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where yFREE(t) and yINT(t) denote the output
containing terms with and without interactions.
In terms of the former definitions (12) is rewritten
as
y1(t) = [11,1] + [12,2] +
[11,1|11,1] + [11,1|12,1] + [11,1|21,1] +
[11,1|22,2] + [12,2|11,1] + [12,2|12,2] +
[12,2|21,1] + [12,2|22,2] + [11,1|11,1|11,1]
+ [11,1|11,1|12,2] + [11,1|12,2|11,1] +
[11,1|12,2|12,2] + [11,1|11,1|21,1] +
[11,1|11,1|22,2] + [11,1|12,2|21|1]
+[11,1|12,2|22,1] +[11,1|11,1|21,1] +
[11,1|11,1|22,2] + [11,1|12,2|21,1]
+[11,1|12,2|22,2] + [11,1|21,1|21,|1] +
[11,1|21,1|22,2] + [11,1|22,2|21,1] +
[11,1|22,2|22,2] +[12,2|11,1|11,1] +
[12,2|11,1|12,2] + [12,2|12,2|11,1]
+[12,2|12,2|12,2] +[12,2|11,1|21,1] +
[12,2|11,1|22,2] + [12,2|12,2|21,1] +
[12,2|12,2|22,2] + [12,2|21,1|11,1] +
[12,2|21,1|12,2] + [12,2|22,2|11,1] +
[12,2|22,2|12,2] + [12,2|21,1|21,1] +
[12,2|21,1|22,2] + [12,2|22,2|21,1] +
[12,2|22,2|22,2]. (13)
Same as (11) the full expression relating the
third order diagonal terms are recognized with
36 additional interactions terms by adding complexities
to the individual output,
y1(t) = Diag3 [11,1] + Diag3 [12,2] +
[11,1|12,1] + [11,1|21,1] + [11,1|22,2] +
[12,2|11,1] + [12,2|21,1] + [12,2|22,2] +
[11,1|11,1|12,2] + [11,1|12,2|11,1] +
[11,1|12,2|12,2] + [11,1|11,1|21,1] +
[11,1|11,1|22,2] + [11,1|12,2|21|1] +
[11,1|12,2|22,1] + [11,1|11,1|21,1] +
[11,1|11,1|22,2] + [11,1|12,2|21,1] +
[11,1|12,2|22,2] + [11,1|21,1|21,|1] +
[11,1|21,1|22,2] + [11,1|22,2|21,1] +
[11,1|22,2|22,2] + [12,2|11,1|11,1] +
[12,2|11,1|12,2] + [12,2|12,2|11,1] +
[12,2|11,1|21,1] + [12,2|11,1|22,2] +
[12,2|12,2|21,1] + [12,2|12,2|22,2] +
[12,2|21,1|11,1] + [12,2|21,1|12,2] +
[12,2|22,2|11,1] + [12,2|22,2|12,2] +
[12,2|21,1|21,1] + [12,2|21,1|22,2] +
[12,2|22,2|21,1] + [12,2|22,2|22,2] (14)
with Diag3 [11,1] = [11,1] + [11,1|11,1] +
[11,1|11,1|11,1] and Diag3 [12,2] = [12,2] +
[12,2|12,2] + [12,2|12,2|12,2]. The hypothesis
CIENCIA, CULTURA Y TECNOLOGÍA - UNIVERSIDAD TECNOLÓGICA DEL PERÚ
in this study is that the equation (14) containing
only in a first instance diagonal terms would be
an identification system tool up to certain grade
of approximation. Nevertheless, it is important
to recall that the non-diagonal terms can also
add more information on the instabilities and intrinsic
properties of system. Now the main task
is that of taking data from plant and to perform
comparisons in order to validate the equations
(11) and (14).
III POWER PLAN AND DATA ACQUISITION
A. Power Plant Generalities and Data
Data have been taped from an ordinary run at
the 160 MW combined cycle plant located at
Lima North (Ventanilla) which is responsible to
produce electricity power for a 10% of the whole
population at Lima City.
Figure 1. Data extracted from combined cycle plant by showng
the mosphologies of input and output curves. Time runs in
seconds.
The combined cycle takes both water vapor and
natural gas extracted from Camisea, a nature
gas reservoir located in Cuzco. From a common
perspective, it can be perceived as a 2×2 MIMO
system. The valve position and the water flux
act as the input ones, whereas the drum level
and pressure as the output ones. In Fig. 1 is
depicted data by showing the behavior at the
first 120 seconds of run. It is noteworthy that
all trajectories share the same morphology. Perhaps
an exception occurs with the drum level
whose history shows a dip on the 45th second
[4]. On the other hand this event is not seen to
be strongly correlated with each other. Indeed, it
should be noted that a good indicator which tell
us about the normal (or healthy) functionality
of the tank is that of the drum pressure which
acquires an interesting stability over the horizon,
starting at the first 35 seconds of run. Two
minor fluctuations appear on the 35th and 55th
seconds. We noted also that the water flux and
valve position posses a similar trajectory. By the
other hand, water flux curve exhibits a substan-
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