Synthesis of system of coordinated control of electric drives with electronic reduction

The paper presents data construction of an electric drive structure with an electronic reduction. The transferred functions of the system for control and disturbing signals are received. The results of mathematical modeling for various operating modes are presented. The sensitivity of the transfer function to specific links is analyzed. Different modes of operation of the coordinated control system are analyzed. The sensitivity of the transfer function to specific links is analyzed. Different modes of operation of the coordinated control system are analyzed.


Introduction
Multi-motor, in particular twin-motor, electric drives with coordinated control are widely used in lifting and transport mechanisms [1][2][3], autonomous objects, electric drives with force reflection and other fields [4]. The issues of coordinated control can be solved in various ways, there are various modifications to the "electric shaft" [8] schemes, electric drives matching the coordinate difference, etc. [6][7][8][9]. At the same time, it is possible to construct parametric systems of coordinated rotation [10].
The main advantage of such systems is the simplicity of construction, high reliability, the possibility of increasing the number of coordinated electric drives. In a number of cases, it becomes necessary to introduce an adjustable reduction ratio for one or more matched electric drives. In this case, the principle of consistency should be preserved: the change in the speed of rotation of one electric drive must be reflected in the second, taking into account the established reduction factor. The system in this case works as a variator, but without mechanical contact of the leading and driven axes.

Object of study and methods
As the executive engines in the study, two-speed asynchronous motors were used, on the basis of which various speed control systems were created. The effectiveness of the use of separate inclusion of two groups of motor windings is substantiated. Such scheme allows simple, including parametric, methods to control the speed of the considered induction motor, it makes it possible to increase its energy efficiency and improve the power factor.
3. The study of the structure of the system of coordinated control of electronic drives with electronic reduction The structural scheme of the electric drive in question is shown in Fig.1 Fig.1. is an electronic model of electric drives of the first and second axes (assuming that their characteristics are identical). Figure 1. A block diagram of the electric drive.
The system of equations for the transfer functions from the master signal has the form: Proceeding from this, the transfer functions of the system from master signal ref ω take the form: Substitution of equations (8-10) into (4) leads to: Expressions (5-7)  can be used to correct the system for disturbing effects.
The formation of signals 1 ω and 2 ω also occurs with the help of real electromechanical links.
Signal ' 2 ω is generated using an electronic model. In the process of working in real parts or models, changes can occur that will lead to a change in the operation of electric drives. To assess this, let us introduce link 4 W in the model chain that will characterize possible changes: To assess the ACS of electric drives with respect to the changes in parameters under consideration and the choice of the way to increase the "roughness" of the system, let us use the sensitivity functions [11] = ; -to reduce the sensitivity functions, one can increase coefficients In the process of the study, the structure shown in Fig. 1 was modeled. In Fig.2,   Analysis of the obtained graphs shows that during the start-up, transient processes 1 ω and 2 ω proceed identically. The change in the reduction ratio on the second electric drive is not reflected in the first. The action of moment М is also reflected by the second electric drive taking into account the reduction coefficient.

Conclusion
The conducted researches allow drawing the following conclusions: -the proposed structure allows one to realize the mode of coordinated rotation; -the circuit provides a controlled electronic reduction mode of the second electric drive; -the proposed system of coordinated rotation provides "reflection" of the moment on an unloaded electric drive taking into account the established reduction ratio; -analysis of sensitivity functions gives the way to reduce it; -in the event that the parameters of the link of the model differ from the actual values, with a change in the reduction ratio in the transient process of the first electric drive, a dynamic error appears; -to eliminate the errors that occur when the time constants of the model and the electric drive deviate, an aperiodic link or an intensity detector can be used by setting it at the output of the reduction ratio setting unit; -in case of difference in transmission factors in the circuits of the model and the electric drive, it is necessary to use the calculator of the real reduction factor and to introduce correction factors into the circuit.