Closed-Loop Identification by Use of Single-Valued Nonlinearities

Closed-loop identification of the ultimate gain (K u ) and critical frequency (ω u ) of a feedback control loop is studied. The accuracy of the Astrom-Hagglund autotuner is discussed, and a simple method of improving the accuracy of the commonly used procedure is proposed and tested by simulation. A modification of the method where the traditional one-parameter relay is replaced by a two-parameter nonlinearity is also proposed. Because the selection of the two parameters of such a nonlinearity is nontrivial, an iterative procedure for the identification of K u and ω u is proposed. The procedure has been found to be convergent and to give reliable and accurate identifications in a number of examples typical of chemical engineering