Tuning of PID Controllers for First Order Plus Time Delay Unstable Systems

  • Saxena Nikita
  • M. ChidambaramEmail author
Conference paper


The focus of the current study is to propose an improved Zeigler-Nichols method for tuning the PID controllers for unstable First Order plus Time Delay (FOPTD) systems. In the proposed method, the controller settings are obtained by solving the magnitude and phase angle criteria. The addition of the controller modifies the overall gain of the system, subsequently changing the values of the controller gain. A second iteration for calculating the updated controller gain is conducted by solving the system’s magnitude and the phase margin criteria, incorporating the Proportional-Derivative-Integral controller transfer function, with unity proportional gain, and with the values of reset time and derivative time. A number of FOPTD systems with varying time delay to time constant ratios are simulated by using the proposed method. A non-linear model of a bioreactor is also simulated to show the enhanced performance over the other methods present in literature. The proposed method significantly improves the performances for the servo and regulatory problems.


Continuous cycling Ziegler-Nichols method Unstable systems PID 


  1. Agarwal, P. Lim, H.C.: Analysis of various control schemes for continuous bioreactors. Adv. Biochem. Eng./Biotechnol 30, 61–90 (1984)Google Scholar
  2. Astrom, K.J., Hagglund, T.: Automatic Tuning of PID controllers. Instument Society of America, North Carolina (1988)Google Scholar
  3. Astrom, K.J., Hagglund, T.: PID Controllers: Theory, Design and Tuning, 2nd edn. Instument Society ofAmerica, North Carolina (1995)Google Scholar
  4. Astrom, K.J., Hagglund, T.: Advanced PID control. Instument Society of America, North Carolina (2006)Google Scholar
  5. Douglas, J.M.: Process Dynamics and Control, 2 Control System Synthesis. Prentice Hall, Englewood Cliffs, NJ (1972)Google Scholar
  6. Majhi, S., Atherton, D.P.: Online tuning of controllers for an unstable FOPTD process. IEEE Proc. CTA 146, 415–425 (2000)Google Scholar
  7. Nikita, S. Chidambaram, M.: Improved Continuous Cycling Method of Tuning PID Controllers for Unstable Systems. Indian Chemical Engineer (2016) in pressGoogle Scholar
  8. O’Dwyer, A.: Handbook of PI/PID Controller Tuning Rules, 3rd Edn. Imperial College Press, (2009)Google Scholar
  9. Smith, C.L.: Intelligently Tune PID Controllers, Chemical Engineering, January, pp. 56–62, (2003)Google Scholar
  10. Thyagarajan, T., Yu, C.C.: Improved auto-tuning using shape factor from relay feedback, Ind. Eng. Chem. Res. 42, 4425–4440 (2003)CrossRefGoogle Scholar
  11. Tyreus, B.D., Luyben, W.L.: Tuning PI controllers for integrator/dead-time processes. Ind. Eng. Chem. Res. 31, 2625 (1992)CrossRefGoogle Scholar
  12. Vilanova, R., Visioli, A.: PID Control in Third Millennium. Springer verlag Ltd., London (2012)CrossRefGoogle Scholar
  13. Yu, C.C.: Auto Tuning of PID Controllers. Springer, Berlin (1999)CrossRefGoogle Scholar
  14. Ziegler, J.G., Nichols, N.B.: Optimum settings for automatic controllers. Trans. ASME 64, 759–765 (1942)Google Scholar

Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of Chemical EngineeringIndian Institute of Technology MadrasChennaiIndia

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