# Iterative Learning Sliding Mode Control for UAV Trajectory Tracking

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## Abstract

**:**

## 1. Introduction

## 2. Iterative Learning Sliding Mode Control

#### 2.1. ILSMC Design

**Definition**

**1.**

**Assumption**

**1.**

#### 2.1.1. Equivalent Control

#### 2.1.2. Learning Control

**Theorem**

**1.**

**Proof.**

**Remark**

**1.**

**Remark**

**2.**

## 3. System Description and Modeling

#### 3.1. Kinematics

#### 3.2. Quadcopter Dynamics

#### 3.3. Discrete-Time Model

## 4. Integrated ILSMC for UAV Attitude Control

#### 4.1. Inner-Loop PID Controller

#### 4.2. Outer-Loop ILSMC

#### 4.3. Implementation Procedure

- Step 1: Declare ${I}_{xx},{I}_{yy},{I}_{zz}$, ${K}_{p},{K}_{i},{K}_{d},c,\mu ,\lambda $.
- Step 2: Set ${x}_{d}\left(k\right)$, $j=0$, and ${\widehat{u}}_{il{c}_{\left(j\right)}}\left(k\right)=0$.
- Step 3: Compute the ILSMC ${\widehat{u}}_{\left(j\right)}\left(k\right)$ from (61) as a reference to the inner loop.
- Step 4: Compute, from the measured states ${x}_{\left(j\right)}\left(k\right)$, ${e}_{\left(j\right)}\left(k\right)$, ${\sigma}_{\left(j\right)}\left(k\right)$, ${S}_{\left(j\right)}\left(k\right)$, and the selected TPI.
- Step 5: Check if the tracking performance requirement is met to terminate the learning process. Otherwise, proceed to Step 6.
- Step 6: Set $j=j+1$, update ${\widehat{u}}_{il{c}_{\left(j\right)}}\left(k\right)$ from (60), then return to Step 3.

## 5. Simulation Results

#### 5.1. Step Response in Nominal Conditions

#### 5.2. Trajectory Tracking Performance under Disturbances and Uncertainties

## 6. Experimental Validation

#### 6.1. Experimental Setup

#### 6.2. Real-Time Data Validation Results

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SMC | Sliding mode control |

ILC | Iterative learning control |

ILSMC | Iterative learning sliding mode control |

UAV | Unmanned aerial vehicle |

PID | Proportional–integral–derivative |

FL | Feedback linearization |

CoG | Center of gravity |

TPI | Tracking performance index |

ITAE | Integral time absolute error |

ATSMC | Adaptive twisting sliding mode control |

AFTC | Finite-time control scheme. |

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

m | $1.5$ | kg |

l | $0.205$ | m |

g | $9.81$ | m/s${}^{2}$ |

${I}_{xx}$ | $9.1\times {10}^{-3}$ | kg m${}^{2}$ |

${I}_{yy}$ | $16.4\times {10}^{-3}$ | kg m${}^{2}$ |

${I}_{zz}$ | $24.1\times {10}^{-3}$ | kg m${}^{2}$ |

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

${c}_{\varphi}$ | 50 | $\mu $ | 10 |

${c}_{\theta}$ | 50 | $\lambda $ | $0.9$ |

${c}_{\psi}$ | 20 | - | - |

UAV Angle (degrees) | ATSMC | AFTC | PD | PD-ILC | ILSMC |
---|---|---|---|---|---|

Roll | $5.03$ | $2.03$ | $3344.2$ | $39.91$ | $0.255$ |

Pitch | $3.87$ | $1.40$ | $3468.4$ | $55.60$ | $0.261$ |

Yaw | $3.47$ | $2.42$ | $3323.0$ | $149.89$ | $0.444$ |

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**MDPI and ACS Style**

Nguyen, L.V.; Phung, M.D.; Ha, Q.P.
Iterative Learning Sliding Mode Control for UAV Trajectory Tracking. *Electronics* **2021**, *10*, 2474.
https://doi.org/10.3390/electronics10202474

**AMA Style**

Nguyen LV, Phung MD, Ha QP.
Iterative Learning Sliding Mode Control for UAV Trajectory Tracking. *Electronics*. 2021; 10(20):2474.
https://doi.org/10.3390/electronics10202474

**Chicago/Turabian Style**

Nguyen, Lanh Van, Manh Duong Phung, and Quang Phuc Ha.
2021. "Iterative Learning Sliding Mode Control for UAV Trajectory Tracking" *Electronics* 10, no. 20: 2474.
https://doi.org/10.3390/electronics10202474