Controller assessment for a class of non-linear systems

The use of autoregressive moving average (ARMA) models to assess the control loop performance for processes that are adequately described by the superposition of a linear dynamic model and linear stochastic or deterministic disturbance model is well known. In this paper, classes of non-linear dynamic/stochastic systems for which a similar result can be obtained are established for single-input single-output discrete system. For these systems, lower mean-square error bounds on performance, can be estimated from the closed-loop routine operating data by using non-linear autoregressive moving average with exogenous inputs (NARMAX) models. It is necessary to know the process time delay. The fitting of these models is greatly facilitated by using efficient algorithms, such as Orthogonal Least Squares or other fast orthogonal search algorithms. These models can also be used to assess the predictive importance of non-linearities over multiple-time horizons.