trans. Autom. Control43(5):689–693, 1998.MATHGoogle Scholar
  28. 28.
    S. Chen, J. Wu, R.H. Istepanian, and J. Chu. Optimizing stability bounds of finite-precision PID controller structures.IEEE Trans. Autom. Control44(11):2149–2153, 1999.MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    J. Wu, R.H. Istepanian, and S. Chen. Stability issues of finite-precision controller structures for sampled-data systems.Int. J. Control72(15):1331–1342, 1999.MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    R.H. Istepanian, S. Chen, J. Wu, and J.F. Whidborne. Optimal finite-precision controller realization of sampled-data systems.Int. J. Syst. Sci.31(4):429–438, 2000.MATHCrossRefGoogle Scholar
  31. 31.
    J. Wu, S. Chen, G. Li, and J. Chu. Optimal finite-precision state-estimate feedback controller realizations of discrete-time systems.IEEE Trans. Autom. Control45(8):1550–1554, 2000.MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    J.F. Whidborne, R.S.H. Istepanian, and J. Wu. Reduction of controller fragility by pole sensitivity minimization.IEEE Trans. Autom. Control46(2):320–325, 2001.MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    D. Williamson and K. Kadiman. Optimal finite wordlength linear quadratic regulation.IEEE Trans. Autom. Control34(12):1218–1228, 1989.MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    D. Williamson and R.E. Skelton. Optimal Q-markov cover for finite word-length implementation.Math. Syst. Theory22(4):255–273, 1989.MathSciNetMATHCrossRefGoogle Scholar
  35. 35.
    K. Liu, R.E. Skelton, and K.M. Grigoriadis. Optimal controllers for finite word length implementation.IEEE Trans. Autom. Control37(9):1294–1304, 1992.MathSciNetMATHCrossRefGoogle Scholar
  36. 36.
    I.J. Fialho and T.T. Georgiou. On stability and performance of sampled-data systems subject to word-length constraint.IEEE Trans. Autom. Control39(12):2476–2481, 1994.MathSciNetMATHCrossRefGoogle Scholar
  37. 37.
    M.A. Rotea and D. Williamson. Optimal realizations of finite word-length digital-filters and controllers.IEEE Trans. Circuits & Syst. II42(2):61–72, 1995.MATHCrossRefGoogle Scholar
  38. 38.
    J.F. Whidborne, J. Wu, and R.H. Istepanian. Finite word length stability issues in an £1 framework.Int. J. Control73(2):166–176, 2000.MathSciNetMATHCrossRefGoogle Scholar
  39. 39.
    R. D’Andrea, and R.S.H. Istepanian Design of full state feedback finite precision controllers’.Int. J. of Robust and Non-Linear Control2001 (to appear).Google Scholar
  40. 40.
    P.M. Mäkilä. Comments on “Robust, fragile, or optimal?”.IEEE Trans. Au-tom. Control43(9):1265–1268, 1998.CrossRefGoogle Scholar
  41. 41.
    P. Dorato. Non-fragile controller design: an overview. InProc. 1998Amer.Contr. Conf., pages 2829–2831, Philadelphia, PA., 1998.Google Scholar
  42. 42.
    D. Kaesbauer and J. Ackermann. How to escape from the fragility trap. InProc. 1998 Amer. Contr. Conf.pages 2832–2836, Philadelphia, PA., 1998.Google Scholar
  43. 43.
    A. Jadbabaie, C.T. Abdallah, D. Famularo, and P. Dorato. Robust, non-fragile and optimal controller design via linear matrix inequalities. InProc. 1998 Amer. Contr. Conf.pages 2842–2846, Philadelphia, PA., 1998.Google Scholar
  44. 44.
    D. Famularo, P. Dorato, C.T. Abdallah, W.M. Haddad, and A. Jadbabaie. Robust non-fragile LQ controllers: the static state feedback case.Int. J. Control73(2):159–165, 2000.MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    W.M. Haddad and J.R. Corrado. Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations.Int. J. Control73(15):1405–1423, 2000.MathSciNetMATHCrossRefGoogle Scholar
  46. 46.
    J. Paattilammi and P.M. Mäkilä. Fragility and robustness: A case study on paper machine headbox control.IEEE Control Syst. Magaz.20:13–22, 2000.CrossRefGoogle Scholar
  47. 47.
    G.H. Yang, J.L. Wang, and Y.C. Soh. Guaranteed cost control for discrete-time linear systems under controller gain perturbations.Linear Alg. Appl.312(1–3):161–180, 2000.MathSciNetMATHCrossRefGoogle Scholar
  48. 48.
    G.H. Yang, J.L. Wang, and C. Lin.?-t. control for linear systems with additive controller gain variations.Int. J. Control, 73(16):1500–1506, 2000.MathSciNetMATHCrossRefGoogle Scholar
  49. 49.
    J.S. Yee, G.H. Yang, and J.L. Wang. Non-fragile 140. flight controller design for large bank-angle tracking manoeuvres.Proc. IMechE Part I: J. Syst. E4 Contr.214(3):157–172, 2000.CrossRefGoogle Scholar
  50. 50.
    G.H. Yang and J.L. Wang. Robust nonfragile Kalman filtering for uncertain linear systems with estimator gain uncertainty.IEEE Trans. Autom. Control46(2):343–348, 2001.MATHCrossRefGoogle Scholar
  51. 51.
    R.H. Middleton and G.C. Goodwin. Improved finite word-length characteristics in digital-control using delta-operators.IEEE Trans. Autom. Control31(11):1015–1021, 1986.MATHCrossRefGoogle Scholar
  52. 52.
    S. Chen, J. Wu, R.H. Istepanian, J. Chu, and J.F. Whidborne. Optimizing stability bounds of finite-precision controller structures for sampled-data systems in the 5-operator domainIEE Proc. Control Theory and Appl.146(6):517–526, 1999.CrossRefGoogle Scholar
  53. 53.
    J. Wu, S. Chen, G. Li, R.H. Istepanian, and J. Chu. Shift and delta operator realisations for digital controllers with finite word length considerations.IEE Proc.-Control Theory Appl.147(6):664–672, 2000.CrossRefGoogle Scholar
  54. 54.
    S. Chen, R.H. Istepanian, J. Wu, and J. Chu. Comparative study on optimizing closed-loop stability bounds of finite-precision controller structures with shift and delta operators.Syst. Control Lett.40(3):153–163, 2000.MathSciNetMATHCrossRefGoogle Scholar
  55. 55.
    T.L. Song, E.G. Collins, and R.H. Istepanian. Improved closed-loop stability for fixed-point controller realizations using the delta operator.Int. J. Robust Nonlinear Control11(1):41–57, 2001.MathSciNetMATHCrossRefGoogle Scholar
  56. 56.
    R. Gessing. Word length of pulse transfer function for small sampling periods.IEEE Trans. Autom. Control44(9):1760–1764, 1999.MathSciNetMATHCrossRefGoogle Scholar
  57. 57.
    J.H. Lang. On the design of a special-purpose digital control processorIEEE Trans. Autom. Control29(3):195–201, 1984.MATHCrossRefGoogle Scholar
  58. 58.
    S. Battilotti and G. Ulivi. An architecture for high performance control using digital signal processor chipsIEEE Control Syst. Magazine10(6):20–23, 1990.CrossRefGoogle Scholar
  59. 59.
    S.C. Chen. Application of one-chip signal processor in digital controller implementationIEEE Control Syst. Magazine2:16–22, 1982.CrossRefGoogle Scholar
  60. 60.
    K. Shimabukuro, M. Kameyama and T. Higuchi. Design of a multiple-valued VLSI processor for digital controlIEICE Trans. Inf. SystemsE-75(5):709–719, 1992.Google Scholar
  61. 61.
    Kitticakoonkit, S., Kampyama, M and Higuchi, T. Design of a matrix multiply-addition VLSI processor for robot inverse dynamics computationIEICE Trans. Inf. Systms, E-74(11 3819–3827, 1994Google Scholar
  62. 62.
    E. Kappos and D.J. Kinniment. Application-specific processor architectures for embedded control: Case studies.Microprocessors and Microsystems20(4):225–232, 1996.CrossRefGoogle Scholar
  63. 63.
    P. Sadayappan, Y.L.C. Ling, K.W. Olson, and D.E. Orin. A restructurable VLSI robotics vector processor architecture for real-time control.IEEE Trans. Robot. Autom.5(5):583–599, 1989.CrossRefGoogle Scholar
  64. 64.
    M.K. Masten and I. Panahi. Digital signal processors for modern control systems.Control Eng. Practice5(4):449–458, 1997.CrossRefGoogle Scholar
  65. 65.
    S. Jones, R. Goodall, and M. Gooch. Targeted processor architectures for high-performance controller implementation.Control Eng. Practice6(7):867–878, 1998.CrossRefGoogle Scholar
  66. 66.
    V. Samoladas and L. Petrou. Special-purpose architectures for fuzzy-logic controllersMicroprocessing and Microprogramming40(4):275–289, 1994.CrossRefGoogle Scholar
  67. 67.
    R.S.H. Istepanian, J. Wu, and J.F. Whidborne. Controller realizations of a teleoperated dual-wrist assembly system with finite word length considerations.IEEE Trans. Control Syst. Technology9(4):624–628, 2001.CrossRefGoogle Scholar
  68. 68.
    J.F. Whidborne and R.S.H. Istepanian. Optimal finite-precision. PID controller structures using genetic algorithms. InProc. 14th IFAC World Congressvolume F, pages 181–186, Beijing, 1999.Google Scholar
  69. 69.
    J.F. Whidborne and R.H. Istepanian. A genetic algorithm approach to designing finite-precision controller structures.IEE Proc. Control Theory and Appl.2000 (submitted).Google Scholar

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© Springer-Verlag London 2001

Authors and Affiliations

  • Robert S. H. Istepanian
  • James F. Whidborne

There are no affiliations available

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