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Related Experiment Videos

PID controller tuning for the first-order-plus-dead-time process model via Hermite-Biehler theorem.

Anindo Roy1, Kamran Iqbal

  • 1Department of Applied Science, University of Arkansas at Little Rock, Little Rock, AR 72204, USA. axroy@ualr.edu

ISA Transactions
|August 9, 2005
PubMed
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This study presents PID stabilization for first-order-plus-dead-time (FOPDT) processes using the Hermite-Biehler theorem. It provides stability bounds and an algorithm for selecting gains, outperforming traditional tuning methods.

Area of Science:

  • Process Control
  • Control Theory
  • Chemical Engineering

Background:

  • First-order-plus-dead-time (FOPDT) models are widely used to represent processes in the chemical and petroleum industries.
  • Proportional-Integral-Derivative (PID) controllers are essential for process stabilization.
  • Analytical stability analysis of FOPDT systems with PID control is crucial.

Purpose of the Study:

  • To analytically investigate PID stabilization of FOPDT processes using the Hermite-Biehler theorem.
  • To derive necessary and sufficient conditions for closed-loop stability.
  • To develop a systematic method for selecting stabilizing PID gains.

Main Methods:

  • Application of the Hermite-Biehler theorem to an FOPDT process model.
  • Utilizing a first-order Padé approximation for the transport delay.

Related Experiment Videos

  • Derivation of stability bounds as functions of plant parameters.
  • Development of an algorithm for feedback gain selection.

    • Main Results:

    • Established necessary and sufficient conditions for PID stabilization of FOPDT systems.
    • Developed stability bounds dependent on process parameters.
    • An algorithm for selecting stabilizing PID gains was created.
    • The proposed PID controller demonstrated competitive sensitivity and disturbance rejection.

    Conclusions:

    • The Hermite-Biehler theorem provides a robust framework for PID stabilization of FOPDT models.
    • The derived stability bounds and gain selection algorithm offer a systematic approach to controller tuning.
    • The proposed method shows advantages over traditional tuning techniques like Ziegler-Nichols and Cohen-Coon.