Relay feedback tests for highly nonlinear processes: Reactive distillation

This paper is intended to demonstrate the effectiveness of the relay feedback test for the identification of highly nonlinear processes, namely, reactive distillation. Because of the multifunctional nature, reactive distillation exhibits strong nonlinearity and possible "sign reversal" in the steady-state gain of product composition and tray temperatures. A methyl acetate reactive distillation is used to illustrate performance of two different identification approaches: step test and relay feedback test. For the composition control, step tests reveal sign changes in steady-state gain as the step size varies from - 10% to + 10%. Moreover, step test is also sensitive to the direction of the step. On the other hand, consistent ultimate gain and the ultimate period can be identified for different relay heights with different initial step directions. The error in the high-frequency information is < 5% for the reactive distillation column that has been studied. Good control performance can be obtained using simple PI controllers tuned with the ultimate gain and ultimate period. Comparison is also made for temperature control and, again, the results indicate that consistent high-frequency information can be obtained with the relay feedback test. Finally, relay feedback is applied to multivariable control of reactive distillation. The resultant PI controllers, designed based on the ultimate information, also gives satisfactory performance for set-point and load changes.