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TUNABLE SYSTEM IDENTIFICATION
AND CONVOLUTION INTEGRALS
Abstract
In this paper, I’ve developed a model of integrals
of convolution where the main point
is based on the possibility of getting tunable
system identification in a much more complete
manner and which is based on the quantitative
measuring of interactions in time. The way for
that consists in implementing a set of parameters
which are solved in each step of computation
of the convolution integrals without losing
the generality. As illustration of this method,
I’ve investigated the sustainability of the systems
which are required to be stable along the
control horizon and which are sensitive to collapse
after a long time.
I. Tunable System Identification
I’ve defined as tunable system identification to
the action of measuring and altering the output
variables from convolution integrals with
several parameters changing in time. When
complex systems variables are changing in
their form and properties, and it is rather fast,
then the observer has not chance to decide the
next step to solve the integrals equations and
preferably make the choice as convenient as
possible. Exceptions occur when the number of
free parameters is small, and most of them are
negligible when the system goes over horizon
and maintains its set point for a longer time
[1]. The case when the system contains a huge
amount of free parameters is much more complicated
because the measuring needs sophisticated
tools to maintain the stability and equilibrium
in each time step. My proposal is the
reconstruction of an algorithm which should
guarantee the measuring in all time steps and
making the measure error much more smalls
CIENCIA, CULTURA Y TECNOLOGÍA - UNIVERSIDAD TECNOLÓGICA DEL PERÚ
or at least leaving the system invariant in a
short future.
I’ve coined the term “tunable” because the parameters
are tuned one-to-one in time and their
values are known previous to the next step.
The solving of these parameters for a time t
has consequences for the new set of parameters
in the time t+T where is assumed the system
is still stable. For times where the system
might fall down by showing weakness and a
possible collapse, the measuring of parameters
previous to these actions, is very important
because it gives us valuable information
of systems in advance, in special their important
parameters. As example I review the case
where the system contains transfer and input
function with up to 10 parameters and which
are solved simultaneously within a systematic
error whose presence is contemplated. In the
next I’m going to explain the main ingredients
of my proposal.
II. Tunable Convolution Integrals
A convolution integral is an operation where
there are two functions to be integrated together:
One can observe that only one is shifted or delayed.
It is more or less used in input/output
(I/O) relations and would serve to apply in control
theory. Now I will write the same but for a
next step in time
Ing. Juan Tisza
Contreras
Decano de la
Facultad de
Ingeniería
Electrónica y
Mecatrónica
Universidad
Tecnológica del
Perú
27