Chapter 4. Empirical Models

The previous two chapters have focused on (i) the development of fundamental models based on material and energy balances (Chapter 2), and (ii) understanding dynamic behavior, with an emphasis on linear systems (Chapter 3). In this chapter we discuss the development of empirical models, that is, developing models based on plant tests. For continuous control-system design (most of the focus of this text), a study of Sections 4.1–4.3 will be sufficient. The discrete models developed in Sections 4.4 and 4.5 will be useful when model predictive control (MPC) techniques are presented in Chapter 16, and when digital control is studied in Module 16.

After studying this chapter the reader should be able to:

• Develop continuous first-order and integrator + dead time models from step tests

• Estimate parameters for discrete-time autoregressive models based on input-output data

• Calculate poles and zeros of discrete-time models

• Develop finite step and impulse response models

The major sections of this chapter are as follows:

4.1 Introduction

4.2 First-Order + Dead Time

4.3 Integrator + Dead Time

4.4 Discrete-Time Autoregressive Models

4.5 Parameter Estimation

4.6 Discrete Step and Impulse Response Models

4.7 Summary