Minimal required excitation for closed-loop identification: Some implications for data-driven, system identification

The development and effective use of all available data is extremely important. Previous work has shown that it is possible to identify process models using closed-loop data even if the reference signal was not being excited. However, such results require that the system have a sufficiently large time delay or alternatively a fast sampling time. Therefore, this paper seeks to examine and provide general results for identifiability of a process using closed-loop data with or without changes in the reference signal. Similarly to the previous case, it is shown that the complexity of the required reference signal depends strongly on the sampling time and time delay. However, since many fast processes without time delay can be modelled as first-order systems, they can indeed be identified when the excitation in the reference signal is a simple step function or sequence of such functions. Using numerical simulations as well as the Tennessee Eastman process, the effect on the continuous time parameters is investigated for different sampling times and excitations signals. It is shown that as expected an external reference signal can identify previously difficult-to-identifiable cases.