Page 100 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

CHAPTER4

A New Domain

and More Process

Models

hapter 3 introduced the reader to a relatively sophisticated
tool, the Laplace transform. It was shown to be handy for
Csolving the differential equations that describe model pro-
cesses. It appeared to have some other features that could yield
insight into a model's behavior without actually doing an inversion.
In this chapter the Laplace transform will be used as a stepping
stone to lead us to the frequency domain where we will learn more
tools for gaining insight into dynamic behavior of processes and con-
trolled systems.
Chapter 3 also got us started with a simple process model, the
first-order model that behaved approximately as many real processes
do. However, this model is not sufficient to cover the wide variety of
industrial processes that the control engineer must deal with. So, to
the first-order process model we will add a pure dead-time model
which will subsequently be combined with the former to produce the
first-order with dead-time or FOWDT model. For technical support
the reader may want to read App. B (complex numbers), App. D (infi-
nite series), App. E (first- and second-order differential equations),
and App. F (Laplace transforms).
As in previous chapters, each new process will be put under con-
trol. In this chapter the new tool of frequency domain analysis will be
used to augment time domain studies.

4-1 Onward to the Frequency Domain

4·1·1 Sinusoidally Disturbing the First-Order Process
Instead of disturbing our tank of liquid with a step change in the
input flow rate, consider an input flow rate that varies as a sinusoid
about some nominal value as shown in Fig. 4-1. The figure suggests

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