Process control, PID and adaptive control - Intelligent Buildings and Building Automation - page 122

+

+ D

V Y

Human
operator

Process

E (de/dt)

U

- +

Y

A

E

E 1,2

t 1 t 2 t 3

B

Figure 7.9 Possible genesis of derivative control.

therefore allow uncontrolled steady-state errors. Thus the discussion in this
section cannot consider derivative functions in isolation. They will always
be considered as supplementing some other function.
Although derivative functions are helpful in solving a variety of control
design problems, one of their most important contributions is in system sta-
bility improvement. If absolute or relative stability is the problem, a suitable
derivative control mode is often the answer.
This stabilization or 'damping' aspect of derivative control can be easily
understood qualitatively from the following discussion. Just as the invention
of integral control may have been stimulated by human process operators'
desire to automate their task of manual reset, derivative control may first
have been devised as a simulation of human response to changing error sig-
nals. In Figure 7.9, we assume a human process operator is given a graphical
display of system error E and has the task of changing manipulated variable
U so as to keep E close to zero.
Let us consider 'If I were the operator, would I produce the same value
of U at time t 1 as at time t 2 ? ' (Note that a proportional controller would do
exactly that.) Most people agree that a higher corrective effort seems appro-
priate at t 1 and a lesser one at t 2 , since at t 1 the error is E 1,2 and increasing,
whereas at t 2 it is also E 1,2 but decreasing. That is, the human eye and brain
senses not only observe the current value of the graph's curve but also its
trend or slope. Slope is clearly dE/dt , so to mechanize this desirable human