PID Single Element Control

  • Paweł D. DomańskiEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 245)


This chapter presents the simulation analysis of the univariate PID controlled loop simulations. Used PID single element control loops include different kind of models proposed by Åström, i.e. multiple equal poles transfer function, fourth order linear system, nonminimumphase plant, time-delayed double lag process, oscillatory transfer function and fast and slow modes plant.


  1. 1.
    Åström, K.J., Hägglund, T.: New tuning methods for PID controllers. In: Proceedings 3rd European Control Conference, pp. 2456–2462 (1995)Google Scholar
  2. 2.
    Bryce, R.M., Sprague, K.B.: Revisiting detrended fluctuation analysis. Sci. Rep. 2, 315 (2012)Google Scholar
  3. 3.
    Ceballos, R.F., Largo, F.F.: On the estimation of the hurst exponent using adjusted rescaled range analysis, detrended fluctuation analysis and variance time plot: a case of exponential distribution. Imp. J. Interdiscip. Res. 3(8), 424–434 (2017)Google Scholar
  4. 4.
    Domański, P.D.: Fractal measures in control performance assessment. In: Proceedings of IEEE International Conference on Methods and Models in Automation and Robotics MMAR, Miedzyzdroje, Poland, pp. 448–453 (2016)Google Scholar
  5. 5.
    Domański, P.D.: Non-Gaussian and persistence measures for control loop quality assessment. Chaos Interdiscip. J. Nonlinear Sci. 26(4), 043,105 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Domański, P.D.: Non-Gaussian statistical measures of control performance. Control Cybern. 46(3), 259–290 (2017)zbMATHGoogle Scholar
  7. 7.
    Domański, P.D.: Statistical measures for proportional-integral-derivative control quality: simulations and industrial data. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 232(4), 428–441 (2018)CrossRefGoogle Scholar
  8. 8.
    Edgeworth, F.Y.: On observations relating to several quantities. Hermathena 6, 279–285 (1887)Google Scholar
  9. 9.
    Hawkins, D.M.: Identification of Outliers. Chapman and Hall, London (1980)CrossRefGoogle Scholar
  10. 10.
    Løvsletten, O.: Consistency of detrended fluctuation analysis (2018). arXiv:1609.09331v2, [math.ST]
  11. 11.
    Plackett, R.L.: Studies in the history of probability and statistics. XXIX the discovery of the method of least squares. Biometrika 59(2), 239–251 (1972)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. Wiley, New York (1987)CrossRefGoogle Scholar
  13. 13.
    Ruckstuhl, A.: Robust fitting of parametric models based on M-estimation, iDP Institute of Data Analysis and Process Design, ZHAW Zurich University of Applied Sciences in Winterthur (2016)Google Scholar
  14. 14.
    Spinner, T., Srinivasan, B., Rengaswamy, R.: Data-based automated diagnosis and iterative retuning of proportional-integral (PI) controllers. Control Eng. Pract. 29, 23–41 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Control and Computation EngineeringWarsaw University of TechnologyWarsawPoland

Personalised recommendations