Process Identification Methods for Discrete-Time Difference Equation Models
10.1 Prediction Models: Autoregressive Exogenous Input Model and Output Error Model
Prediction models are used to predict the future process output on the basis of the past process input and/or past process output. In this section, two types of discrete-time prediction model are introduced. One is the ARX model and the other is the output error (OE) model. Various discrete-time difference models have been used for modeling of a process. The most useful in process systems engineering are the ARX model and the OE model. Other discrete-time difference models, such as the autoregressive, moving-average, exogenous input (ARMAX) model and the autoregressive, integrated-moving-average, exogenous input (ARIMAX) model, are useful for noisy environments. All the models for noisy processes assume that the noise is white noise. But noise in process systems engineering is small and uncertainties such as disturbances and noises are also quite different from white noise. Also, the models for noisy environments have complicated structures compared with an ARX or OE model. So, the ARX model and OE model are more useful for most cases in process systems engineering than the other more complicated models.
10.1.1 Autoregressive Exogenous Input Model
The ARX model has the following model structure:
where Δt is the sampling ...