Time-Delay Approximation: Its Influence on the Structure and Performance of the IMC-PI/PID Controller

  • P. V. Gopi Krishna Rao
  • M. V. Subramanyam
  • K. Satyaprasad
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 308)


Proportional integral (PI) and proportional integral derivative (PID) controllers have been at the heart of control engineering practice for several decades. 95 % of the controllers employed in the industry are PI/PID. In process control, one often encounters systems described by transfer functions with time delays, which become transcendental functions. The design of the controller demands the rational transfer function approximation of the time-delay term. This paper focuses on the effect of time-delay approximation techniques, viz. Taylor series expansion and Padé approximation, on the structure and performance of PI/PID controllers designed with Internal Model Control (IMC). The performance of the PI/PID controllers was tested in simulation environment on various processes with time delay. For uniform comparison, the controllers were tuned to have a same robustness measure, in terms of maximum sensitivity (M S). The results indicate, irrespective of time-delay approximation considered, the controllers provide good set point tracking and poor disturbance rejection.


Time delay Padé approximation Taylor series Internal model control PI/PID Disturbance Set point 


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Copyright information

© Springer India 2015

Authors and Affiliations

  • P. V. Gopi Krishna Rao
    • 1
  • M. V. Subramanyam
    • 2
  • K. Satyaprasad
    • 1
  1. 1.Department of ECEJNTUKKakinadaIndia
  2. 2.Shantiram Engineering CollegeNandyalIndia

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