Estimation of parameters of the differential equation describing the processes of starting and stopping the pumping unit

This article presents the results of the study of various transient modes of the pumping unit of an oil pumping station, in particular, the stator currents of the drive motor and the speed characteristic of its rotor rotation. The characteristics of the pumping unit can change quite significantly during operation. This is due to the fact that the parameters of the pumped oil change almost continuously, physical wear of the parts of the pumping unit also occurs, and the impeller is especially susceptible to wear. The input and output variables of this object are, respectively, the time and the angular velocity of rotation of its rotor. The combination of the above factors has a significant impact on the change in the speed of rotation of the rotor during operation, which can adversely affect the operation of the system as a whole. In order to eliminate the influence of external factors on the operation of the pumping unit, the relationship between the input and output variables was described by an ordinary differential equation with constant coefficients. The purpose of this work is to illustrate the possibilities and "technology" of applying the sensitivity algorithm for estimating the parameters of a given equation and to show that the proposed method and the numerical algorithm that implements it allow us to quite successfully solve the problem under consideration and they are suitable for solving many similar applied problems related to estimation of parameters of ordinary differential equations.Based on the results of the work, the proposed method and the numerical algorithm that implements it have shown their efficiency and can be further used to automate real control objects in various fields of science and technology.