Systems with Unstable Zeros or Poles

Abstract

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 D — BR (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.