Exact tuning of PID controllers in control feedback design

Exact tuning of PID controllers in control feedback design

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In this study, the authors introduce a range of techniques for the exact design of PID controllers for feedback control problems involving requirements on the steady-state performance and standard frequency-domain specifications on the stability margins and crossover frequencies. These techniques hinge on a set of simple closed-form formulae for the explicit computation of the parameters of the controller in finite terms as functions of the specifications, and therefore they eliminate the need for graphical, heuristic or trial-and-error procedures. The relevance of this approach is (i) theoretical, since a closed-form solution is provided for the design of PID-type controllers with standard frequency-domain specifications; (ii) computational, since the techniques presented here are readily implementable as software routines, for example, using MATLAB®; (iii) educational, because the synthesis of the controller reduces to a simple exercise on complex numbers that can be solved with pen, paper and a scientific calculator. These techniques also appear to be very convenient within the context of adaptive control and self-tuning strategies, where the controller parameters have to be calculated online. Furthermore, they can be easily combined with graphical and first/second-order plant approximation methods in the cases where the model of the system to be controlled is not known.


    1. 1)
      • K.J. Astrom , T. Hagglund . (1995) PID controllers: theory, design, and tuning.
    2. 2)
      • K.J. Astrom , T. Hagglund . (2005) Advanced PID control.
    3. 3)
      • A. Datta , M. Ho , S.P. Bhattacharya . (2000) Structure and synthesis of PID controllers.
    4. 4)
      • A. Visioli . (2006) Practical PID control: advances in industrial control.
    5. 5)
    6. 6)
    7. 7)
      • Kim, K., Kim, Y.C.: `The complete set of PID controllers with guaranteed gain and phase margins', Proc. 44th IEEE Conf. on Decision and Control, and the European Control Conf. 2005, 12–15 December 2005, Seville, Spain, p. 6533–6538.
    8. 8)
    9. 9)
    10. 10)
      • G.F. Franklin , J.D. Powell , A. Emami-Naeini . (1991) Feedback control of dynamic systems.
    11. 11)
      • A. Ferrante , A. Lepschy , U. Viaro . (2000) Introduzione ai controlli automatici.
    12. 12)
      • K. Ogata . (1997) Modern control engineering.
    13. 13)
    14. 14)
    15. 15)
      • Zanasi, R., Marro, G.: `New formulae and graphics for compensator design', Proc. 1998 IEEE Int. Conf. on Control Applications, 1–4 September 1998, 1, p. 129–133.
    16. 16)
      • G. Marro . (1998) TFI: insegnare ed apprendere i controlli automatici di base con MATLAB.
    17. 17)

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