Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction Techniques

Abstract

The results of theoretical and practical research studies most widely used in the industry of variable frequency drives (VFD) are presented in this manuscript. Such objects are characterized by dynamic nonlinearities that are difficult to take into account in the mathematical description for the development of control algorithms. Accounting for these nonlinearities leads to equations that are very problematic to solve. Therefore, the equations of the mathematical model on which the vector control system is based are compiled with the assumption of the sinusoidality of the processes occurring in the control object. Comparative results of the analysis of dynamic of VFD with two types of sensorless control, vector and scalar, show the problems that these assumptions lead to.. For identification of nonlinearities, dynamic formulas of transfer functions of torque generator in VFD are proposed, taking into account slip and stator voltage frequency The nonlinear transfer functions obtained in this work made it possible to substantiate structural solutions that linearize the VFD and substantially increase their efficiency. The use of dynamic feedback on the stator current allowed to significantly increase the dynamics and efficiency of a more stable scalar control.• If in the "right" part of the equation, that is, at any input of the system, there is a harmonic signal of a certain frequency, then all blocks will have harmonic input and output signals of only this frequency, different in amplitude about the phase.Naturally, real electric drives can be identified by LSS with only very large approximations. In direct-current drives with independent excitation, these approximations are insignificant; they mostly relate to mechanical structures with stiffness and gaps. In asynchronous electric drives, the reduction to LSS is associated with much larger errors. The equations of a generalized AC motor, even with significant assumptions, can be reduced to linear equations with variable coefficients or to nonlinear control systems. For engineering calculations, the differences between these systems are very conditional. If variable coefficients depend on the same coordinates of the electric drive (rotational speed, stator current, etc.), the 2 Control Theory in Engineering

Frequency Criterion for the Existence of Sliding Processes in Control Systems with an Arbitrary Variable Structure

“…An example of correction of discontinuous processes in the control of electromechanical automatic control systems is a complex of asynchronous electric drives with frequency control of transport mechanisms, as discussed in articles [21,22]. When transporting sheet materials, the moment of "double" sheet gripping occurred, when two drives simultaneously acted on the sheet.…”

Is It Possible to Stably Manage Complexes of Unstable Aggregates?

“…In the early studies presented in [12,13], the author and colleagues propose a non-linear continuous transfer function, which shows how the dynamics of AC machines depends on the frequency of the stator voltage and the slip in the MIS, which is determined by the load. Such transfer functions will make it possible to draw up a general equation for a wind generator and analyze its stability.…”

The experimental identification method of the dynamic efficiency for frequency regulation algorithms of AEDs

“…Sophisticated methods of analysis of nonlinear systems and methods of their linearization [24], [25] make it possible to assess the stability of such systems in engineering analysis, but it is rather difficult to theoretically substantiate the advantages of one or another AED control algorithm with variations in the reference signals. In this regard, an experimental technique is proposed that allows you to evaluate the effectiveness of a particular control method.…”