*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.