Identification and Tuning Methods for PI Control Systems Based on Symmetric Send-on-delta Sampling

  • José Sánchez MorenoEmail author
  • María Guinaldo Losada
  • Antonio Visioli
  • Sebastián Dormido Bencomo


Two procedures for the definition of an autotuning algorithm for event-based proportional-integral (PI) control systems are proposed in this contribution. Firstly, a method for the identification of the most common transfer functions used for tuning PI controllers is explained. The rationale of the identification method is based on the limit cycles that the event-based sampler and a convenient tuning of the PI controller can produce in the closed loop. The identification method is designed for controller tuning, that is, fitting the behaviour of the process in the range of frequencies between ω-180° and ω-135°. Secondly, a new method for tuning the event-based PI controller is explained. The main control objective of the new tuning rule is to generate a set of parameters that introduces the process in a limit cycle at a user-specified inter-event time. However, by introducing an oscillation margin in the tuning rule, the method generalizes to produce controller parameters that avoid limit cycles with a certain robustness margin. Simulations demonstrate the effectiveness of the tuning rule to force the system to oscillate at a specified frequency as a consequence of the events triggered by the event-based sampler.


Events identification limit cycle PI controller send-on-delta tuning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



  1. [1]
    M. Beschi, S. Dormido, J. Sánchez, A. Visioli, and L. J. Yebra, “Event-based PI plus feedforward control strategies for a distributed solar collector field,” IEEE Transactions on Control System Technology, vol. 22, pp. 1615–1622, 2014.CrossRefGoogle Scholar
  2. [2]
    M. Beschi, S. Dormido, J. Sánchez, and A. Visioli, “Closed-loop automatic tuning technique for an eventbased PI controller,” Industrial and Engineering Chemical Research, vol. 54, pp. 6362–6370, 2015.CrossRefGoogle Scholar
  3. [3]
    M. Beschi, S. Dormido, J. Sánchez, and A. Visioli, “An event-based PI controller autotuning technique for integral processes,” Proceedings of the 1st IEEE International Conference on Event-Based Control, Communication, and Signal Processing, Krakow, Poland, 2015.Google Scholar
  4. [4]
    J. Sánchez, M. Guinaldo, A. Visioli, and S. Dormido, “Identification of process transfer function parameters in event-based PI control loops,” ISA Transactions, vol. 75, pp. 157–171, 2018.CrossRefGoogle Scholar
  5. [5]
    J. Sánchez, M. Guinaldo, S. Dormido, and A. Visioli, “Enhanced event-based identification procedure for process control,” Industrial and Engineering Chemical Research, vol. 57, pp. 7218–7231, 2018.CrossRefGoogle Scholar
  6. [6]
    V. Vasyutynskyy and K. Kabitzsch, “Implementation of PID controller with send-on-delta sampling,” Proceedings of International Control Conference, Glasgow, UK, 2006.Google Scholar
  7. [7]
    M. Beschi, S. Dormido, J. Sánchez, and A. Visioli, “Characterization of symmetric send-on-delta PI controllers,” Journal of Process Control, vol. 22, pp. 1930–1945, 2012.CrossRefGoogle Scholar
  8. [8]
    A. Pawlowski, M. Beschi, J. L. Guzmán, A. Visioli, M. Berenguel, and S. Dormido, “Application of SSOD-PI and PI-SSOD event-based controllers to greenhouse climatic control,” ISA Transactions, vol. 65, pp. 525–536, 2016.CrossRefGoogle Scholar
  9. [9]
    J. A. Romero and R. Sanchís, “Tuning and robustness analysis of event-based PID controllers under different event generation strategies,” International Journal of Control, vol. 91, pp. 1567–1587, 2018.MathSciNetCrossRefGoogle Scholar
  10. [10]
    M. Beschi, S. Dormido, J. Sanchez, and A. Visioli, “Tuning rules for event-based SSOD-PI controllers,” Proceedings of the 20th Mediterranean Conference on Control and Automation, Barcelona, Spain, 2012.Google Scholar
  11. [11]
    M. Beschi, S. Dormido, J. Sánchez, and A. Visioli, “Tuning of symmetric send-on-delta proportional-integral controllers,” IET Control Theory & Applications, vol. 8, pp. 248–259, 2014.MathSciNetCrossRefGoogle Scholar
  12. [12]
    J. A. Romero and R. Sanchís, “A new method for tuning PI controllers with symmetric send-on-delta sampling strategy,” ISA Transactions, vol. 64, pp. 161–173, 2016.CrossRefGoogle Scholar
  13. [13]
    A. Ruiz, M. Beschi, A. Visioli, S. Dormido, and J. E. Jiménez, “A unified event-based control approach for FOPTD and IPTD processes based on the filtered Smith predictor,” Journal of the Franklin Institute, vol. 354, pp. 1239–1264, 2017.MathSciNetCrossRefGoogle Scholar
  14. [14]
    A. Gelb and W. E. V. der Velde, Multiple-input Describing Functions and Nonlinear System Design, McGraw-Hill, New York, NY, 1968.zbMATHGoogle Scholar
  15. [15]
    S. Vivek and M. Chidambaram, “Identification using single symmetrical relay feedback test,” Computer and Chemical Engineering, vol. 29, pp. 1625–1630, 2005.CrossRefGoogle Scholar
  16. [16]
    R. C. Panda, V. Vijayan, V. Sujatha, P. Deepa, D. Manamali, and A. B. Mandal, “Parameter estimation of integrating and time delay processes using single relay feedback test,” ISA Transactions, vol. 50, pp. 529–537, 2011.CrossRefGoogle Scholar
  17. [17]
    R. Bajarangbali and S. Majhi, “Identification of integrating and critically damped systems with time delay,” Control Theory Technology, vol. 13, pp. 29–36, 2015.MathSciNetCrossRefGoogle Scholar
  18. [18]
    L. Tao and G. Furong, “Identification of integrating and unstable processes from relay feedback,” Comput. Chem. Eng., vol. 32, pp. 3038–3056, 2008.CrossRefGoogle Scholar
  19. [19]
    R. Bajarangbali, S. Majhi, and S. Pandey, “Identification of FOPDT and SOPDT process dynamics using closed loop test,” ISA Transactions, vol. 53, pp. 1223–1231, 2014.CrossRefGoogle Scholar
  20. [20]
    K. Srinivasan and M. Chidambaram, “Modified Relay feedback method for improved system identification,” Computers & Chemical Engineering, vol 27, pp. 727–732, 2003.CrossRefGoogle Scholar
  21. [21]
    K. J. Aström, and T. Hägglund, Advanced PID Control, International Society of Automation (ISA): Research Triangle Park, NC, 2006.Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.Department of Computer Sciences and Automatic ControlUniversidad Nacional de Educación a Distancia (UNED)MadridSpain
  2. 2.Antonio Visioli is with the Department of Mechanical and Industrial EngineeringUniversity of BresciaBresciaItaly

Personalised recommendations