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Intuitive robust stability metric for PID control of self-regulating processes.

Jeffrey E Arbogast1, Brett M Beauregard, Douglas J Cooper

  • 1University of Connecticut, Chemical Engineering Program, CMBE Department, U-3222, 191 Auditorium Rd., Storrs, CT 06269-3222, United States.

ISA Transactions
|July 16, 2008
PubMed
Summary

This study introduces the robust stability factor (RSF) to assess how plant-model mismatch in gain, dead time, and time constant affects closed-loop stability. The RSF metric provides a new way to understand and visualize stability robustness in control systems.

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Area of Science:

  • Control Systems Engineering
  • Process Dynamics and Control
  • Robust Control Theory

Background:

  • Existing methods for analyzing closed-loop stability primarily focus on plant-model mismatch in process gain and dead time.
  • These methods often overlook the significant impact of plant-model mismatch in the process time constant on system stability.

Purpose of the Study:

  • To introduce a novel metric, the robust stability factor (RSF), for quantifying the effects of plant-model mismatch across gain, dead time, and time constant.
  • To provide both an equation and a visual representation of the RSF using robustness plots derived from Bode and Nyquist criteria.
  • To enhance the understanding of robust stability by illustrating its relationship with closed-loop performance under varying degrees of plant-model mismatch.

Main Methods:

  • Development of the robust stability factor (RSF) metric.
  • Application of Bode and Nyquist stability criteria to generate robustness plots.
  • Theoretical analysis of the impact of dead time to time constant ratios on stability.
  • Comparison of the robust stability of Internal Model Control (IMC)-PI tuning with other common tuning correlations (PI, PID, PID with Filter).

Main Results:

  • The RSF metric effectively quantifies the influence of plant-model mismatch in gain, dead time, and time constant on closed-loop stability.
  • Plant-model mismatch in the time constant can be as critical to stability as mismatch in gain or dead time.
  • The impact of time constant mismatch is amplified for systems with small dead time to time constant ratios.
  • Decreasing the closed-loop time constant in Internal Model Control (IMC) tuning broadens the range of dead time to time constant ratios for which time constant mismatch significantly affects stability.

Conclusions:

  • The robust stability factor (RSF) offers a comprehensive approach to evaluating closed-loop stability robustness against plant-model mismatch.
  • The findings highlight the critical, often underestimated, role of time constant mismatch in process control.
  • The RSF provides valuable insights for controller tuning, particularly when comparing IMC-PI with other PID-based tuning strategies to ensure robust performance.