**4.5 Justification of PDF for transfer functions of AED**

According to the formulas, it is possible to explain the efficiency of the positive feedback on the current of the stator of the electric motor, described in the articles [6, 15, 18]. Consider the option of applying local feedback on the electromagnetic torque in this structure. The structural diagram is shown in **Figure 30**.

In this case, the transfer function of the torque driver will take the form:

$$\mathcal{W}\_{eq} = \frac{\frac{2\mathcal{M}\_k \left[T\_2' p + 1\right] \mathcal{S}\_k}{\alpha\_1 \left[\left(1 + T\_2/p\right)^2 \mathcal{S}\_k^2 + \beta^2\right]}}{1 + \frac{2\mathcal{M}\_k \mathcal{S}\_k \left(T\_2' p + 1\right) \mathcal{W}\_{DF}}{\alpha\_1 \left[\left(1 + T\_2/p\right)^2 \mathcal{S}\_k^2 + \beta^2\right]}} = \frac{2\mathcal{M}\_k \mathcal{S}\_k \left(T\_2' p + 1\right)}{\alpha\_1 \left[\left(1 + T\_2/p\right)^2 \mathcal{S}\_k^2 + \beta^2\right] + 2\mathcal{M}\_k \mathcal{S}\_k \left(T\_2' p + 1\right) \mathcal{W}\_{DF}}\tag{13}$$

Under the following conditions,

$$
\rho\_1 \rho^2 = -2\mathbf{M}\_k \mathbf{S}\_k \left( T\_2' p + \mathbf{1} \right) W\_{DF} \tag{14}
$$

those, if the corrective link has the following transfer function,

$$\text{BW}\_{\text{DF}} = -\frac{\alpha\_1 \boldsymbol{\beta}^2}{2\mathbf{M}\_k \mathbf{S}\_k \left(T\_2' p + \mathbf{1}\right)}\tag{15}$$

the transfer function of the torque driver takes the form:

$$\mathcal{W}\_{eq} = \frac{2\mathbf{M}\_k\mathbf{S}\_k\left(T\_2'p + \mathbf{1}\right)}{o\nu\_1\left[\left(\mathbf{1} + T\_2/p\right)^2\mathbf{S}\_k^2\right]} = \frac{2\mathbf{M}\_k}{o\nu\_1\mathbf{S}\_k(\mathbf{1} + T\_2/p)}\tag{16}$$

Becomes a linear link, independent of the slip (load) and fully coinciding with the transfer function given in the Usoltsev monograph for small loads [14]. Pay attention to formula (15). A dynamic link is a first-order inertia with a coefficient that ultimately depends on the frequency of the stator voltage and on the absolute

**Figure 30.** *Structural diagram of AED with a local feedback electromagnetic torque.*

### *Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction… DOI: http://dx.doi.org/10.5772/intechopen.88223*

slip. The sign (�) in front of the formula means that the relationship must be positive. We call this relationship positive dynamic feedback (PDF). It should be noted that the correction of the coefficient from the frequency is very easy to implement in frequency converters; several options for partial (indirect) adaptation of the connection to the load will be discussed below. Thus, the proposed positive feedback, selected by condition (15), makes it possible to compensate for the effect of the external load and the nonlinearity of the AED, spreading the transfer function of the motor as a link of the first order for any values of β. In addition, the block diagram (**Figure 13**) and the transfer function of the torque formation link (6) connecting the torque and slip allow us to offer an estimate of the efficiency of the torque formation algorithm: the algorithm that generates the necessary torque with the smallest absolute slip will be more effective.

Next, we consider the correction of the AED with the parameters corresponding to the frequencies of the supply voltage of 10 and 50 Hz. The initial frequency characteristics are shown in **Figure 19**. The transfer functions of the original AED with such parameters and the transfer functions of the corrective units are given in **Table 3**, and the initial and corrected frequency characteristics of the AED are shown in **Figures 31** and **32** for the frequencies of the supply voltage of 10 and 50 Hz, respectively.

As expected, the frequency characteristics of the AED with the structural correction proposed in the work are close to the frequency characteristics of the firstorder linear link.

In widely used AEDs, it is very difficult to realize the mechanical torque feedback. Given that the electromagnetic torque is equal to *I1\*Ψ<sup>2</sup>* and in almost all calculations it is assumed that the rotor flux linkage is constant, you can replace the original signal in this local connection with the effective value of the stator current or its active component, which is calculated in all the inverters.

To communicate with the stator current, the linearization conditions will vary somewhat:

$$
\rho\_1 \rho^2 = -2\mathbf{M}\_k \mathbf{S}\_k \left( T\_2' p + \mathbf{1} \right) \frac{\mathbf{W}\_{DF}}{\mathbf{W}\_2} \tag{17}
$$

This expression shows that when controlling the flux linkage, the linearization conditions can be refined, thereby providing high-quality regulation.

On the other hand, it is easy to show that with some inaccuracy in the fulfillment of the linearization condition, that is,

$$\frac{\rho}{S\_k} - \frac{2M\_k(T\_2'p + 1) \cdot W\_1}{\Psi\_2} \neq 0 = \Delta,\tag{18}$$


#### **Table 3.**

*The transfer functions of the channel of formation of the electromagnetic torque and dynamic feedback for different values of the frequency of the stator voltage and slip.*

stability (and in some cases improving it), this relationship provides full compensation for the load torque and not only in statics. The effect of such a relationship is described in [5, 6] and the patent [9, 11] and also confirmed by numerous experiments. The effectiveness of this connection is also confirmed by the calculation of the transfer function and frequency characteristics of the link for the formation of the torque with a positive feedback of the stator current (PDF—positive dynamic

According to the formulas, it is possible to explain the efficiency of the positive feedback on the current of the stator of the electric motor, described in the articles [6, 15, 18]. Consider the option of applying local feedback on the electromagnetic

<sup>¼</sup> <sup>2</sup>*MkSk <sup>T</sup>*<sup>0</sup>

2 *S*2 *<sup>k</sup>* <sup>þ</sup> *<sup>β</sup>*<sup>2</sup> h i

<sup>2</sup>*<sup>p</sup>* <sup>þ</sup> <sup>1</sup> � �

þ 2*MkSk T*<sup>0</sup>

<sup>2</sup>*<sup>p</sup>* <sup>þ</sup> <sup>1</sup> � �*WDF* (14)

<sup>2</sup>*<sup>p</sup>* <sup>þ</sup> <sup>1</sup> � � (15)

*ω*1*Sk* 1 þ *T*<sup>2</sup> <sup>0</sup> ð Þ *p* <sup>2</sup>*<sup>p</sup>* <sup>þ</sup> <sup>1</sup> � �*WDF*

(13)

(16)

torque in this structure. The structural diagram is shown in **Figure 30**.

In this case, the transfer function of the torque driver will take the form:

*ω*<sup>1</sup> 1 þ *T*<sup>2</sup> <sup>0</sup> ð Þ *p*

*<sup>ω</sup>*1*β*<sup>2</sup> ¼ �2*MkSk <sup>T</sup>*<sup>0</sup>

WDF ¼ � *<sup>ω</sup>*1*β*<sup>2</sup>

<sup>2</sup>*<sup>p</sup>* <sup>þ</sup> <sup>1</sup> � �

2 *S*2 *k* h i <sup>¼</sup> <sup>2</sup>*Mk*

Becomes a linear link, independent of the slip (load) and fully coinciding with the transfer function given in the Usoltsev monograph for small loads [14]. Pay attention to formula (15). A dynamic link is a first-order inertia with a coefficient that ultimately depends on the frequency of the stator voltage and on the absolute

2*MkSk T*<sup>0</sup>

those, if the corrective link has the following transfer function,

the transfer function of the torque driver takes the form:

*ω*<sup>1</sup> 1 þ *T*<sup>2</sup> <sup>0</sup> ð Þ *p*

*Weq* <sup>¼</sup> <sup>2</sup>*MkSk <sup>T</sup>*<sup>0</sup>

*Structural diagram of AED with a local feedback electromagnetic torque.*

**4.5 Justification of PDF for transfer functions of AED**

feedback).

*Control Theory in Engineering*

*Weq* ¼

**Figure 30.**

**194**

2*Mk T*<sup>0</sup> <sup>2</sup> ð Þ *<sup>p</sup>*þ<sup>1</sup> *Sk*

2*MkSk T*<sup>0</sup>

*ω*<sup>1</sup> 1þ*T*<sup>2</sup> <sup>0</sup> ð Þ *<sup>p</sup>* <sup>2</sup> *S*2 *<sup>k</sup>*þ*β*<sup>2</sup> ½ �

Under the following conditions,

<sup>2</sup> ð Þ *<sup>p</sup>*þ<sup>1</sup> *WDF*

*ω*<sup>1</sup> 1þ*T*<sup>2</sup> <sup>0</sup> ð Þ *<sup>p</sup>* <sup>2</sup> *S*2 *<sup>k</sup>*þ*β*<sup>2</sup> ½ �

1 þ

the transfer function (TF) and frequency characteristic (FC) of the torque driver

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction…*

Consider the case of the deviation of the parameters of the corrective element by

It was previously shown that when the signal of the motor rotation speed deviates by 5%, the vector control at some speeds "falls apart." Thus, the proposed method of analyzing processes in an asynchronous drive with frequency control according to varying frequency characteristics ("families" of characteristics with frozen frequency and slip parameters) made it possible to offer effective, from the point of view of theoretical analysis, correction without speed sensors, which allows

In the future, the effectiveness of the proposed relationship is confirmed by

Comparative speed diagrams (static and dynamic characteristics) for an openloop system, speed closed system, and stator current closed system are shown in **Figure 35**. The results of studies of the frequency properties of AED are presented

The formulas of the frequency characteristics of the electric drive with positive feedback on the stator current shown in **Figure 36** have significantly less variability in frequency characteristics due to changes in frequency (f) and slip (S). This

*Frequency characteristics of the torque driver and transfer functions of the corrective element for the frequency of the stator voltage of 10 Hz, accurate (W1) and with a deviation of the transmission coefficient of the corrective*

will differ slightly from the TF and FC of the first-order linear link.

linearizing a substantially nonlinear structure.

*DOI: http://dx.doi.org/10.5772/intechopen.88223*

**Figures 33** and **34**.

modeling and experiment.

in **Table 4**.

**Figure 33.**

**197**

*element by 5% (W2).*

5% for the frequencies of the supply voltage of 10 and 50 Hz. The frequency characteristics of the torque driver link with accurate correction (W1, W2) and the correction factor transfer coefficient deviation of 5% (W3, W4) are presented in

#### **Figure 31.**

*Frequency characteristics of the formation of the torque: the original (W1, W2) and adjusted (W3, W4) for the frequency of the supply voltage 10 Hz.*

#### **Figure 32.**

*Frequency characteristics of the formation of the torque: the original (W1, W2) and adjusted (W3, W4) for the frequency of the supply voltage 50 Hz.*

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction… DOI: http://dx.doi.org/10.5772/intechopen.88223*

the transfer function (TF) and frequency characteristic (FC) of the torque driver will differ slightly from the TF and FC of the first-order linear link.

Consider the case of the deviation of the parameters of the corrective element by 5% for the frequencies of the supply voltage of 10 and 50 Hz. The frequency characteristics of the torque driver link with accurate correction (W1, W2) and the correction factor transfer coefficient deviation of 5% (W3, W4) are presented in **Figures 33** and **34**.

It was previously shown that when the signal of the motor rotation speed deviates by 5%, the vector control at some speeds "falls apart." Thus, the proposed method of analyzing processes in an asynchronous drive with frequency control according to varying frequency characteristics ("families" of characteristics with frozen frequency and slip parameters) made it possible to offer effective, from the point of view of theoretical analysis, correction without speed sensors, which allows linearizing a substantially nonlinear structure.

In the future, the effectiveness of the proposed relationship is confirmed by modeling and experiment.

Comparative speed diagrams (static and dynamic characteristics) for an openloop system, speed closed system, and stator current closed system are shown in **Figure 35**. The results of studies of the frequency properties of AED are presented in **Table 4**.

The formulas of the frequency characteristics of the electric drive with positive feedback on the stator current shown in **Figure 36** have significantly less variability in frequency characteristics due to changes in frequency (f) and slip (S). This

#### **Figure 33.**

**Figure 31.**

**Figure 32.**

**196**

*frequency of the supply voltage 50 Hz.*

*frequency of the supply voltage 10 Hz.*

*Control Theory in Engineering*

*Frequency characteristics of the formation of the torque: the original (W1, W2) and adjusted (W3, W4) for the*

*Frequency characteristics of the formation of the torque: the original (W1, W2) and adjusted (W3, W4) for the*

*Frequency characteristics of the torque driver and transfer functions of the corrective element for the frequency of the stator voltage of 10 Hz, accurate (W1) and with a deviation of the transmission coefficient of the corrective element by 5% (W2).*

**Figure 34.**

*Frequency characteristics of the torque driver and transfer functions of the corrective element for the frequency of the stator voltage of 50 Hz, accurate (W3) and with a deviation of the transmission coefficient of the corrective element by 5% (W4).*

explains the stability of transients during acceleration and load buildup at various speeds of rotation. This also explains the significantly smaller differences in processes at different speeds of rotation. These frequency characteristics are close to the frequency characteristics of DC drives, which open up prospects for their use in complex mechanisms, including in drives of complex industrial mechanisms.

Spectral analysis of rotor currents also showed a higher efficiency of the proposed correction—both the model and experimental studies showed significantly lower frequencies of rotor currents and the absence of a spectrum below the fundamental frequency.

Particular attention should be paid to the same frequency of rotor currents in the model when the load is loaded at different speeds of rotation. This indicates the stabilization of the rotor flux linkage, which will be confirmed by special modeling. Attention should be paid to smaller values of stator currents, both in models (**Figure 37**) and in experiments (**Figure 36**).

The frequency of the rotor current under load (at a speed of 90 rad/s) with vector control, scalar without feedback, and scalar with feedback on the stator current is 10.6, 2.72, and 1.74 Hz, respectively.

The frequency of the rotor currents is the lowest in the model of the system with a positive feedback on the stator current, which indicates a more efficient algorithm for the formation of a mechanical torque. At that, in comparison with the scalar control in an electric drive with a positive stator current connection, work at low speeds is stabilized, and, in practice, there are no speed dips in the case of load surges, and in comparison with the vector, there are significantly lower frequencies of the rotor current and, accordingly, the frequency of real slip. Analytic way to explain and, even more so, to predict this situation is almost impossible, so let us

turn to experiments. The values of the fundamental frequencies under load and no-

*Comparative speed diagrams (static (a) and dynamic (b, c) characteristics) for an open-loop system, speed*

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction…*

*DOI: http://dx.doi.org/10.5772/intechopen.88223*

Open-loop system 10 0.3 5.03 84 2.19 270 Speed closed system 10 0.6 4.99 84 3.31 230 Stator current closed system (PDF) 4 0.1 6.4 72 1.19 200

**Ttp, s Δω, rad/s**

**reference**

**Δφ, el. deg**

**Periodic load**

**Δφ, el. deg**

**Δω, rad/s**

**Electric drive control system Static load Periodic speed**

**Δω, rad/s**

Attention should be paid to the possibilities of further improvement of control

1.You can get accurate information about the speed of electric motor rotor

algorithms, which are opened using the rotor current signal, for example:

*The parameters of the experimental signals for various control systems AED shown in* **Figure 35***.*

load are shown in **Table 5**.

*closed system, and stator current closed system.*

rotation.

**Figure 35.**

**Table 4.**

**199**

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction… DOI: http://dx.doi.org/10.5772/intechopen.88223*

#### **Figure 35.**

explains the stability of transients during acceleration and load buildup at various speeds of rotation. This also explains the significantly smaller differences in processes at different speeds of rotation. These frequency characteristics are close to the frequency characteristics of DC drives, which open up prospects for their use in complex mechanisms, including in drives of complex industrial mechanisms. Spectral analysis of rotor currents also showed a higher efficiency of the proposed correction—both the model and experimental studies showed significantly lower frequencies of rotor currents and the absence of a spectrum below the

*Frequency characteristics of the torque driver and transfer functions of the corrective element for the frequency of the stator voltage of 50 Hz, accurate (W3) and with a deviation of the transmission coefficient of the corrective*

Particular attention should be paid to the same frequency of rotor currents in the model when the load is loaded at different speeds of rotation. This indicates the stabilization of the rotor flux linkage, which will be confirmed by special modeling. Attention should be paid to smaller values of stator currents, both in models

The frequency of the rotor current under load (at a speed of 90 rad/s) with vector control, scalar without feedback, and scalar with feedback on the stator

The frequency of the rotor currents is the lowest in the model of the system with a positive feedback on the stator current, which indicates a more efficient algorithm for the formation of a mechanical torque. At that, in comparison with the scalar control in an electric drive with a positive stator current connection, work at low speeds is stabilized, and, in practice, there are no speed dips in the case of load surges, and in comparison with the vector, there are significantly lower frequencies of the rotor current and, accordingly, the frequency of real slip. Analytic way to explain and, even more so, to predict this situation is almost impossible, so let us

fundamental frequency.

**Figure 34.**

**198**

*element by 5% (W4).*

*Control Theory in Engineering*

(**Figure 37**) and in experiments (**Figure 36**).

current is 10.6, 2.72, and 1.74 Hz, respectively.

*Comparative speed diagrams (static (a) and dynamic (b, c) characteristics) for an open-loop system, speed closed system, and stator current closed system.*


#### **Table 4.**

*The parameters of the experimental signals for various control systems AED shown in* **Figure 35***.*

turn to experiments. The values of the fundamental frequencies under load and noload are shown in **Table 5**.

Attention should be paid to the possibilities of further improvement of control algorithms, which are opened using the rotor current signal, for example:

1.You can get accurate information about the speed of electric motor rotor rotation.

2. It is possible to accurately calculate the rotor flux linkage and remove one of the essential assumptions from the control.

These changes in algorithms can significantly improve the controllability of asynchronous electric motors. To solve the problem of measurement in various ways, the most obvious is to use electric motors with a phase rotor, which the Russian industry continues to produce. They are not as technologically advanced as squirrel-cage induction motor, but as the experience of the entire twentieth century shows, controllability is worth the price. You only need to define it.

Thus, spectral analysis of the rotor currents of an asynchronous electric drive can be a very effective method of identifying control algorithms for nonlinear structures, which include an asynchronous electric drive with frequency control. This analysis showed that the most effective method used in standard frequency converters for the formation of time would be frequency control with positive feedback of the stator current. This control is dominated by pronounced harmonic components, which indicates the proximity of this structure to the linear and significantly better controllability of the drives, which makes them promising to be used in high-tech mechanisms, in particular, in industrial robots.

**4.6 Structural stability of AED**

*DOI: http://dx.doi.org/10.5772/intechopen.88223*

**Table 5.**

conditions (7) and (8) will be as follows:

and for the phase shift,

whole frequency range.

applied.

**201**

**5. Conclusions**

of the AED with "PDF."

The described analysis and examples show that stability of electric drive or a good stability margin ensuring required processes may be obtained not only by bringing the system elements closer to ideal as first- and second-order elements (which often entails material costs) but also by finding necessary structural solutions. Along with that, for systems with oscillations in the direct channel elements, the best effect is reached with the help of additional cross couples and, for nonlinear negative couples, with the help of dynamically adjusted positive feedback. It should be admitted that there is still no universal method of solving nonlinear differential equations, but in some cases the effective solution is possible. The suggested interpretation of the criterion allows the logic transition to the notion of "structural stability." For that, conditions of stability at К ! ∞ should be considered. Here,

*Frequency and value of the fundamental harmonic for various control algorithms.*

**Control system No-load Under load** Vector control 2.1 Hz 6.25 Hz Vector speed feedback control 2.1 Hz 8.75 Hz Scalar control without feedback 1.69 Hz 4.75 Hz Scalar control with stator current feedback 1.75 Hz 3.5 Hz

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction…*

along with that, stability will influence the Bode phase plot throughout the

In the real electric drive, especially in alternating current one, there are both nonlinearities and high-order dynamic elements; therefore, it is not permissible to reduce them to linear variants. The suggested interpretation makes it possible to analyze stability and stability margin and to find structural solutions for stability problem for nonlinear structures. At the same time, the structural correction effectively works with sinusoidal disturbance signals, which suggests the possibility of applying frequency-controlled AEDs in systems with master signals and disturbances of complex spectral composition. In which until today, they have not been

The proposed structural transformations - positive dynamic feedback on the stator current does not require constructive changes in the engines (e.g., installation of flow coupling sensors) and complex calculations (as in DTC). At the same time, it can provide a state of AED that is closer to LSS than scalar and vector control. Experiments will be conducted to ensure the best dynamic and static characteristics

Re 1 ½ � ð Þ þ *jωq W*� >0 (19)

*φ*½ � ð Þ 1 þ *jωq W*� > � 90°*,* (20)

#### **Figure 36.**

*Diagram of the speed and current of the rotor of an asynchronous drive with scalar control and stator current feedback. Spectrum of the rotor current signal.*

#### **Figure 37.**

*Modeling processes in an asynchronous electric drive with scalar control with feedback on the stator current (PDF).*

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction… DOI: http://dx.doi.org/10.5772/intechopen.88223*


**Table 5.**

2. It is possible to accurately calculate the rotor flux linkage and remove one of

These changes in algorithms can significantly improve the controllability of asynchronous electric motors. To solve the problem of measurement in various ways, the most obvious is to use electric motors with a phase rotor, which the Russian industry continues to produce. They are not as technologically advanced as squirrel-cage induction motor, but as the experience of the entire twentieth century

Thus, spectral analysis of the rotor currents of an asynchronous electric drive can be a very effective method of identifying control algorithms for nonlinear structures, which include an asynchronous electric drive with frequency control. This analysis showed that the most effective method used in standard frequency converters for the formation of time would be frequency control with positive feedback of the stator current. This control is dominated by pronounced harmonic components, which indicates the proximity of this structure to the linear and significantly better controllability of the drives, which makes them promising to be

*Diagram of the speed and current of the rotor of an asynchronous drive with scalar control and stator current*

*Modeling processes in an asynchronous electric drive with scalar control with feedback on the stator current*

the essential assumptions from the control.

*Control Theory in Engineering*

shows, controllability is worth the price. You only need to define it.

used in high-tech mechanisms, in particular, in industrial robots.

**Figure 36.**

**Figure 37.**

*(PDF).*

**200**

*feedback. Spectrum of the rotor current signal.*

*Frequency and value of the fundamental harmonic for various control algorithms.*

#### **4.6 Structural stability of AED**

The described analysis and examples show that stability of electric drive or a good stability margin ensuring required processes may be obtained not only by bringing the system elements closer to ideal as first- and second-order elements (which often entails material costs) but also by finding necessary structural solutions. Along with that, for systems with oscillations in the direct channel elements, the best effect is reached with the help of additional cross couples and, for nonlinear negative couples, with the help of dynamically adjusted positive feedback. It should be admitted that there is still no universal method of solving nonlinear differential equations, but in some cases the effective solution is possible. The suggested interpretation of the criterion allows the logic transition to the notion of "structural stability." For that, conditions of stability at К ! ∞ should be considered. Here, conditions (7) and (8) will be as follows:

$$\operatorname{Re}[(\mathbf{1} + jaq)\mathcal{W}\_{\sim}] > 0 \tag{19}$$

and for the phase shift,

$$
\rho[(\mathbf{1} + jaq)\mathbf{W}\_{\sim}] > -\mathbf{90}^{\circ},\tag{20}
$$

along with that, stability will influence the Bode phase plot throughout the whole frequency range.

In the real electric drive, especially in alternating current one, there are both nonlinearities and high-order dynamic elements; therefore, it is not permissible to reduce them to linear variants. The suggested interpretation makes it possible to analyze stability and stability margin and to find structural solutions for stability problem for nonlinear structures. At the same time, the structural correction effectively works with sinusoidal disturbance signals, which suggests the possibility of applying frequency-controlled AEDs in systems with master signals and disturbances of complex spectral composition. In which until today, they have not been applied.

### **5. Conclusions**

The proposed structural transformations - positive dynamic feedback on the stator current does not require constructive changes in the engines (e.g., installation of flow coupling sensors) and complex calculations (as in DTC). At the same time, it can provide a state of AED that is closer to LSS than scalar and vector control. Experiments will be conducted to ensure the best dynamic and static characteristics of the AED with "PDF."


**Author details**

**203**

Vladimir L. Kodkin\*, Alexandr S. Anikin and Alexandr A. Baldenkov

\*Address all correspondence to: kodkina2@mail.ru

provided the original work is properly cited.

South Ural State University (National Research University), Chelyabinsk, Russia

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction…*

*DOI: http://dx.doi.org/10.5772/intechopen.88223*

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

*Nonlinear Dynamics of Asynchronous Electric Drive: Engineering Interpretation and Correction… DOI: http://dx.doi.org/10.5772/intechopen.88223*
