# PSO-Based Algorithm Applied to Quadcopter Micro Air Vehicle Controller Design

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. PSO-Based Algorithm Applied Controller Design

_{i}(t) and generates X

_{j}(t) = [x

_{j}

_{1}(t), x

_{j}

_{2}(t), … , x

_{j}

_{D}(t)] by using Equation (1):

_{j}

_{D}is the jth individual error data, and N(0,1) is a random normal distribution of x. The mutation rate is noted as mr.

_{j}

_{D}from the set of all X

_{j}, then updates v

_{i}and x

_{i}by the major equation of the PSO-based algorithm. In this article, the proposed algorithm creates an elite PSO-based algorithm by the combination of PSO and EP. These effects usually attain a better result than either the PSO or the existing algorithms alone.

_{i}

_{D}and x

_{i}

_{D}, respectively. The best particle historical position is p

_{i}

_{D}, and the global best position is p

_{g}

_{D}. In order to go along with learning rates l

_{1}and l

_{2}, the inertia weight ω is a user-defined parameter. It manages the relationship of the previous values of particle velocities to the current value. The rand

_{1}(·), rand

_{2}(·) items are uniformly distributed random numbers [0,1]. The l

_{1}× rand

_{1}(·) × (p

_{i}

_{D}(t) − x

_{i}

_{D}(t)) term refers to the cognitive component. It reflects the distance at which the best solution P

_{i}(t) of a particle is located. The combination of the PSO-based algorithm and EP will generate and update the parameters of the control system performance index. Some specific performance indicators are usually designed to evaluate and determine the minimum error criterion [14]. Due to system advantages, the ISE performance index is chosen as shown in Equation (3):

_{P}, k

_{I}, k

_{D}, k

_{e}, and k

_{de}. After that, each new particle is said to represent a group of solutions. The four items rising time, settling time, peak time, and maximum overshoot are of significant focus on each control system. They are exploited to find out the minimum ISE fitness function, as shown in Equation (4).

_{i}. The rising time, settling time, peak time, and maximum overshoot are estimated via the output performance, and then its values are recorded. Afterward, the particle groups which contain a large error can be eliminated. Thus, the convergence speed of the system is also accelerated. The fitness function settles in the range:

## 3. Quadcopter as a Micro Air Vehicle

## 4. Simulation Results

_{1}, α

_{2}, α

_{3}, α

_{4}] = [40, 25, 10, 5], and PID gains are set in the range [0, 20]. The mutation rate is mr = 0.105. The attitude control performances are displayed in each channel: Roll angle is set 1 rad (~60°), Pitch angle is set 0.5 rad (~30°) and Yaw angle is set 1 rad (~60°). The sampling time in this simulation is 0.01 s.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Particle swarm optimization based (PSO)-based algorithm applies to the micro air vehicle controller design.

**Figure 4.**Roll channel control with the PSO-based algorithm. (

**a**) Roll angle response; (

**b**) The ISE fitness function; (

**c**) Bode diagram.

**Figure 5.**Pitch channel control with the PSO-based algorithm. (

**a**) Pitch angle response; (

**b**) The ISE fitness function; (

**c**) Bode diagram.

**Figure 6.**Yaw channel control with the PSO-based algorithm. (

**a**)Yaw angle response; (

**b**) The ISE fitness function; (

**c**) Bode diagram.

CI(t) | e(t) | |||||||
---|---|---|---|---|---|---|---|---|

NB | NM | NS | ZE | PS | PM | PB | ||

de(t) | NB | ZE | NS | NS | NM | NM | NB | NB |

NM | PS | ZE | NS | NS | NM | NM | NB | |

NS | PS | PS | ZE | NS | NS | NM | NM | |

ZE | PS | NM | PS | ZE | NS | NS | NM | |

PS | PM | PM | PS | PS | ZE | NS | NS | |

PM | PB | PM | PM | PS | PS | ZE | NS | |

PB | PB | PB | PM | PM | PS | PS | ZE |

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**MDPI and ACS Style**

Tran, H.-K.; Chiou, J.-S.
PSO-Based Algorithm Applied to Quadcopter Micro Air Vehicle Controller Design. *Micromachines* **2016**, *7*, 168.
https://doi.org/10.3390/mi7090168

**AMA Style**

Tran H-K, Chiou J-S.
PSO-Based Algorithm Applied to Quadcopter Micro Air Vehicle Controller Design. *Micromachines*. 2016; 7(9):168.
https://doi.org/10.3390/mi7090168

**Chicago/Turabian Style**

Tran, Huu-Khoa, and Juing-Shian Chiou.
2016. "PSO-Based Algorithm Applied to Quadcopter Micro Air Vehicle Controller Design" *Micromachines* 7, no. 9: 168.
https://doi.org/10.3390/mi7090168