Page 168 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

Matrices and High e r-0 rd e r Process Models 143

0
~ -20 .. .. . . ... . .
:2.
., -40
cu
.a 0
:.::1 -60 .. . : . . . .. .. ........ · .
c..
~ -80 Q
-100
1Q-2 to-1 100 10 1 1o2
0
-FOWDT
o N-Tanker
- -150 ..........
~
~
tU
f -1000 i. ... ·,·
-1500 ........... . . . .......
1o-2 1Q-1 100 101 1o2
Frequency (Hz)

F1auRE 5-17 Matching a FOWDT model with multitank system in the
frequency domain.

For a complementary point of view, the two models are compared
in the frequency domain in Fig. 5-17. The comer frequencies of the
two models are approximately the same but for higher frequencies
the amplitude drops off much more quickly for the 20-tank model.
This makes sense because the FOWDT model is basically first order
so the magnitude drops off at 20 dB/decade while the other model's
attenuation rate is 20 times that. On the other hand, the phase plot
shows that the FOWDT model with the true dead time has a much
higher drop-off rate. Furthermore, we know that each of the tanks in
the 20-tank model contributes 90° of phase so the maximum phase
lag at infinite frequency will be 1800°.
For simulation purposes and control algorithm testing, the
FOWDT model might provide a simple computational approxima-
tion to the multiple tank process.

5-6 Summary
The toolkit of model processes has been expanded to include multi-
ple-stage systems. The mathematical toolkit has been expanded to
include matrix methods to simplify and enhance the mathematical
bookkeeping and to pave the road to more methods using state-space
concepts. In the next chapter our process toolkit will be enlarged to
include yet another model process-one that rings.