Closed loop identification of nonlinear systems

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 two of these methods to the nonlinear case: we consider that both the plant and the controller can be nonlinear. The first method is a two-step procedure. 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. The second method identifies the right coprime factors of the plant through an open loop like identification of the filtered sensitivity and complementary sensitivity functions. For both methods, we assume that the measurement noise enters the system under a high S/N ratio assumption.