The accumulation of dust on solar panels significantly reduces photovoltaic conversion efficiency and may cause permanent damage to panel surfaces. To address this challenge, autonomous cleaning robots have emerged as essential maintenance tools for large-scale solar farms. This paper presents an innovative anti-deflection control system combining particle swarm optimization (PSO) with fuzzy PID control to improve motion stability and cleaning efficiency in solar panel maintenance robots.
1. Dynamic Modeling of Solar Panel Cleaning Robots
1.1 Permanent Magnet Synchronous Motor (PMSM) Model
The driving system of solar panel cleaning robots utilizes PMSM with the following mathematical model in d-q coordinates:
$$
\begin{cases}
L_d \frac{di_d}{dt} = -R_s i_d + n_p \omega L_q i_q + u_d \\
L_q \frac{di_q}{dt} = -R_s i_q – n_p \omega L_d i_d – n_p \omega \Phi + u_q \\
J_m \frac{d\omega}{dt} = \tau – \tau_{Lm} – R\omega \\
\frac{d\beta}{dt} = \omega \\
\tau = n_p[(L_d – L_q)i_d i_q + \Phi i_q]
\end{cases}
$$
Where parameters are defined as:
| Symbol | Description |
|---|---|
| \(L_d, L_q\) | d-q axis inductances |
| \(R_s\) | Stator resistance |
| \(n_p\) | Pole pairs |
| \(\Phi\) | Magnetic flux |
| \(J_m\) | Moment of inertia |
1.2 Kinematic Model
The motion dynamics of solar panel cleaning robots considering deflection angles can be expressed as:
$$
\begin{cases}
x” = \frac{(F_1 + F_2)\cos\theta – \mu\dot{x} + 2k(L-L_0)(\sec\theta-1)\sin\theta + (mg\sin\alpha + y\cos\alpha)\tan\theta}{m} \\
y” = \frac{(F_1 + F_2)\sin\theta – \mu\dot{y} + 2k(L-L_0)(\sec\theta-1)\cos\theta + mg\sin\alpha + y\cos\alpha}{m} \\
\theta” = \frac{F_2 s_2 – F_1 s_1 – 2ka\tan\theta – \mu_3\dot{\theta}}{J}
\end{cases}
$$
2. Hybrid Control Strategy Design
2.1 Fuzzy PID Architecture
The proposed control system integrates three essential components:
| Component | Function |
|---|---|
| Fuzzification | Convert numerical errors to linguistic variables |
| Rule Base | 48 control rules for deflection compensation |
| Defuzzification | Convert fuzzy outputs to crisp control signals |
2.2 PSO Optimization Process
The optimization objective function for solar panel cleaning efficiency enhancement:
$$
\text{Fitness} = \frac{1}{N} \sum_{i=1}^{N} \left[ w_1|\theta_e(t_i)| + w_2|\dot{\theta}_e(t_i)| + w_3 u(t_i)^2 \right]
$$
PSO parameter configuration:
| Parameter | Value |
|---|---|
| Swarm Size | 50 |
| Iterations | 100 |
| Inertia Weight | 0.9→0.4 |
| Learning Factors | \(c_1=1.5, c_2=1.7\) |
3. Performance Evaluation
3.1 Deflection Control Comparison
| Control Method | Max Deflection (rad) | Settling Time (s) |
|---|---|---|
| Conventional PID | 0.12 | 2.8 |
| Fuzzy PID | 0.08 | 2.1 |
| PSO-Fuzzy PID | 0.04 | 1.3 |
3.2 Solar Panel Cleaning Efficiency
The proposed method achieves 94.22% cleaning efficiency compared to conventional approaches:
$$
\eta_{\text{clean}} = \frac{A_{\text{effective}}}{A_{\text{total}}} \times 100\% = \frac{2.38}{2.52} \times 100\% = 94.22\%
$$
4. Implementation Considerations
Key implementation aspects for solar panel maintenance robots:
- Real-time processing requirements: 10ms control cycle
- Environmental adaptability: 15° panel inclination tolerance
- Power management: 24V battery with 8h continuous operation
5. Conclusion
The PSO-optimized fuzzy PID controller demonstrates superior performance in maintaining solar panel cleaning robot stability, reducing maximum deflection by 66.7% compared to conventional PID control. This advancement enables more efficient solar panel maintenance with 94.22% cleaning efficiency, significantly improving photovoltaic system performance. Future work will focus on multi-robot coordination for large-scale solar farms and enhanced obstacle detection algorithms.
$$
\Delta \eta_{\text{system}} = \frac{\eta_{\text{proposed}} – \eta_{\text{baseline}}}{\eta_{\text{baseline}}} \times 100\% = \frac{94.22 – 85.66}{85.66} \times 100\% = 9.99\%
$$
This improvement in solar panel cleaning efficiency directly translates to increased energy output, making the proposed control strategy particularly valuable for utility-scale photovoltaic installations.