Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

Shift and delta operator realisations for digital controllers with finite word length considerations

Shift and delta operator realisations for digital controllers with finite word length considerations

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Add to cart
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)
Add to cart

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IEE Proceedings - Control Theory and Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

  • Author(s): J. Wu 1 ; S. Chen 2 ; G. Li 3 ; R.H. Istepanian 4 ; J. Chu 1
    • View affiliations
    • Affiliations: 1: National Laboratory of Industrial Control Technology, Institute of Advanced Process Control, Zhejiang University, Hangzhou, P. R. China
      2: Department of Electronics and Computer Science, University of Southampton, Highfield, UK
      3: School of of Electrical and Electronic Engineering, Nanyang Technological University, Singapore
      4: Department of Electronic and Computer Engineering, Brunel University, Uxbridge, UK
  • Source: Volume 147, Issue 6, November 2000, p. 664 – 672
    DOI:  10.1049/ip-cta:20000750 , Print ISSN 1350-2379, Online ISSN 1359-7035
IEE
Published

The implementation issues of digital controllers with finite word length (FWL) considerations are addressed. Both the shift and delta operator parameterisations of a general controller structure are considered. A unified formulation is adopted to derive a computationally tractable stability related measure that describes FWL closed-loop stability characteristics of different controller realisations. Within a given operator parameterisation, the optimal FWL controller realisation, which maximises the proposed stability related measure, is the solution of a nonlinear optimisation problem. The relationship between the z-operator and δ-operator controller parameterisations is analysed, and it is shown that the δ parameterisation has a better FWL closed-loop stability margin than the z-domain approach under a mild condition. A design example is included to verify the theoretical analysis and to illustrate the proposed optimisation procedure.

Inspec keywords: closed loop systems; stability; digital control; optimisation; matrix algebra; discrete time systems

Other keywords: matrix algebra; optimisation; closed-loop system; digital controllers; shift operator; finite word length; delta operator; stability

Subjects: Algebra; Discrete control systems; Control system analysis and synthesis methods; Stability in control theory; Optimisation techniques

References

    1. 1)
      • C.M. FONSECA , P.J. FLEMING . Multiobjective optimisation and multiple constraint handling with evolutionary algorithms - Part I: A unified formulation. IEEE Trans. Syst. Man Cybern. A, Syst. Humans , 26 - 37
    2. 2)
      • K.F. MAN , K.S. TANG , S. KWONG . (1998) , Genetic algorithms: Concepts and design.
    3. 3)
      • S. CHEN , J. WU , R.H. ISTEPANIAN , J. CHU . Optimising stability bounds of finite-precision PID controller structures. IEEE Trans. Autom. Control , 11 , 2149 - 2153
    4. 4)
      • G. LI , M. GEVERS . Comparative study of finite wordlength effects in shift and delta operator parameterisations. IEEE Trans. Autom. Control , 5 , 803 - 807
    5. 5)
      • FIALHO, I.J., GEORGIOU, T.T.: `Optimal finite worldlength digital controller realisation', Proceedings of American control conference, 1999, San Diego, USA, p. 4326–4327.
    6. 6)
      • J. O'Reilly . (1983) , Observers for linear systems.
    7. 7)
      • S. BOYD , L. EL GHAOUI , E. FERON , V. BALAKRISHNAN . (1994) , Linear matrix inequalities in system and control theory.
    8. 8)
      • R.M. GOODALL , B.J. DONOGHUE . Very high sample rate digital filters using the δ operator. IEE Proc., Circuits Devices Syst. , 199 - 206
    9. 9)
      • L.C.W. DIXON . (1972) , Nonlinear optimisation.
    10. 10)
      • D.E. GOLDBERG . (1989) , Genetic algorithms in search, optimisation and machine learning.
    11. 11)
      • R.H. MIDDLETON , G.C. GOODWIN . (1990) , Digital control and estimation: A unified approach.
    12. 12)
      • S. CHEN , J. WU , R.H. ISTEPANIAN , J. CHU , J.F. WHIDBORNE . Optimising stability bounds of finite-precision controller structures for sampled-data systems in the delta operator domain. IEE Proc., Control Theory Appl. , 6 , 517 - 526
    13. 13)
      • L. INGBER . Adaptive simulated annealing (ASA): lessons learned. J. Control Cybern. , 1 , 33 - 54
    14. 14)
      • G. Li . On the structure of digital controllers with finite word length consideration. IEEE Trans. Autom. Control , 689 - 693
    15. 15)
      • G.S.G. BEVERIDGE , R.S. SCHECHTER . (1970) , Optimisation: Theory and practice.
    16. 16)
      • C.P. NEUMAN . Properties of the delta operator model of dynamic physical systems. IEEE Trans. Syst. Man Cybern. , 296 - 301
    17. 17)
      • J. WU , S. CHEN , G. LI , J. CHU . Optimal finite-precision state-estimate feedback controller realisation of discrete-time systems. IEEE Trans. Autom. Control , 1550 - 1557
    18. 18)
      • M. GEVERS , G. LI . (1993) , Parameterisations in control, estimation and filtering problems: Accuracy aspects.
    19. 19)
      • G. LI , M. GEVERS . Optimal finite precision implementation of a state-estimate feedback controller. IEEE Trans. Circuits Syst. , 1487 - 1498
    20. 20)
      • R.H. ISTEPANIAN , G. LI , J. WU , J. CHU . Analysis of sensitivity measures of finite-precision digital controller structures with closed-loop stability bounds. IEE Proc., Control Theory Appl. , 5 , 472 - 478
    21. 21)
      • R.J. Schwarz , B. Friedland . (1965) , Linear systems.
    22. 22)
      • S. CHEN , B.L. LUK . Adaptive simulated annealing for optimisation in signal processing applications. Signal Process. , 11 , 117 - 128
    23. 23)
      • I.J. FIALHO , T.T. GEORGIOU . On stability and performance of sampled data systems subject to word length constraint. IEEE Trans. Autom. Control , 12 , 2476 - 2481
    24. 24)
      • C.P. NEUMAN . Transformations between delta and forward shift operator transfer function models. IEEE Trans. Syst. Man Cybern. , 295 - 296
    25. 25)
      • R.E. SKELTON , T. IWASAKI , K.M. GRIGORIADID . (1998) , A unified algebraic approach to linear control design.
    26. 26)
      • L. Ingber . Simulated annealing: practice versus theory. Math. Comput.Model. , 11 , 29 - 57
    27. 27)
      • ISTEPANIAN, R.H.: `Implementational issues for discrete PID algorithms using shift and delta operator parameterisations', Proceedings of 4th IFAC workshop on Algorithms and architectures for real-time control, 1997, Vilamoura, Portugal, p. 117–122.
    28. 28)
      • Y. SUNG , M. KUNG . Lower finite word length effect on state space digital filter by δ operator realisation. Int. J. Electron. , 1135 - 1141
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-cta_20000750
Loading

Related content

content/journals/10.1049/ip-cta_20000750
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address