Identification of linear systems operating in closed loop

Identification of linear systems to obtain empirical models for process control is widely practiced in industry, and typically involves applying designed perturbations to an open-loop system to obtain the necessary data for identification. The question is sometimes asked if this disruptive testing procedure can be avoided by collecting normal process operating data obtained with the process in closed loop. The conditions under which suitable models can be identified with this type of data are described by the closed-loop identifiability conditions. The conditions relate to system order, structure of identified model and type of excitation applied to the system. In this paper we illustrate closed-loop identifiability by generating various sets of closed-loop data from a known simulation system, a Fluid Catalytic Cracking Unit. The simulated process is subjected to different types of excitation and the resulting data is used to identify several different classes of transfer function and finite impulse response models. The results clearly illustrate the combinations of system order, model structure and system excitation that lead to acceptable identified models.