# A Novel Nonsingular Terminal Sliding Mode Control-Based Double Interval Type-2 Fuzzy Systems: Real-Time Implementation

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## Abstract

**:**

## 1. Introduction

- A MINTSMC controller with SM observer was adopted for the internal loop control of RSC in a DFIG WT test system.
- An auxiliary DIT2-FLC controller was established to improve the DFIG performance and eliminate the SM observer estimation error.
- The comprehensive real-time model-in-the-loop (RT-MiL) examinations were made to validate the applicability of the suggested MINTSMC based DIT2-FLC controller in a real-time testbed.

## 2. Modeling of DFIG WT Test-System

#### 2.1. Modeling of the Generator System

#### 2.2. Modeling of the Drive Train System

#### 2.3. Rotor Side Converter (RSC) Control

_{qr}component, MINTSMC was employed to improve the overall performance of the system, which will be explained in detail. After that, these variables need to be decoupled for sending to PWM.

#### 2.4. Grid Side Converter (GSC) Control

_{a}and i

_{L}are the DC link voltage and inductor current vector of the GSC. Besides, the control procedure works in a grid voltage reference frame that is an asynchronously rotating reference frame with its axis centered towards vector control of grid voltage. Thereby it acquires autonomous control of the active power, as well as reactive power parameters, between the power grid and GSC.

## 3. Design of Model-Independent NTSMC Based DIT2-FLC

#### 3.1. Model-Independent NTSMC Technique

**Definition**

**1.**

**Definition**

**2.**

**Theorem**

**1**

**[46].**The error in the specified state-space (12) converges to zero in finite time,$e\to 0$, if the NTSMC manifold is considered as (13) and control law is formulated as follows

**Proof.**

#### 3.2. Design of SM Observer

**Theorem**

**2**

**[46].**For (13), choosing the SM manifold as$s=e$and$\sigma $appropriately results in the asymptotical convergence of the error to zero.

**Proof.**

#### 3.3. Dual Input Interval Type 2 FLC

#### 3.3.1. General Structure of Dual Input IT2-FL

#### 3.3.2. DIT2-FL Design Strategy

#### 3.4. The Strategy of MINTSMC Based DIT2-FPI Scheme

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Illustration of the design curves of the DFIG WT test system. (

**a**) Output mechanical power base on wind speed and (

**b**) electrical power based on the speed of the generator.

**Figure 10.**The voltage of the DC link capacitor in the DFIG system for scenario I via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.

**Figure 11.**Magnitude rotor current of DFIG system under scenario I via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.

**Figure 14.**The DFIG responses according to the scenario I (

**a**) measured active power of DFIG WT, (

**b**) measured reactive power of DFIG WT, (

**c**) Generator speed of DFIG system.

**Figure 15.**Capacitor DC-link voltage of the DFIG system via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.

**Figure 16.**Magnitude rotor current of the DFIG system via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.

**Figure 19.**The DFIG responses according to scenario II (

**a**) measured active power of the DFIG WT, (

**b**) measured reactive power of the DFIG WT, (

**c**) generator speed of the DFIG system.

**Figure 20.**DC link capacitor voltage of the DFIG system under scenario III via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.

**Figure 21.**Magnitude rotor current of the DFIG system under scenario III via the PI controller, MINTSMC controller, MINTSMC controller-based DIT2-FLC.

**Figure 24.**The DFIG responses according to scenario III (

**a**) active power of the DFIG system, (

**b**) reactive power of the DFIG system, (

**c**) generator speed of the DFIG system.

${\mathit{\lambda}}_{2}$ | ${\mathit{\lambda}}_{1}$ | ||
---|---|---|---|

N | Z | P | |

N | N | N | Z |

Z | N | Z | P |

P | Z | P | P |

Region | Description |
---|---|

${\Gamma}_{1}$ | $\left\{\left\{{\lambda}_{1},{\lambda}_{2}\right\}\in {[-1,1]}^{2}|{\lambda}_{2}\ge -1,{\lambda}_{2}\le {\beta}_{12}\left({\lambda}_{1}\right)\right\}$ |

${\Gamma}_{2}$ | $\left\{\left\{{\lambda}_{1},{\lambda}_{2}\right\}\in {[-1,1]}^{2}|{\lambda}_{1}{\beta}_{12}\left({\lambda}_{1}\right),{\lambda}_{2}{\beta}_{23}\left({\lambda}_{1}\right)\right\}$ |

${\Gamma}_{3}$ | $\left\{\left\{{\lambda}_{1},{\lambda}_{2}\right\}\in {[-1,1]}^{2}|{\lambda}_{2}\ge {\beta}_{23}\left({\lambda}_{1}\right),{\lambda}_{2}\le 1\right\}$ |

Parameter | Value | Unit |
---|---|---|

DC link Capacitor | 10 | $\mathrm{mF}$ |

Rated power | 250 | $\mathrm{kW}$ |

Rated voltage | 575 | $\mathrm{V}\left(\mathrm{rms}\right)$ |

Rated frequency | 50 | $\mathrm{Hz}$ |

Rated current | 185 | $\mathrm{A}\left(\mathrm{rms}\right)$ |

Number of poles | 4 | ---- |

Stator resistor | 20 | $\Omega \mathrm{m}$ |

Stator leakage inductor | 0.2 | $\mathrm{mH}$ |

Rotor resistor | 20 | $\Omega \mathrm{m}$ |

Rotor leakage inductor | 0.2 | $\mathrm{mH}$ |

Magnetizing inductor | 4.2 | $\mathrm{mH}$ |

Inertia | 0.685 | $\mathrm{s}$ |

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**MDPI and ACS Style**

Mohammadi Moghadam, H.; Gheisarnejad, M.; Yalsavar, M.; Foroozan, H.; Khooban, M.-H.
A Novel Nonsingular Terminal Sliding Mode Control-Based Double Interval Type-2 Fuzzy Systems: Real-Time Implementation. *Inventions* **2021**, *6*, 40.
https://doi.org/10.3390/inventions6020040

**AMA Style**

Mohammadi Moghadam H, Gheisarnejad M, Yalsavar M, Foroozan H, Khooban M-H.
A Novel Nonsingular Terminal Sliding Mode Control-Based Double Interval Type-2 Fuzzy Systems: Real-Time Implementation. *Inventions*. 2021; 6(2):40.
https://doi.org/10.3390/inventions6020040

**Chicago/Turabian Style**

Mohammadi Moghadam, Hooman, Meysam Gheisarnejad, Maryam Yalsavar, Hossein Foroozan, and Mohammad-Hassan Khooban.
2021. "A Novel Nonsingular Terminal Sliding Mode Control-Based Double Interval Type-2 Fuzzy Systems: Real-Time Implementation" *Inventions* 6, no. 2: 40.
https://doi.org/10.3390/inventions6020040