Pseudo-random binary sequence closed-loop system identification error with integration control

This paper studies the closed-loop system identification (ID) error when a dynamic integral controller is used. Pseudo-random binary sequence (PRBS) q-Markov covariance equivalent realization (Cover) is used to identify the closed-loop model, and the open-loop model is obtained based upon the identified closed-loop model. Accurate open-loop models were obtained using PRBS q-Markov Cover system ID directly. For closed-loop system ID, accurate open-loop identified models were obtained with a proportional controller, but when a dynamic controller was used, low-frequency system ID error was found. This study suggests that extra caution is required when a dynamic integral controller is used for closed-loop system identification. The closed-loop identification framework also has significant effects on closedloop identification error. Both firstand second-order examples are provided in this paper.