Systems with Unstable Zeros or Poles

  • Cheng-Ching Yu
Part of the Advances in Industrial Control book series (AIC)


Despite the success of relay feedback tests in process industries, a few cases of unsuccessful applications have been reported. Papastathopoulou and Luyben (1990) show that a relay feedback test cannot generate sustained oscillation on a DBR (distillate-boilup ratio) controlled C 3 splitter. Another example is that the relay feedback test fails to generate a stable limit cycle for the incorrectly paired WB (Wood and Berry, 1973) column. Obviously, the relay feedback test cannot generate sustained oscillation in all systems. The failure can come from lack of process understanding, incorrect knowledge about process system, system inherent property or, even worse, ignoring known process information.


Nyquist Plot Stable Limit Cycle Sustained Oscillation Process Gain Relay Feedback 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Devia, N.; Luyben, W. L.“Reactor: Size versus Stability”. Hydrocarbon Proc. 1978, 6, 119.Google Scholar
  2. [2]
    Fendrich, O. R.“Describing Function and Limit Cycles”. IEEE Trans. Autom. Contr. 1992 37, 486.Google Scholar
  3. [3]
    Huang, H. P.; Chen, C. C. “On Stabilizing a Time Delayed Unstable Processes”. J. Chin. Inst. Chem. Eng. 1997 28,289.Google Scholar
  4. [4]
    Luyben, W. L.Process Modeling Simulation and Control for Chemical Engineers. 2nd Ed.; McGraw-Hill: New York, 1990. Google Scholar
  5. [5]
    Ogata, K. Modern Control Engineering 2nd Ed.; Prentice Hall: Englewood Cliffs, 1990.Google Scholar
  6. [6]
    Papastathopoulou, H. S.; Luyben, W. L. “Potential Pitfalls in Ratio Control Schemes”.Ind. Eng. Chem. Res. 1990 292044.Google Scholar
  7. [7]
    Slotine E. J. J.; Li, W. Applied Nonlinear Control; Prentice Hall: Englewood Cliffs, 1991.zbMATHGoogle Scholar
  8. [8]
    Wood, R. K.; Berry, M. W.“Terminal Composition Control of Binary Distillation Column”. Chem. Eng. Sci. 1973, 28, 1707.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Cheng-Ching Yu
    • 1
  1. 1.Department of Chemical EngineeringNational Taiwan University of Science & TechnologyTaipeiTaiwan

Personalised recommendations