A direct approach to identify closed loop Wiener systems, whose linear dynamics are open-loop unstable

A Wiener system is a series connection of a linear dynamic system followed by a static non-linearity. The identification of Wiener systems has been an active research topic for years. We extend the algorithm proposed by Zhao & Westwick, [Proceedings, ACC2003] (2003) to identify Wiener systems that are unstable in open loop, but being operated stably in a closed-loop configuration. The variant of the MOESP (multivariable output-error state space) algorithm developed in Y. Zhao & D.T. Westwick (2003) is used to identify a state space model of the linear part of a Wiener system operating in closed loop. Since the linear dynamics of the Wiener system are unstable in open loop, the output of the linear subsystem cannot be obtained by direct simulation. Without an estimate of the linear output, the nonlinearity can´t be estimated. The main contribution of this paper is the design of an extended Kalman filter, which is used to estimate the states of the linear subsystem as well as the parameters of the nonlinearity.