# On the Physical Nature of Frequency Control Problems of Induction Motor Drives

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Formulation of the Problem

## 3. Analysis Methods and Problems

## 4. The Imperfection of Vector Control Algorithms

_{u}= 0):

## 5. Solutions

_{2}is the transient time constant; M

_{k}and S

_{k}are the critical torque and critical slip, depending on the frequency ω

_{1}):

_{1}is the frequency of the stator voltage, and J

_{d}is the moment of inertia of the motor.

_{k}and S

_{k}change, and these changes show how W(p) changes with a particular control method. Strictly speaking, this transfer function is also a simplified version of the description of the nonlinear dynamics of an IMD. Variable parameters depending on ${\omega}_{1}$ and $\beta $ are present in a “frozen” form. It is impossible to obtain such an expression after Laplace transformations (and the transfer function results from this very operation). But this formulation of the nonlinear transfer function encompasses the entire state space, describing processes in electric motors with any spectrum of signals of currents and voltages. That is, the complex state space, described by an unsolvable nonlinear equation, is identified by a nonlinear space, covered by a nonlinear transfer function that exists for any variables, and the space is divided into an infinite number of “slices” for any value describing the dynamic process in this slice. Since the transfer function Equation (15) is continuous, it can be argued that there are inverse Laplace transforms for signals obtained using this Equation. However, we cannot get the exact value of these transformations to assert the same in relation to the signals obtained from the vector equations because of their discontinuity.

## 6. Experimental Results

## 7. Results Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Diagrams of stator speed and current during acceleration to speed 92.4 rps, in induction motor drives (IMD) with scalar (

**a**) and vector (

**b**) control and with load surge.

**Figure 2.**Speed diagrams in IMD with vector control with a PI speed controller at three different speeds.

**Figure 7.**Speed diagrams in IMD with scalar control with dynamic positive feedback (DPF) at three different speeds.

**Figure 8.**Diagram of the speed and current of the rotor of the IMD with vector control (

**a**) and the spectrum of the rotor current (

**b**).

**Figure 9.**Diagrams of stator speed and current at no-load and load surge in a stator-current-closed system with DPF (

**a**) and rotor current spectrum (

**b**).

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**MDPI and ACS Style**

Vladimir, K.; Alexander, A.
On the Physical Nature of Frequency Control Problems of Induction Motor Drives. *Energies* **2021**, *14*, 4246.
https://doi.org/10.3390/en14144246

**AMA Style**

Vladimir K, Alexander A.
On the Physical Nature of Frequency Control Problems of Induction Motor Drives. *Energies*. 2021; 14(14):4246.
https://doi.org/10.3390/en14144246

**Chicago/Turabian Style**

Vladimir, Kodkin, and Anikin Alexander.
2021. "On the Physical Nature of Frequency Control Problems of Induction Motor Drives" *Energies* 14, no. 14: 4246.
https://doi.org/10.3390/en14144246