Identification of Hammerstein-Wiener Systems using Subspace Method and Separable Least-Squares

Abstract

We deal with identification of Hammerstein-Wiener systems, or NLN systems, in which a linear subsystem is sandwiched by two nonlinearities. First we identify an approximate linear state space model of the NLN system by using the ORT (orthogonal projection) subspace method or PO-MOESP method. Then, initialized by the estimated state space model, we optimize the output error (OE) model, which is derived based on the basis functions expansion of nonlinearities, by using a gradient-based optimization method. Numerical results are included to show the applicability of the present approach.

A Joint Input-Output Approach to Closed-loop Identification of Hammerstein-Wiener Systems

“…The optimal solutions are given by 2 so that we define v 0 (t) = γ * v (t) and w 0 (t) =ŵ(t)/μ * , and set κ * = 1/(γ * μ * ) as shown in Fig. 3.…”

“…It has extensively been used in model predictive controls [5,8,15] and process controls [23,22]. Moreover, a number of papers have been published for the identification of NLN systems in open loop [4,23,22,16,21,2]. Further, using a subspace method and the kernel technique, a method for identifying a closed-loop NLN system is derived [19].…”

Identification of Hammerstein-Wiener Systems in Closed-loop

“…We apply the ORT method [14] or PO-MOESP method [22] to the input-output data {u(t), y(t)} in order to obtain an approximate state space modelĜ d (z) = (A (0) , B (0) , C (0) ) of the plant in the forward loop [1].…”

“…A number of papers have been published for the identification of Hammerstein and Hammerstein-Wiener (NLN) 1 systems [2,27,8,26,20,25,1], and several methods have been developed for the closed-loop identification of Hammerstein systems. In fact, a subspace identification method is developed for MIMO closedloop Hammerstein systems [15].…”

“…This paper presents a direct method for identifying a Hammerstein-Wiener system in closed-loop by extending the open-loop result [1]. Under the assumption that the linear plant is stable or semi-stable, we derive an output error (OE) model simulating the forward loop with the help of basis function expansions of nonlinearities.…”