Conditions for Identifiability Using Routine Operating Data for a First-Order ARX Process Regulated by a Lead-Lag Controller

The conditions for closed-loop identifiability using routine operating data are largely unknown. In this paper, the closed-loop identifiability conditions for a first-order autoregressive process with exogenous input (ARX) that is regulated using a 3-parameter lead-lag controller and that has no external excitation will be examined using an analytical approach. Despite the convoluted nature of the intermediate results, the final conditions for absolute identification of the stable region can be concisely stated. These results suggest that the class of internal model controllers (IMCs) can, despite their aggressive behaviour, successfully identify an ARX model without any external excitation. As well, Monte Carlo simulations performed using MATLAB confirmed the analytical results that were obtained. Future work in this area can focus on extending the results to other model structures, to other types of controllers, and to higher order processes.