A Two Step Method For The Closed Loop Identification Of Nonlinear Systems

In recent years, several new methods for the identification of approximate models of an open loop plant on the basis of closed loop data have been presented. In this paper, we extend such a method to the nonlinear case: we consider that both the plant and the controller can be nonlinear. The method that is considered is a two-step procedure, i.e. the sensitivity function of the closed loop system is identified through a high order nonlinear model and it is used in the second step to simulate a noise free input signal for an open loop like identification of the plant. We assume that the closed loop operators are smooth functions of both the reference signal and the disturbance signal and that the measurement noise enters the system under a high SNR assumption. We show that under these assumptions, the linear ideas of [9] carry over to a nonlinear framework. The validity of the theoretical results is verified using simulations.