Identification of the parameters of the first order dynamic object by difference schemes

E.V. Bolovin, A.S. Glazyrin.

Department of Electric Drives and Equipment, National Research Tomsk Polytechnic University, Tomsk, Russia

Abstract

In this paper a method for determining the parameters of the first-order dynamic object is developed based difference schemes.

Key words: first-order dynamic object, identification of the parameters, difference schemes.

Introduction

In modern production necessary using drives. Different motors are used in drives, both in structure and purpose, and by age category. Effective control of these motors is possible if you know the values of their parameters. But, often determine the parameters is impossible or very difficult. It is connected with the new imported motors, where only the specified power and speed, and the aged motors which have served ten years in which the passport data, were either lost or took the motor is not one-time repairs. Accordingly, the acute question of identification of their parameters. The aim of this paper is selection the optimal method for identifying parameters of objects in the electric control.

Identification of the parameters of the first order dynamic object

The dynamic object of the first order RL-circuit is considered

Form the equation of equilibrium:

₍₁₎

The algebraization of the differential equation (1) is made

₍₂₎

where - the operator of differentiation.

Make a discretization of (2), the values of the input voltage and current RL-circuit will be determined at time

₍₃₎

where - the sampling interval or time step, j - number of time step or at a constant argument of the difference equation obtained from (2)

₍₄₎

To identify the two parameters RL-circuit (resistance and inductance) form a system of linear algebraic equations (SLAE) on the basis of (1.4), consisting of the first equation in and the second equation in

₍₅₎

To implement procedures for identification of parameters of RL-circuit SLAE (5) must be submitted in the form of a matrix of the form

₍₆₎

here - the vector of input variables, - matrix of output values, - the vector of parameters.

The mathematical model of the object was constructed, including evaluation of the unknown parameters

₍₇₎

The parameters of the method of the inverse matrix was estimated

₍₈₎

Considering that the

– vector of parameter estimates for the j-th step,

– first left on the difference between the j-th step,

- step time.

Conclusion

The procedure of compilation the difference equations for identification the parameters of the dynamic object of the first order is presented. This procedure can be applied to DSP-controlled motor drives.