Identification of linear, multivariable systems operating under linear feedback control

Decentralized closed-loop parameter identification for multivariable processes from step responses

“…In the 1970s, Söderstrom and Ljung, etc. initially extended the prediction error method (PEM) to the identification of multivariable systems in [8], gave system identifiability conditions in [10] and discussed accuracy aspects in [3]. In their works, closedloop identification methods were classified into three approaches, i.e.…”

Identifiability analysis of interconnected zero-memory composite systems

“…(2.7)) of the system component inside the complex system, or (ii) system identifiability problem-the problem of determining any member of the set (c., Uj) e CCj x HiK·(~} of parameters indistinguishable from ajQ inside the complex system (for terminology, see Ljung et al 1974, Ljung 1976, 1978or Gustavsson et al 1977.…”

“…Further, owing to the terminology originated by Ljung et al 1974 (see also references above), the subsystem (2.1) will be said to be parameter (respectively, system) identifiable inside the complex system, if the parameter (respectively, system) identifiability problem can be solved satisfactorily for this subsystem. If, in turn, the parameter (system) identifiability problem can be solved for all subsystems jointly, the composite system will be called parameter (system) identifiable.…”

Decentralized identification for multivariable integrating processes with time delays from closed-loop step tests

“…This may result in a wrong estimation of the process model with non-parametric closedloop identification methods, if the closed-loop system is not excited by some persistent excitations as references (set points) [11,21,25,32,33]. Thus one of the most popular closedloop identification approaches is to build a parametric model in the prediction error framework introduced by Söderstrom, Ljung and Gustavsson, [7,12,20,21] in the 1970s. It has recently been shown that the identifiability of a closed-loop prediction error method is possible even if the experiment is deemed not to be informative enough [4,6] (more details can be seen in [23,24,34]).…”