New Trajectory Tracking Approach for a Quadcopter Using Genetic Algorithm and Reference Model Methods
Abstract
:1. Introduction
2. Quadcopter Mathematical Model
- The quadcopter structure is rigid and symmetrical;
- The center of gravity lies at the origin of the body reference frame;
- Wind, ground effect disturbances, and the gyroscopic effect are neglected;
- The thrust and drag are proportional to the square of the speed of the rotor.
3. Hierarchical Controllers for Trajectory Tracking
3.1. Reference Model-Based Hierarchical Controller (RMHC)
3.2. Genetic Algorithm-Based Hierarchical Controller (GAHC)
- For attitude
- For position:
4. Trajectory Tracking via Attitude Stabilization
4.1. Trajectory Tracking Using the Reference Model Method (TTRM)
4.2. Trajectory Tracking Using Genetic Algorithms Method (TTGA)
5. Simulation Results
5.1. Hierarchical Controllers for Trajectory Tracking
5.2. Trajectory Tracking via Attitude Stabilization
5.3. Trajectory Tracking in the Presence of Disturbance
5.3.1. Hierarchical Controllers
5.3.2. Trajectory Tracking via Attitude Stabilization
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
PD | Proportional, Derivative |
PID | Proportional, Integral, Derivative |
GA | Genetic Algorithm |
RM | Reference Model |
RMHC | Reference Model besed Hierarchical Controller |
GAHC | Genetic Algorithm besed Hierarchical Controller |
TTRM | Trajectory Tracking by using Reference Model |
TTGA | Trajectory Tracking by using Genetic Algorithm |
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RMHC Method | Controllers | ||||||
---|---|---|---|---|---|---|---|
PD Parameters | 16.67 | 16.67 | 16.67 | 0.10 | 0.10 | 190.8 | |
1.21 | 1.21 | 1.21 | 0.20 | 0.20 | 34.98 | ||
PID Parameters | 37.17 | 37.17 | 33.34 | 18.34 | 37.17 | 6.60 | |
65.22 | 65.22 | 7.28 | 0.25 | 65.22 | 0.05 | ||
2.35 | 2.35 | 1.4 | 10.41 | 2.35 | 6.24 |
GAHC Method | Controllers | ||||||
---|---|---|---|---|---|---|---|
PD Parameters | 16.83 | 15.78 | 22.82 | 7.92 | 7.41 | 184.0 | |
2.82 | 2.55 | 42.48 | 6.45 | 6.40 | 23.05 | ||
PID Parameters | 48.63 | 35.83 | 34.18 | 13.34 | 7.61 | 17.67 | |
8.45 | 1.36 | 7.57 | 0.16 | 0.92 | 0.10 | ||
2.29 | 2.35 | 6.50 | 5.23 | 5.46 | 10.40 |
TTRM Method | Controllers | ||||
---|---|---|---|---|---|
PD Parameters | 16.67 | 16.67 | 16.67 | 190.8 | |
1.27 | 1.27 | 1.27 | 34.98 | ||
PID Parameters | 23.48 | 23.48 | 42.38 | 29.01 | |
13.58 | 13.58 | 0.81 | 23.58 | ||
1.42 | 1.42 | 1.71 | 8.58 |
TTGA Method | Controllers | ||||
---|---|---|---|---|---|
PD Parameters | 17.53 | 6.13 | 10.33 | 176.91 | |
2.59 | 2.92 | 1.03 | 45.55 | ||
PID Parameters | 27.73 | 23.92 | 34.18 | 21.85 | |
17.86 | 13.52 | 1.71 | 12.51 | ||
3.43 | 0.68 | 6.31 | 5.25 |
Parameter (Unit) | Value |
---|---|
m (Kg) | 0.53 |
g (m/s) | 9.81 |
l (m) | 0.4 |
b (N/rad/s) | 4.15 × |
d (N·m/rad/s) | 7.5 × |
, (Kg·m) | 7.86 × |
(Kg·m) | 1.173 × |
(Kg·m) | 2.8385 × |
, , , (N/rad/s) | 5.567 × |
(N/rad/s) | 6.354 × |
(N/rad/s) | 3.354 × |
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Siti, I.; Mjahed, M.; Ayad, H.; El Kari, A. New Trajectory Tracking Approach for a Quadcopter Using Genetic Algorithm and Reference Model Methods. Appl. Sci. 2019, 9, 1780. https://doi.org/10.3390/app9091780
Siti I, Mjahed M, Ayad H, El Kari A. New Trajectory Tracking Approach for a Quadcopter Using Genetic Algorithm and Reference Model Methods. Applied Sciences. 2019; 9(9):1780. https://doi.org/10.3390/app9091780
Chicago/Turabian StyleSiti, Imane, Mostafa Mjahed, Hassan Ayad, and Abdeljalil El Kari. 2019. "New Trajectory Tracking Approach for a Quadcopter Using Genetic Algorithm and Reference Model Methods" Applied Sciences 9, no. 9: 1780. https://doi.org/10.3390/app9091780