*113137*
Time delay adjustment for the
method of parameter identification of dynamic object
A.S. Glazyrin, E.V. Bolovin.
Department of Electric Drives and Equipment,
National Research Tomsk Polytechnic University, Tomsk, Russia
e-mail: asglazyrin.tpu.ru
Abstract
The paper
presents the results of a study on the influence of the delay time on the value
of the coefficient matrix determinant in the process of identifying the
parameters of RL-circuit based on the least-squares method.
Keywords: time
delay, parameter identification, the coefficient matrix determinant
Introduction
When identifying
the parameters of dynamic objects on the basis of difference schemes and the
method of least squares problem ill-conditioning of the coefficient matrix
system of linear algebraic equations, the determinant tends to zero and can not
find the inverse matrix. One way of solving problems is to improve the method
by which a system of linear algebraic equations on the basis of difference
schemes. Demonstrate
this RL-circuit.
The test procedure
We write the
equation of the second Kirchhoff's law for the RL-circuit
, or
where – at the time th
step calculation, – current, – resistance, – inductance, – harmonic voltage, sinusoidal or
cosinusoidal.
To determine the
scores of the two unknown parameters and construct a system of equations by adding the second equation is
obtained based on the time delay , and – during the sample sensor signal
voltage and current, and – the number of time delays:
We varied so that the time delay was in the range from 0 up to a quarter
period of the input harmonic voltage. What is the determinant of the
coefficient matrix is, the more correct is the problem of parameter
identification. The average value of the determinant is evaluated at the same
time as the
In the modeling
it was assumed that
, , , , .
The dimensions of
all quantities in the International System of Units (SI). Dependence on the number of time delays is shown in Fig. A.
Fig.
A
Conclusion
The influence of
time delay signals an average value of the determinant in the process of
parameter identification of dynamic objects of the first order. As can be seen
from the figure, the optimum time delay in the preparation of the difference
equations in the parameter identification procedure based on the method of
least squares is about a quarter of the period.