Tuning Rules for PID Controllers for Unstable Systems

Part of the Advances in Industrial Control book series (AIC)


This chapter proposes the tuning formula for the parameters of the PID controller for a first-order plus time delay unstable system. The correlations between controller settings (K c, τ I and τ D) and the system parameters (gain, time delay and time constant) are proposed so that there is no need to perform the second test to calculate the update controller gain as done in the previous chapter. In addition, to improve the ZN continuous cycling method, correlations between the controller parameter and the ultimate values of the control system gains (K c,max, P u) are proposed. These can be applied by the using the results of the single relay feedback test or the stability criteria.


  1. Agarwal P, Lim HC (1984) Analysis of various control schemes for continuous bioreactors. In: Advances in biochemical engineering/biotechnology, vol 30, pp 61–90Google Scholar
  2. Chidambaram M, Vivek S (2014) Relay auto-tuning for identification and control. CambridgeGoogle Scholar
  3. Jeng JH, Fu EP (2015) Closed loop tuning of set point weighted proportional integral derivative controllers for stable, integrating and unstable processes: a unified data based method. Ind Eng Chem Res 54:1041–1058Google Scholar
  4. Lee Y, Lee J, Park S (2000) PID controller tuning for integrating and unstable processes with time delay. Chem Eng Sci 55(17):3481–3493CrossRefGoogle Scholar
  5. Majhi S, Atherton DP (2000) Online tuning of controllers for an unstable FOPTD process. IEEE Proc CTA 146:415–425Google Scholar
  6. Pai NS, Chang SC, Huang CT (2010) Tuning PI/PID controllers for integrating processes with dead time and inverse response by simple calculations. J Process Control 20(6):726–733Google Scholar
  7. Shiu SJ, Hwang SH, Lin ML (1998) Automatic tuning of systems with one or two unstable poles. Chem Eng Comm 167:51–72Google Scholar
  8. Smith CL (2003) Intelligently tune PID controllers. Chem Eng 56–62Google Scholar
  9. Thyagarajan T, Yu CC (2003) Improved auto-tuning using shape factor from relay feedback. Ind Eng Chem Res 42:4425–4440CrossRefGoogle Scholar
  10. Yu CC (2006) Auto tuning of PID controllers—a relay feedback approach, 2nd edn. Springer, LondonGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

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

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