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System identification
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System identification is the field of mathematical modeling
of systems from experimental data, and is categorized
into nonparametric and parametric methods according to
the model structure. When the model structure of a system
is considerably complex or largely scaled like a power
transformer, nonparametric identification is deemed to
be suitable. The nonparametric identification is characterized
by the property that resulting models are curves or functions
(e.g. spectral analysis for the diagnosis of a power transformer).
On the other hand, parametric identification is favorable
to the system whose model structure is simply described
with simple mathematical static and/or dynamic equations.
Most researches in parametric identification area focus
on discrete-time systems owing to the easiness and simplicity
of required mathematics. However, the performance of the
discrete-time identification depends on a sampling time,
and the obtained parameters give little physical insight
into the system. Therefore, in the case of a diagnosis
or modeling, continuous-time parametric identification
is preferred despite the mathematical complexities.
DEAS has been applied to the continuous-time parametric
identification of an induction motor with both simulation
and experimental data. The induction motor is modeled
as the fifth-order nonlinear equations |
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| All the parameters in the model are combinations of
motor parameters, e.g. the resistances and inductances
of a stator and a rotator. Thus an analytical method such
as the continuous-time prediction error method requires
intricate derivation of a parameter update rule, and a
numerical method such as the genetic algorithm (GA) consumes
too long an execution time. However, DEAS needs no complex
analysis with fast search speed (eDEAS performs 20 times
faster than GA with higher solution quality for the parametric
identification of an induction motor). Fig. 1 is an illustration
of the performance of DEAS for parametric identification
of an induction motor with simulation data. See [J2] for
more detail description. |
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Fig. 1 Convergence of estimated
parameters located by eDEAS |
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Gain tuning of PID controllers
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The proportional-integral-derivative (PID) controllers
are widely used in the process control industry owing
to their relatively simple structures and robust performances.
This popularity has stimulated researchers to develop
various methods for the design of PID controllers, which
can be roughly classified into two approaches; frequency-based
and time-based methods. The frequency-based tuning methods
encompass most of the conventional methods, e.g. the Ziegler-Nichols
rule, the Cohen-Coon method, the internal mode control,
Wang's and Ho's tuning rules, and so on.
These methods generally guarantee the stability of the
controlled systems, but often design poorly tuned PID
controllers in terms of time-domain specifications. On
the other hand, the time-based tuning methods which resort
to the tools of soft computing, such as the fuzzy inference
system, the neural network, and the genetic algorithm,
are recently being researched in addition to the conventional
criteria such as IAE and ITAE. However, despite their
excellent control performance in time domain, the time-based
methods often lack the guarantee of the system's stability.
Therefore, both the frequency-based and time-based approaches
have to be considered together for determining the gains
of stable and well-performing PID controllers. This approach
can be implemented by a constrained optimization technique
in which frequency-domain related factors (i.e. phase
and gain margins) serve as a constraint, and the three
gains enabling the output response to well agree with
a desired response are sought by a nonlinear optimization
algorithm as |
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| Penalty function methods transform the constrained optimization
problem into alternative formulations such that numerical
solutions are sought by solving an unconstrained optimization
problem. Fig. 2 shows that the proposed gain tuning method
with eDEAS enables a controlled output profile to have
the smallest overshoot with medium rising time for the
system |
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Fig. 2 Comparison of PID controlled
step responses |
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Weight training of
artificial neural networks |
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Copyright
¨Ï2003 by DEAS. All rights reserved...... |
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