# A Combined Control Scheme of Direct Torque Control and Field-Oriented Control Algorithms for Three-Phase Induction Motor: Experimental Validation

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background of the DTC Algorithm

^{o}between each of them so that the first sector starts at the angle (for instants $-{30}^{\circ}$) of a width of ${60}^{\circ}$. The four active vectors to control both the stator flux and the electromagnetic torque in the DTC algorithm are shown in Table 1 [42], where the up arrow indicates an increase in flux or torque, while the down arrow indicates a decrease in flux or torque.

## 3. DTRFC Versus DTSFC in Terms of Pull-Out Torque

## 4. Theoretical Background of the FOC Algorithm

#### 4.1. Working Principle

#### 4.2. Setting Gain Controls of the FOC Algorithm

## 5. The Proposed Combined FOC and DTC Algorithms over a Wide Torque Operation Range

## 6. Simulation Results and Implementation

#### 6.1. Simulation Results of DTRFC Versus DTSFC

#### 6.2. Simulation Results of FOC with Rotor Flux Vector Orientation towards $(\alpha -Axis)$

#### 6.3. Simulation Results of the Combined FOC and DTC Algorithm

#### 6.4. Transition Case Results between FOC and DTC Algorithms

#### 6.4.1. Case 1: Assuming a Positive Torque Error

#### 6.4.2. Case 2: Voltage Vector Switching Is Higher

## 7. Experimental Results Using a dSPACE-DS1103-Based Platform

## 8. Robustness and Evaluation against Previous and Recent Related Techniques

## 9. Conclusions

- Offered high dynamics of flux and torque due to the use of the DTSFC algorithm within the nominal torque range of 0.5 ms.
- Enabled the generation of high torque beyond the breakdown torque due to the use of the DTRFC algorithm 6/1.76 N.m * 100 = 340% T${}_{em-n}$.
- Excellent, low steady-state error of torque and torque ripple that was reduced to a great extent due to the use of the FOC algorithm at 0.05 N.m and 0.028% T${}_{em-n}$.
- Excellent transition between the transient state and steady state with the best values of switch-on= 0.5 N.m, switch-off = 0.1 N.m.
- Constant switching frequency was achieved at f${}_{pwm}$ = 10 kHz due to the use of the FOC algorithm during the steady-state condition.
- The results of the experiment distinguished the findings of the proposed study, which provided full validation for the adopted methodology and were in complete agreement with the simulated outcomes.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Variable | Unit Value |
---|---|

Nominal voltage | 230/400 V |

Phase resistance stator | ${R}_{s}$ = 45.83 $\Omega $ |

Phase resistance rotor | ${R}_{r}$ = 31 $\Omega $ |

Phase inductance stator | ${L}_{s}$ = 1.24 H |

Phase inductance rotor | ${L}_{r}$ = 1.11 H |

Mutual inductance | ${L}_{m}$ = 1.05 H |

Inertia | J = 0.006 kg.m${}^{2}$ |

Friction factor | f = 0.001 N.m. sec/rad |

Number of poles pairs | p = 2 |

Nominal stator flux | ${\mathsf{\Phi}}_{s}$ = 1.14 Wb |

Nominal rotor flux | ${\mathsf{\Phi}}_{r}$ = 0.945 Wb |

Nominal power | ${P}_{n}$ = 0.25 kW |

Nominal frequency | F = 50 Hz |

Nominal speed | ${\omega}_{n}$ = 282 rad/s |

Nominal torque | ${T}_{em}$ = 1.76 N.m |

## Appendix B

Kp and Ki Gains for $(\mathit{\alpha}-\mathit{\beta})$ Frame | Calculation of Kp and Ki Gains |
---|---|

${K}_{P\left(\alpha \right)-I}$ = 100 | ${K}_{I\left(\alpha \right)-I}$ = ${a}_{5}.{K}_{P\left(\alpha \right)-I}$ |

${K}_{P\left(\beta \right)-I}$ = 100, 200, 300 and 400. | ${K}_{I\left(\beta \right)-I}$ = ${a}_{5}.{K}_{P\left(\beta \right)-I}$ |

## Appendix C. Motor Constants

## Appendix D

Abbreviation | Definition |
---|---|

IM | Induction Motor |

DTSFC | Direct Torque ans Stator Flux Control |

DTRFC | Direct Torque and Rotor Flux Control |

FOC | Field-Oriented Control |

VSI | Voltage Source Inverter |

VEs | Voltage Vectors |

HCs | Hysteresis Controllers |

LUT | Lookup Table |

PWM | Pulse Width Modulation |

TSR | Transient State Response |

SSR | Steady State Response |

Ref | Reference |

## Appendix E

## References

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**Figure 3.**The two block diagrams of the induction motor according to (

**a**) $\alpha $ and (

**b**) $\beta $ axes.

**Figure 4.**(

**a**) Control scheme of rotor flux for the $\alpha $-axis. (

**b**) Current controller for ${i}_{s\beta}$ component on the $\beta $-axis.

**Figure 7.**The DTSFC with successive steps of torque references for testing stator and rotor flux responses.

**Figure 8.**The DTSFC algorithm with successive steps of the reference torque for testing torque response.

**Figure 17.**The testbed behaviour of the FOC algorithm for stator current vector components responses.

**Figure 24.**Torque profile in the proposed combined FOC-DTC algorithm with different values of $\left(\delta \right)$.

**Figure 25.**(

**a**) Torque response of the proposed combined FOC-DTC algorithm for three values of ${K}_{P\left(\beta \right)-I}$. (

**b**) Stator voltage vector modulus ${V}_{s}$ in the FOC algorithm.

**Figure 27.**Torque response in the proposed combined FOC-DTC with different values of switch-on and -off.

**Figure 28.**Torque response in the proposed combined FOC-DTC with different values of switch-on and -off.

**Figure 36.**The torque response in the combined FOC-DTC algorithm with different values of switch-on/off.

Hysteresis Level | Applied Inverter Voltage Space Vectors | |||
---|---|---|---|---|

${C}_{F}$ | ↓ | ↑ | ↓ | ↑ |

${C}_{T}$ | ↓ | ↓ | ↑ | ↑ |

i = 1 | ${V}_{5}$ | ${V}_{6}$ | ${V}_{3}$ | ${V}_{2}$ |

i | ${V}_{\mathrm{i}-2}$ | ${V}_{\mathrm{i}-1}$ | ${V}_{\mathrm{i}+2}$ | ${V}_{\mathrm{i}+1}$ |

Unit with Time | Command Torque Sequence | |||||
---|---|---|---|---|---|---|

Time (s) | 1 | 3 | 5 | 7 | 8 | 9 |

T${}_{em-ref}$ (N.m) | 1.76 | 4.22 | 6 | −1.76 | −4.22 | −6 |

Used Method | Flux Ripples | Torque Response for (TSR) | Torque Response for (SSR) | High Torque Prod. | Switching Frequency | Optional Gains |
---|---|---|---|---|---|---|

Proposed | Lower | 0.65 ms | Lower | Yes | Constant | 2 |

Ref. [24] | Low | 1 ms | Low | Yes | Constant | 4 |

Ref. [25] | High | 4 ms | High | No | Variable | - |

Ref. [26] | No plot | 10 ms | Low | No | Variable | Unknown |

Ref. [28] | High | 1 ms | Low | No | Variable | - |

Ref. [29] | High | 10 ms | High | No | Variable | - |

Ref. [30] | Low | 10 ms | Low | No | Constant | - |

Ref. [31] | High | 1 ms | High | No | Variable | 12 |

Ref. [34] | Low | 16 ms | Low | No | Variable | 2 |

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**MDPI and ACS Style**

Elgbaily, M.; Anayi, F.; Alshbib, M.M.
A Combined Control Scheme of Direct Torque Control and Field-Oriented Control Algorithms for Three-Phase Induction Motor: Experimental Validation. *Mathematics* **2022**, *10*, 3842.
https://doi.org/10.3390/math10203842

**AMA Style**

Elgbaily M, Anayi F, Alshbib MM.
A Combined Control Scheme of Direct Torque Control and Field-Oriented Control Algorithms for Three-Phase Induction Motor: Experimental Validation. *Mathematics*. 2022; 10(20):3842.
https://doi.org/10.3390/math10203842

**Chicago/Turabian Style**

Elgbaily, Mohamed, Fatih Anayi, and Mussaab M. Alshbib.
2022. "A Combined Control Scheme of Direct Torque Control and Field-Oriented Control Algorithms for Three-Phase Induction Motor: Experimental Validation" *Mathematics* 10, no. 20: 3842.
https://doi.org/10.3390/math10203842