Control Performance Assessment for Hammerstein-Wiener Models

Control performance assessment, or CPA, is an increasingly vital tool to quantify the performance of industrial control loops. While most of the research and commercial activity in CPA has been applied to linear systems to date, those researchers investigating nonlinear systems fall into one of two groups. The first group focussed on the diagnosis of a common specific nonlinearity, namely valve stiction (A. Horch, 1999, M.A.A.S. Choudhury and S.L. Shah and N.F. Thornhill and David S. Shook, 2006, Nina F. Thornhill and Alexander Horch, 2007), while the second group tried to establish the minimum variance performance lower bound (MVPLB) (T.J. Harris and W. Yu, 2007, Yu et al., 2008, 2009, 2010). In this paper we will continue to investigate CPA for a popular and versatile class of nonlinear model; the Hammerstein-Wiener (HW) model. Since the minimum performance lower bound is hard to establish for nonlinear systems, we propose two new performance indices which can be reliably estimated from the routine closed loop data. These indices can be used in a manner similar to the standard linear CPA performance index. The estimates are obtained by fitting the output data to a nonlinear autoregressive and moving average (NARMA) model. The results of two simulation examples illustrate that the proposed methodology is efficient and accurate for the class of HW models.