Using limit cycle data for parameter estimation

Abstract

Exact expressions for the periods and amplitudes of limit cycles in relay controlled loops, with first order plus dead time (FOPDT) and second order plus dead time (SOPDT) transfer functions have been obtained using the A-locus method. The method has also been extended to unstable FOPDT and SOPDT transfer functions since it is possible to have unstable transfer function models for some chemical processes. For these processes, it is shown that analysis using the DF method can give large errors. Several examples have been given to illustrate application of the method and it has been shown that the method will work well for small measurement errors when compared with the DF method.