Computing value sets from one point of frequency response with applications

The aim of this paper is to present an explicit parametrization of the value set boundary for a model family consistent both with the process-control-oriented a priori information about the class of candidate models and with one experimentally obtained point of the process frequency response. More precisely, it is assumed that the real process can be described by a multiple fractional order pole model with or without a restriction on the total model order. The result obtained is further extended to the case where more points of a process frequency response are available. However, then only hard bounds of value sets can be computed. The presented results have important applications in design of robust controllers, in particular in the field of automatic tuning procedures.