Page 113 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

88 Chapter Four

1

0.5
>- 0
-0.5

10 20 30 40 50 60 70 80 90 100
1

0.5
>- 0
I
-0.5

30 70
Time

F18UAE4-11 Negating a quantity.

Now, go back to Fig. 4-10. What can we say about the process
output at the cut point? First, we can guess that, relative to the set
point (the input) the process output will have less amplitude and
more phase lag because of inertial effects in the process (which has
unity gain). The controller also might modify the amplitude and
phase of this signal. But, for the time being, assume that neither the
process nor the control adds phase lag and that neither attenuates the
amplitude.
When the loop is closed and Y is subtracted from S, the phase
lag of Y immediately gains 180°. So, a signal with -180° of phase
and unity amplitude is now being added to a signal (the set point)
having zero phase and unity amplitude. The result is "annihilation"
or cancellation.
Now, what if the process and controller were to add -180° of
phase to the process output without changing the amplitude from
unity? When the addition takes place at the summing junction, the set
point with zero phase and unity amplitude will be added to a signal
with a phase of -360° (sum of the phase lag &om the process/ controller
and the negation) and unity amplitude. So, the result of the summing
junction will be to produce a signal with an amplitude that is larger
than either the set point alone or the process variable alone. When
this enlarged signal passes through the loop again, the result of the
summing will produce a signal with yet a larger amplitude. This
sequence is shown in Fig. 4-12.