# Development of an Automatic Solar Tracker Control System for a Tandem-Winged UAV and Its Implementation Strategies

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case Study: The FTMD’s HALE ITB V4 1:2

#### 2.1. General Specification

#### 2.2. Forces and Moments

#### 2.2.1. Aerodynamic Characteristics

^{3}, and the vehicle airspeed V is 10 m/s. The directional cosine matrix ${C}_{b}^{a}$ is as presented in Equation (5):

#### 2.2.2. Propulsion Characteristics

#### 2.2.3. Weight and Inertia Characteristics

#### 2.3. Non-Linear Equation of Motion

#### 2.4. Linear Equation of Motion

^{3}) at a 20 m/s speed. This derivation is a common process in flight dynamics that can be observed in [16].

**A**matrix, as presented in Table 3. The resulting values are similar to the dynamics observed in the non-linear model simulation in Figure 7. As shown in Table 3, all the characteristics roots are stable. However, since one of the characteristics roots is a neutral root with harmonic oscillation, while two others have long settling time, a stability augmentation system might be warranted.

## 3. Automatic Solar Tracking System for HALE UAV

#### 3.1. Local Solar Model

#### 3.2. Roll Attitude Automatic Control System

#### 3.3. Heading and Solar Tracker Automatic Control Systems

#### 3.3.1. Mode-Switching Solar Tracker Strategy

#### 3.3.2. Simultaneous Solar Tracker Strategy

**Q**and

**R**, listed in Equations (26) and (27), were derived via this scheme utilizing the linear model of the HALE ITB V4 1:2, as shown in Section 2.4. The

**Q**-matrix is a 5 × 5 matrix with five lateral–directional states (the side slip angle ($\beta $), the roll attitude angle ($\phi $), the rolling rates ($p$), yawing rates ($r$), and the yaw angle ($\psi $)), while the

**R**-matrix is a 2 × 2 matrix that outputs the two control inputs (aileron deflection (${\delta}_{a}$) and the differential thrust (${\delta}_{dT}$)). With both matrices derived, the ${K}_{LQR}$ matrix, used as the solar tracker controller in the simultaneous strategy, can be derived as presented in Equations (26)–(28):

## 4. Simulations and Results

#### 4.1. Simulation Scenarios

#### 4.2. Scenario #1: Pure Solar Tracker

#### 4.3. Scenario #2: Mode-Switching Strategy

#### 4.4. Scenario #3: Simultaneous Strategy

## 5. Discussion

#### 5.1. Overall Flight Performance and Stability

#### 5.2. Solar Power Generation and Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Aerodynamic characteristics of the HALE ITB V4 1:2, i.e., (

**a**) drag force coefficient, (

**b**) roll moment coefficient, (

**c**) side-force coefficient, (

**d**) pitch moment coefficient, (

**e**) lift force coefficients, and (

**f**) yaw moment coefficient.

**Figure 4.**The use of differential thrust in HALE ITB V4 1:2, instead of traditional rudders. The Blue arrows shows the normal (operational) thrust for the two propulsions, which then each alternated into the yellow ones, and generates a right yawing moment at the CG (red circle arrow).

**Figure 5.**Propulsion characteristics of the HALE ITB V4 1:2, i.e., (

**a**) thrust force due to velocities, (

**b**) thrust pitching moment due to thrust generated, (

**c**) thrust rolling moment due to differential thrust control, and (

**d**) thrust yawing moment due to differential thrust.

**Figure 8.**Solar tracker concept: (

**a**) the land solar panel, and (

**b**) the solar tracker scheme in HALE ITB V4 1:2.

**Figure 11.**Simulation of the closed loop roll attitude control system for HALE ITB V4 1:2, under aileron disturbances.

**Figure 12.**The heading and solar tracker automatic control system in the mode-switching strategy of implementation.

**Figure 13.**The heading and solar tracker automatic control system in the simultaneous strategy of implementation.

**Figure 15.**Simulation results of Scenario #1: pure solar tracker. (

**a**) The trajectory, and (

**b**) the roll tracker performance.

**Figure 16.**Simulation results of Scenario #2: mode-switching solar tracker. (

**a**) The mission trajectory, (

**b**) first circular charging mode trajectory, and (

**c**) the roll angle response following the (first) desired solar incidence.

**Figure 17.**Simulation results of Scenario #3: simultaneous solar tracker. (

**a**) The mission trajectory, and (

**b**) roll angle response following the solar incidence.

**Figure 18.**Energy input comparison between the based (no solar tracking), the mode-switching, and the simultaneous strategies, during the same mission trajectory.

Parameters | Value | Unit |
---|---|---|

Front wingspan | 6.0 | m |

Front wing area | 6.345 | m^{2} |

Rear wingspan | 7.5 | m |

Rear wing area | 7.0 | m^{2} |

Mean aerodynamic chord | 0.47 | m |

MTOW | 24.9 | kg |

Design speed | 20.0 | m/s |

Maximum thrust | 4.0 | kg |

Derivatives of | Coefficients | Value (. /rad) |
---|---|---|

Roll moment due to roll rates p | ${C}_{{\ell}_{p}}$ | −4.52 |

Roll moment due to yaw rates r | ${C}_{{\ell}_{r}}$ | 1.13 |

Pitch moment due to pitch rates q | ${C}_{{m}_{q}}$ | −141.37 |

Yaw moment due to roll rates p | ${C}_{{n}_{p}}$ | −0.28 |

Yaw moment due to yaw rates r | ${C}_{{n}_{r}}$ | −1.70 |

Eigenvalues | Damping Ratios | Half Times [s] | Frequencies [Hz] |
---|---|---|---|

0 | - | - | - |

−0.013 | 1 | 53.445 | - |

−0.0145 ± 0.505i | 0.029 | 47.786 | 0.507 |

−7.542 | 1 | 0.092 | - |

Eigenvalues | Damping Ratios | Half Times (s) | Frequencies (Hz) |
---|---|---|---|

−3 | 1 | 0.231 | 3 |

−5 | 1 | 0.139 | 5 |

−5 ± 2i | 0.928 | 0.139 | 5.39 |

−10 | 1 | 0.069 | 10 |

State Variables | Feedback Amplifier for Ailerons ${\mathit{\delta}}_{\mathit{a}}$ | Feedback Amplifier for Differential Thrust ${\mathit{\delta}}_{\mathit{d}\mathit{T}}$ |
---|---|---|

$\beta $ | 1.415 | −0.541 |

$\phi $ | 10.209 | −1.474 |

$p$ | 1.073 | −0.323 |

$r$ | 1.075 | 3.99 |

$\psi $ | 33.095 | 2.078 |

Parameters | Heading Tracker | Solar Tracker |
---|---|---|

Proportional gain ($P$) | 30.13 | −0.01 |

Integration gain ($I$) | 33.25 | 0 |

Derivative gain ($D$) | 6.7 | −0.26 |

Filter coefficient gain ($N$) | 127.52 | 0.08 |

**Table 7.**Scenarios to test the performance of HALE ITB V4 1:2 under the designed solar tracker system.

Scenario | Implementation Strategy | Intended Trajectory |
---|---|---|

1 | Pure solar tracker | |

2 | Mode-switching | |

3 | Simultaneous solar tracker |

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**MDPI and ACS Style**

Jenie, Y.I.; Pardomoan, G.Y.; Moelyadi, M.A.
Development of an Automatic Solar Tracker Control System for a Tandem-Winged UAV and Its Implementation Strategies. *Drones* **2023**, *7*, 442.
https://doi.org/10.3390/drones7070442

**AMA Style**

Jenie YI, Pardomoan GY, Moelyadi MA.
Development of an Automatic Solar Tracker Control System for a Tandem-Winged UAV and Its Implementation Strategies. *Drones*. 2023; 7(7):442.
https://doi.org/10.3390/drones7070442

**Chicago/Turabian Style**

Jenie, Yazdi Ibrahim, Gerald Yohanes Pardomoan, and Mochammad Agoes Moelyadi.
2023. "Development of an Automatic Solar Tracker Control System for a Tandem-Winged UAV and Its Implementation Strategies" *Drones* 7, no. 7: 442.
https://doi.org/10.3390/drones7070442