Skip to main content
SpringerLink
Log in

Design of Feedback Systems

  • Chapter
Discrete Systems

Part of the book series: Communications and Control Engineering Series ((CCE))

  • 164 Accesses

Abstract

Our main objective in this chapter is to introduce some of the central concepts involved in the design of linear feedback controllers for discrete time systems. On the basis of these concepts, we will develop different techniques to compute the feedback gain matrix. The material covered is divided into five major sections. In section 4.2, we discuss the concept of feedback in linear control problems and illustrate its utility by means of typical systems applications. Next, we examine the effect of state and output feedback on the structural properties of the system. Algorithms for eigenvalue assignment are then given. An important class of discrete-type controllers, that is, deadbeat controllers is next investigated in section 4.3. The properties of these controllers are examined and the different approaches are brought together to show their interrelationships.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bishop, A.B. “Introduction fo Discrete Linear Controls”, Academic Press, New York, 1975.

    Google Scholar 

  2. Cadzow, J.A. and H.R. Martens, “Discrete-Time and Computer Control Systems”, Prentice-Hall, Inc., New Jersey, 1970.

    Google Scholar 

  3. Cadzow, J.A. “Discrete-Time Systems”, Prentice-Hall, Inc., New Jersey, 1973.

    Google Scholar 

  4. Gill, A. “Linear Sequential Circuits: Analysis, Synthesis and Applications”, McGraw-Hill, New York, 1967.

    Google Scholar 

  5. Ogata, K. “Modern Control Engineering”, Prentice-Hall, Inc., New Jersey, 19

    Google Scholar 

  6. Power, H.M. and R.J. Simpson, “Introduction to Dynamics and Control”, McGraw-Hill, London, 1978.

    Google Scholar 

  7. Truxal, J.G.“Introductory System Engineering”, McGraw-Hill, New York, 19. 72.

    Google Scholar 

  8. Wolovich, W.A. “Linear Multivariable Systems”, Springer-Verlag, New York, 1974.

    Book  MATH  Google Scholar 

  9. Young, P. and B. Beck, “The Modelling and Control of Water Quality in a River System”, Automatica, Vol. 10, 1974, 455–468.

    Article  Google Scholar 

  10. Singh, M.G. and A. Titli, “Systems: Decomposition, Optimisation and Control”, Pergamon Press, Oxford, 1978.

    MATH  Google Scholar 

  11. Runyan, H.M. “Cybernetics of Economic Systems”, IEEE Trans. Systems, Man and Cybernetics, Vol. SMC-1, 1971, 8–18.

    Google Scholar 

  12. Perkins, W.R., J.B. Cruz, Jr. and N. Sundarajan, “Feedback Control of a Macroeconomic System using an Observer”, IEEE Trans. Systems, Man and Cybernetics, Vol. SMC-2, 1972, 275–278.

    Google Scholar 

  13. Allen, R.G.D. “Macro-Economic Theory - A Mathematical Treatment”, St. Martin’s, New York, 1968.

    Google Scholar 

  14. Singh, M.G. and H. Tamura, “Modelling and Hierarchical Optimisation for Oversaturated Urban Road Traffic Networks”, Int. J. Control, Vol. 20, 1974, 913–934.

    Article  MATH  MathSciNet  Google Scholar 

  15. Mitter, S.K. and R. Foulkes,“Controllability and Pole Assignment for Discrete Time Linear Systems Defined over Arbitrary Fields”, SIAM J. Control, Vol. 9, 1971, 1–7.

    MATH  MathSciNet  Google Scholar 

  16. Kalman, R.E. “On the General Theory of Control Systems”, Preprint First IFAC Congr. Automat. Contr. Moscow, 4, 1960, 2020–2030.

    Google Scholar 

  17. Kalman, R.E., P.L. Falb and M. Arbib, “Topics in Mathematical System Theory”, McGraw-Hill, New York, 1969.

    MATH  Google Scholar 

  18. Davison, E.J. “On Pole Assignment in Linear Systems with Incomplete State-Feedback”, IEEE Trans. Automat. Contr., Vol. AC-15, 1970, 348–351.

    Google Scholar 

  19. Young, P.C. and J.C. Willems, “An Approach to the Linear Multivariable Servomechanism Problem”, Int. J. Control, Vol. 15, 1972, 961–979.

    Article  MathSciNet  Google Scholar 

  20. Brogan, W.L. “Modern Control Theory”, Quantum Publishers, Inc., New York, 1974.

    Google Scholar 

  21. Munro, N. “Pole Assignment”, Proc. IEE, Vol. 126, 1979, 549–554.

    Article  MathSciNet  Google Scholar 

  22. Chen, C.T. “Introduction to Linear System Theory”, Holt, Rinehart and Winston, New York, 1970.

    Google Scholar 

  23. Weiss, L. “Controllability, Realisation and Stability of Discrete-Time Systems”, SIAM J. Control, Vol. 10, 1972, 230–251.

    MATH  Google Scholar 

  24. Mullis, C.T. “Time-Optimal Discrete Regulator Gains”, IEEE Trans. Automat. Contr., Vol. AC-17, 1972, 265–266.

    Article  MathSciNet  Google Scholar 

  25. O’Reilly, J. “The Discrete Linear Time-Invariant Time-Optimal Control Problem - An Overview”, Automatica, Vol. 17, 1981, 363–370.

    Google Scholar 

  26. Leden, B. “Multivariable Deadbeat Control”, Automatica, Vol. 13, 1977, 185–188

    Google Scholar 

  27. Cadzow, J.A. “Nilpotency Property of the Discrete Regulator”, IEEE Trans. Automat. Contr., Vol. AC-13, 1968, 734–735.

    Google Scholar 

  28. Halmos, P.R. “Finite-Dimensional Vector Spaces”, Van Nostrand, New Jersey, 1958.

    MATH  Google Scholar 

  29. Porter, B. “Deadbeat Control of Linear Multivariable Discrete-Time Systems”, Electr. Lett., Vol. 9, 1973, 83–84.

    Article  Google Scholar 

  30. Porter, B. and T.R. Crossley, “Modal Control”, Taylor & Francis, London, 1972.

    MATH  Google Scholar 

  31. Luenberger, D.G. “Observers for Multivariable Systems”, IEEE Trans. Automat. Contr., Vol. AC-11, 1966, 190–197.

    Google Scholar 

  32. Fahmy, M.M., A.A.R. Hanafy and M.F. Sakr, “On the Discrete Time-Optimal Regulator Control Problem”, Information and Control, Vol. 44, 1980, 223–235.

    Article  MATH  MathSciNet  Google Scholar 

  33. O’Reilly, J. “The Deadbeat Control of Linear Multivariable Systems with Inaccessible States”, Int. J. Control, Vol. 31, 1980, 645–654.

    Article  MATH  MathSciNet  Google Scholar 

  34. Ichikawa, K. “Discrete-Time Fast Regulator with Fast Observer”, Int. J. Control, Vol. 28, 1978, 733–742.

    Article  MATH  MathSciNet  Google Scholar 

  35. Mahmoud, M.S. and M.G. Singh, “Large Scale Systems Modellinn”, Pergamon Press, Oxford, 1981.

    Google Scholar 

  36. Wilson, R.G., D.G. Fisher and D.E. Seborg, “Model Reduction for Discrete-Time Dynamic Systems”, Int. J. Control, Vol. 16, 1972, 549–558.

    Article  MATH  Google Scholar 

  37. Wilson, R.G., D.G. Fisher and D.E. Seborg, “Model Reduction and the Design of Reduced-Order Control Laws”, AIChE Journal, Vol. 20, 1974.

    Google Scholar 

  38. Arbel, A. and E. Tse, “Reduced-Order Models, Canonical Forms and Observers”, Int. J. Control, Vol. 30, 1979, 513–531.

    Article  MATH  MathSciNet  Google Scholar 

  39. Noble, B. “Applied Linear Algebra”, Prentice-Hall, New Jersey, 1969.

    MATH  Google Scholar 

  40. Aoki, M. “Control of Large Scale Dynamic Systems by Aggregation”, IEEE Trans. Automat. Contr., Vol. AC-13, 1968, 246–253.

    Google Scholar 

  41. Mahmoud, M.S., Y. Chen and M.G. Singh, “Discrete Two-Time-Scale Systems”, UMIST Control Systems Centre Report No. 497, December, 1980.

    Google Scholar 

  42. Mahmoud, M.S. “Order Reduction and Control of Discrete Systems”, Proc. IEE, Vol. 129, 1982, 129–135.

    Google Scholar 

  43. Mahmoud, M.S. “Structural Properties of Discrete Systems with Slow and Fast Modes”, Large Scale Systems, Vol. 3, 1982, 227–236.

    MATH  MathSciNet  Google Scholar 

  44. Mahmoud, M.S., Y. Chen and M.G. Singh, “A Two-Stage Output Feedback Design”, UMIST Control Systems Centre Report No. 516, May, 1981.

    Google Scholar 

  45. Mahmoud, M.S., Y. Chen and M.G. Singh, “On the Eigenvalue Assignment in Discrete Systems with Fast and Slow Modes”, UMIST Control Systems Centre Report No. 499, February, 1981.

    Google Scholar 

  46. Moore, B.C. “On the Flexibility Offered by State Feedback in Multivariable Systems Beyond Closed Loop Eigenvalue Assignment”, IEEE Trans. Automat. Contr., Vol. AC-21, 1976, 689–692.

    Google Scholar 

  47. Klein, G. and B.C. Moore, “Eigenvalue-Generalised Eigenvector Assignment with State Feedback”, IEEE Trans. Automat. Contr., Vol. AC-22, 1977, 140–141.

    Google Scholar 

  48. Fahmy, M.M. and J. O’Reilly, “On Eigenstructure Assignment in Linear Multivariable Systems”, IEEE Trans. Automat. Contr., Vol. AC-27, 1982, 690–693.

    Google Scholar 

  49. Porter, B. and J.J. D’Azzo “Algorithm for the Synthesis of State-Feedback Regulators by Entire Eigenstructure Assignment”, Electron. Lett., Vol. 13, 1977, 230–231.

    Article  Google Scholar 

  50. Porter, B. and J.J. D’Azzo, “Closed-Loop Eicenstructure Assignment by State Feedback in Multivariable Linear Systems”, Int. J. Control, Vol. 27, 1978, 487–492.

    Article  MATH  MathSciNet  Google Scholar 

  51. Mahmoud, M.S. and Y. Chen, “Design of Feedback Controllers by Two-Stage Methods”, Applied Mathematical Modelling, Vol. 7, 1983, pp. 163–68.

    Article  MATH  Google Scholar 

  52. Nicholson, H. “Structure of Interconnected Systems”, Peregrinus, London, 1978.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical and Computer Engineering Dept., Kuwait University, Kuwait

    Magdi S. Mahmoud (Professor)

  2. Manchester, UK

    Madan G. Singh (Professor of Control Engineering at U.M.I.S.T.)

Authors
  1. Magdi S. Mahmoud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Madan G. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin, Heidelberg

About this chapter

Cite this chapter

Mahmoud, M.S., Singh, M.G. (1984). Design of Feedback Systems. In: Discrete Systems. Communications and Control Engineering Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82327-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-82327-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82329-9

  • Online ISBN: 978-3-642-82327-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation