# An Enhanced Sliding Mode Speed Control for Induction Motor Drives

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Robust Speed ISMC Design

#### 2.1. Model of the Mechanical Loop of IM

#### 2.2. Basic Principles of ISMC

#### 2.3. Conventional ISMC for IM (D1 Design)

**(A1)**The constant ${K}_{\omega}$ should be chosen such that ${K}_{\omega}>0$ for all time. The law ${u}_{\omega}$ should be designed in a way that guarantees convergence to the sliding surface in a finite time. Therefore:

**(A2)**The gain ${\beta}_{\omega}$ must be chosen so that $|{d}_{\omega}|<{\beta}_{\omega}$, for all times.

**Theorem**

**1.**

**Proof.**

#### 2.4. Enhanced ISMC for IM (D2 Design)

**Remark**

**1.**

## 3. Simulation and Experimental Design

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbols of Induction Motor | |

${B}_{v}$ | Viscous friction coefficient |

J | Moment of inertia |

${L}_{m}$ | Magnetizing inductance |

${L}_{s}$ | Stator inductance |

${L}_{r}$ | Rotor inductance |

${R}_{r}$ | Rotor resistance |

${R}_{s}$ | Stator resistance |

p | Number of poles |

$\sigma $ | Coefficient of magnetic dispersion |

${T}_{e}$ | Electromagnetic torque |

${T}_{L}$ | Load or disturbance torque |

${\omega}_{m}$ | Mechanical rotor speed |

${\omega}_{s}$ | Synchronous speed |

${\psi}_{r}$ | Rotor flux |

I | Stator rated current |

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**Figure 3.**IM performance by using 1000 rpm reference speed and two load torque step changes: (

**3-1**) simulation and (

**3-2**) experimental (D2 design): (

**a**) Rotor speed; (

**b**) Speed error; (

**c**) ${T}_{e},{T}_{L}$; (

**d**) Torque current; (

**e**) Rotor flux; (

**f**) Rotor flux current and (

**g**) Stator current.

**Figure 4.**Experimental tests for performance comparison between the proposed ISMC (D2 design) regulator and the conventional ISMC by using 1000 rpm reference speed (D1 design) and also with PI regulator.

**Figure 5.**Experimental results by using 1445 rpm reference speed and two load torque step changes (D2 design): (

**a**) Rotor speed; (

**b**) Speed error; (

**c**) ${T}_{e},{T}_{L}$; (

**d**) Torque current and (

**e**) Rotor flux current.

**Figure 6.**Experimental tests for performance comparison between the D1, D2 and the PI regulators by using 1445 rpm reference speed.

**Figure 7.**Experimental results by using 100 rpm reference speed and two load torque steps changes (D2 design): (

**a**) Rotor speed; (

**b**) Speed error and (

**c**) ${T}_{e},{T}_{L}$.

**Figure 8.**Experimental tests for performance comparison between the proposed ISMC (D2 design) and the PI regulators by using 100 rpm reference speed.

**Figure 9.**IM performance with $60\%$ of uncertainties in J at 1200 rpm reference speed and two load torque step changes, (

**9-1**) Simulation and (

**9-2**) Experimental (D2 design): (

**a**) Rotor speed; (

**b**) Speed error; (

**c**) ${T}_{e},{T}_{L}$; (

**d**) Torque current; (

**e**) Rotor flux current and (

**f**) Stator current.

Symbol | Rated Value |

${B}_{v}$ | 0.0105 [Kg m/(rad/s)] |

J | 0.0503 [Kg m^{2}] |

${L}_{m}$ | 0.1125 [H] |

${L}_{s}$ | 0.1138 [H] |

${L}_{r}$ | 0.1152 [H] |

$\sigma $ | 0.0346 |

${R}_{r}$ | 0.400 $[\Omega ]$ |

${R}_{s}$ | 0.729 $[\Omega ]$ |

p | 4 poles |

${\omega}_{m}\left(n\right)$ | 151.32 [rad/s] (1445[rpm]) |

${\varphi}_{r}$ | 0.9030 [Wb] |

${I}_{sd}$ | 8.026 [A] |

${I}_{sq}$ | 20 [A] |

${I}_{s}$ | 15.3 [A] |

V | 380 [V] |

${P}_{N}$ | 7500 [W] |

$\mu $ | 87% |

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**MDPI and ACS Style**

Shiravani, F.; Alkorta, P.; Cortajarena, J.A.; Barambones, O.
An Enhanced Sliding Mode Speed Control for Induction Motor Drives. *Actuators* **2022**, *11*, 18.
https://doi.org/10.3390/act11010018

**AMA Style**

Shiravani F, Alkorta P, Cortajarena JA, Barambones O.
An Enhanced Sliding Mode Speed Control for Induction Motor Drives. *Actuators*. 2022; 11(1):18.
https://doi.org/10.3390/act11010018

**Chicago/Turabian Style**

Shiravani, Fahimeh, Patxi Alkorta, Jose Antonio Cortajarena, and Oscar Barambones.
2022. "An Enhanced Sliding Mode Speed Control for Induction Motor Drives" *Actuators* 11, no. 1: 18.
https://doi.org/10.3390/act11010018