Page 167 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

142 Chapter Five

• : ~ • • • • • 1 I ••
.
.
I o\ o o ....... I ......
to-I tOO to2 t<P
Or---~~~~--~:-----:----:----1
-tOO
- Onetank
~ -200 ... lWotanks . .
~ - - Three tanks
tU -300 --~~-------
f ·- · Four tanks ·--,..~---·-·-·~-
-
Fivetanks
-400 c....,....,.. ..................................... ; ••••
-~~~~~~~~~--~~~~~~--~~~
to-3 to-2 to-I tOO 10 1 to2 t<P
Frequency (Hz)
F1auRE 5-15 Bode plot of multitank system.

Matching the N-Tank Model with a FOWDT Model
The FOWDT model introduced in Chap. 4 has quite a bit of flexibility
and is simple to use. Figure 5-t6 shows how a 20-tank model with
each tank having a time constant of t/20 can be approximated by a
FOWDT having a time constant of 0.2 and a dead time of 0.732.
t
N = 20 tau = 0.2 FOWDT
0.9
dead time = 0.73236
0.8
I
0.7 .. . ' . . ' .
I-N-Tanks I
0.6 · · .... FOWDT .
0.5 .. ••• 0 0

0.4
0.3 .. : 0 0 0 0 0 0
0.2 . . ...
O.t '. •• 0 0 0 •'

0
0 0.2 0.4 0.6 0.8 t t.2 t.4 t.6 t.8 2
Tune
FlauAE 5-16 Matching a FOWDT model with N-tanks in the time domain.