4.7 Summary

The first sections of this chapter illustrated the development of first-order + time-delay and integrator + time-delay models based on step input changes. These models will be sufficient for many simplified controller designs. Higher order models can easily be developed by "fitting" (adjusting) parameters to obtain a best match between model predictions and the actual measured process output responses.

Linear regression (least squares) techniques can be used to estimate parameters in discrete time autoregressive models. Usually, parameters are estimated based on a subset of the available experimental data. The model parameters are then verified by applying the model to a different subset of the data. If the model predictions match the measured outputs reasonably well, then the discrete model is usually acceptable for discrete control system design and analysis.

The stability of a discrete transfer function model is determined from the values of the poles of the denominator polynomial. If the poles are less than 1 in magnitude, the discrete model is stable. Module 16 covers classical discrete controller design procedures. Discrete step and impulse response models are often used in model predictive control (Chapter 16).