Structural interpretation of matched pole–zero discretisation

Structural interpretation of matched pole–zero discretisation

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The paper deals with matched pole–zero discretisation, which has been used in practice for hand calculations in the digital redesign of continuous-time systems but available only in the transfer-function form. Since this form is inconvenient for characterising the time-domain properties of sampled-data loops and for computerising the design of such systems, a state–space formulation is developed. Under the new interpretation, the matched pole–zero model is shown to be structurally identical to a hold-equivalent discrete-time model, where the generalised hold takes integral part, thus unifying the most widely used discretisation approaches. An algorithm for obtaining the generalised hold function is presented. The hold-equivalent structure of the matched pole–zero model clarifies several discrete-time system properties, such as controllability and observability, and their preservation or loss with a matched pole–zero discretisation. With the proposed formulation, the matched pole–zero, hold-equivalent, and mapping models can now all be constructed with a single schematic model. This is of considerable practical importance in digital redesign, especially with the so-called plant-input mapping methods which use the matched pole–zero discretisation of the closed-loop system, and in digital simulations performed with a block-diagram language.


    1. 1)
      • R.M. Golden . Digital filter synthesis by sampled-data transformation. IEEE Trans. Audio Electroacoust. , 321 - 329
    2. 2)
      • G.F. Franklin , J.D. Powell , A. Emami-Naeini . (1991) Feedback control of dynamic systems.
    3. 3)
    4. 4)
      • P.T. Kabamba . Control of linear systems using generalized sampled-data hold functions. IEEE Trans. Autom. Control , 772 - 783
    5. 5)
      • T. Mori , P.N. Nikiforuk , M.M. Gupta , N. Hori . A class of discrete-time models for a continuous-time system. IEE Proc. D, Control Theory Appl. , 79 - 83
    6. 6)
      • Rabbath, C.A., Hori, N., Nikiforuk, P.N., Kanai, K.: `Order reduction of PIM-based digital flight control systems', Proceedings of the IFAC World Congress, July 1999, Beijing, China, Q, p. 127–132.
    7. 7)
      • N. Hori , T. Mori , P.N. Nikiforuk . Discrete-time Models of continuous-time Systems. Control Dyn Syst. , 1 - 45
    8. 8)
      • Rabbath, C.A., Hori, N.: `Continuous-time lifting analysis of digitally redesigned control systems', Proceedings of the Annual Conference of the Society of Instrumentation and Control Engineers, 1998, p. 779–784.
    9. 9)
      • Rabbath, C.A., Hori, N.: `On a comparative study of digital redesign methods', Proceedings of the American Control Conference, 2000, p. 1154–1158.
    10. 10)
      • N. Hori , R. Cormier , K. Kanai . On matched pole-zero discrete-time models. IEE Proc. D, Control Theory Appl. , 273 - 278
    11. 11)
      • P. Katz . (1981) Digital control using microprocessors.
    12. 12)
      • Markazi, A.H.D., Hori, N.: `A new method with guaranteed stability for discretization of continuous-time control systems', Proceedings of American Control Conference, 1992, p. 1397–1402.
    13. 13)
      • T. Chen , B. Francis . (1995) Optimal sampled-data control systems.
    14. 14)
      • Araki, M.: `Recent developments in digital control theory', Proceedings of IFAC Congress, 1993, Sydney, Australia, 9, p. 251–260.
    15. 15)
      • G.C. Goodwin , R.H. Middleton . (1990) Digital control and estimation-a unified approach.
    16. 16)
      • T. Kailath . (1980) Linear systems.
    17. 17)
      • B.C. Kuo . (1980) Digital control systems.

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