In recent years, the accumulation of dust on solar panels in photovoltaic power stations has become a significant issue, reducing power generation efficiency and potentially damaging the panels. Regular cleaning of these solar panels is essential to maintain high performance and longevity. To address this, robotic cleaners have been widely adopted for large-scale solar panel maintenance. However, these robots often experience deflection during motion, leading to unstable cleaning paths and reduced efficiency. This paper proposes an improved control method that combines particle swarm optimization (PSO) with fuzzy PID control to enhance the anti-deflection motion stability of solar panel cleaning robots. By optimizing the quantization and scaling factors of the fuzzy PID controller using PSO, we aim to minimize the robot’s deflection angle and improve cleaning performance. The approach involves modeling the robot’s motor and kinematics, designing a PSO-optimized fuzzy PID controller, and validating it through simulations and prototype testing. The results demonstrate that this method effectively maintains the robot’s deflection angle near the desired value of 0 radians, even under disturbances, and increases cleaning efficiency to 94.22%. This study highlights the potential of intelligent control strategies in optimizing the operation of solar panel cleaning systems.
The increasing adoption of solar energy has emphasized the importance of maintaining solar panels to ensure optimal efficiency. Dust and debris accumulation on solar panels can significantly reduce their energy output, making regular cleaning a necessity. Automated cleaning robots offer a practical solution for large-scale solar farms, but their motion control remains challenging due to factors like uneven surfaces and external disturbances. Deflection during movement can lead to incomplete coverage and reduced cleaning effectiveness. Traditional control methods, such as standard PID or fuzzy logic, often fall short in handling nonlinearities and real-time adjustments. To overcome these limitations, this research integrates PSO, a global optimization algorithm, with fuzzy PID control to dynamically adjust control parameters. The focus is on developing a robust anti-deflection controller that ensures stable robot motion on solar panels, thereby enhancing overall system reliability and performance. The following sections detail the modeling, controller design, simulation experiments, and results, providing a comprehensive analysis of the proposed method’s efficacy.
Modeling of Solar Panel Cleaning Robot for Anti-Deflection Motion
To design an effective anti-deflection controller, it is essential to develop accurate models of the robot’s drive motor and motion dynamics. The solar panel cleaning robot typically uses a permanent magnet synchronous motor (PMSM) for propulsion, which influences its stability and responsiveness. The PMSM model in the d-q coordinate system is described by the following equations, which account for electrical and mechanical behaviors:
$$L_d \frac{di_d}{dt} = -R_s i_d + n_p \omega L_q i_q + u_d$$
$$L_q \frac{di_q}{dt} = -R_s i_q – n_p \omega L_d i_d – n_p \omega \Phi + u_q$$
$$J_m \frac{d\omega}{dt} = \tau – \tau_{Lm} – R\omega$$
$$\frac{d\beta}{dt} = \omega$$
$$\tau = n_p \left[ (L_d – L_q) i_d i_q + \Phi i_q \right]$$
where ( u_d, u_q ) are the d-axis and q-axis voltages, ( i_d, i_q ) are the currents, ( L_d, L_q ) are the stator inductances, ( J_m ) is the motor inertia, ( R ) is the viscous friction coefficient, ( \Phi ) is the flux linkage, ( n_p ) is the pole pairs, ( R_s ) is the stator resistance, ( \omega ) is the angular velocity, ( \beta ) is the angular displacement, ( \tau_{Lm} ) is the load torque, and ( \tau ) is the electromagnetic torque. This model forms the basis for understanding the motor’s impact on robot motion, particularly in terms of torque and speed control, which are critical for maintaining stability on solar panels.
For the motion kinematics, the robot is modeled using D’Alembert’s principle and the virtual displacement principle, assuming no slippage between the tracks and the solar panels and neglecting the cleaning brush’s influence. The coordinate systems include a global frame ( oxy ) attached to the solar panel array and a local frame ( px_p y_p ) fixed to the robot’s center of mass. The transformation matrix ( \mathbf{R} ) between these frames is given by:
$$\mathbf{R} = \begin{bmatrix} \cos\theta & \sin\theta \ -\sin\theta & \cos\theta \end{bmatrix}$$
where ( \theta ) is the deflection angle of the robot. According to Newton’s second law, the force balance equation is:
$$\mathbf{F}_m + \mathbf{F}_f + \mathbf{F}_n + \mathbf{F}_g = m \mathbf{v}$$
where ( m ) is the robot mass, ( \mathbf{v} ) is the velocity vector, ( \mathbf{F}_m ) is the motor drive force, ( \mathbf{F}_f ) is the frictional resistance, ( \mathbf{F}_n ) is the elastic force from anti-deflection spring wheels, and ( \mathbf{F}_g ) is the gravitational force. The external moment ( M ) for rotational motion is expressed as:
$$M = J \theta”$$
where ( J ) is the moment of inertia, and ( \theta” ) is the angular acceleration. The moment equation incorporates driving, spring, and resistance moments:
$$J \theta” = M_m + M_n + M_f = F_1 s_1 – F_2 s_2 – 2ka \tan\theta – \mu_3 \theta’$$
Here, ( F_1 ) and ( F_2 ) are friction forces, ( s_1 ) and ( s_2 ) are distances from the track centers to the mass center, ( 2ka ) is the distance between spring wheels with curvature coefficient ( k ) and stiffness ( a ), and ( \mu_3 ) is the rotational resistance coefficient. Based on these, the kinematic model of the robot is derived as:
$$x” = \left[ (F_1 + F_2) \cos\theta – u x’ + 2k(L – L_0) (\sec\theta – 1) \sin\theta + (mg \sin\alpha + y \cos\alpha) \tan\theta \right] / m$$
$$y” = \left[ (F_1 + F_2) \cos\theta – u x’ + 2k(L – L_0) (\sec\theta – 1) \cos\theta + mg \sin\alpha + y \cos\alpha \right] / m$$
$$\theta” = (F_2 s_2 – F_1 s_1 – 2ka \tan\theta – \mu_3 \theta’) / J$$
where ( x” ) and ( y” ) are accelerations in the x and y directions, ( u ) is the resistance coefficient, ( x’ ) is the velocity in the x-direction, ( L ) is the spring length, ( L_0 ) is the natural spring length, ( \alpha ) is the installation angle of the solar panels, and ( y ) is the displacement in the y-direction. This model captures the key dynamics affecting the robot’s deflection on solar panels and serves as the foundation for controller design.
Design of the Controller for Solar Panel Cleaning Robots
The core of the anti-deflection control system is a fuzzy PID controller, whose parameters are optimized using PSO to enhance performance. Fuzzy PID control combines the adaptability of fuzzy logic with the precision of PID control, allowing real-time adjustment of parameters based on the error ( e ) (deviation from the desired deflection angle) and its rate of change ( ec ). The structure of the fuzzy PID controller is illustrated in the block diagram below, where ( \Delta K_p ), ( \Delta K_i ), and ( \Delta K_d ) represent adjustments to the proportional, integral, and derivative gains, respectively. This integration enables robust handling of nonlinearities and disturbances commonly encountered by solar panel cleaning robots.
To optimize the fuzzy PID controller, PSO is employed to fine-tune the quantization and scaling factors, which are typically set empirically. PSO is a population-based optimization algorithm that iteratively improves candidate solutions. The optimization process involves the following steps:
- Initialize PSO parameters, such as population size and particle dimensions, with the quantization and scaling factors as optimization targets.
- In each iteration, compute the particle fitness using the formula:
$$\text{fitness} = \frac{1}{n} \sum_{i=1}^{n} \text{accuracy}_i$$
where ( n ) is the number of iterations, and ( \text{accuracy}_i ) is the training accuracy at step ( i ).
- Compare fitness values across particles and select the maximum as the individual best.
- Terminate the process when stopping criteria are met, outputting the optimized factors for the fuzzy PID controller.
- Evaluate the controller’s performance under these parameters; if it meets the desired threshold, the optimization concludes.
Using the PSO-optimized parameters, the fuzzy PID controller is designed with the following steps:
- Fuzzification: The input variables \( e \) and \( ec \) are mapped to fuzzy sets with a universe of discourse of \([-6, 6]\), corresponding to a deflection angle range of \([-5^\circ, 5^\circ]\) in radians for practical applicability on solar panels.
- Membership Functions: Gaussian functions are used for the left and right boundaries, and triangular functions for the central regions, to define fuzzy sets such as Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (Z), Positive Small (PS), Positive Medium (PM), and Positive Big (PB).
- Optimized Factors: PSO determines the best quantization and scaling factors to minimize deflection.
- Fuzzy Rules: A rule base is constructed based on the robot’s operational characteristics on solar panels, as shown in Table 1. These rules dictate how \( \Delta K_p \), \( \Delta K_i \), and \( \Delta K_d \) are adjusted according to \( e \) and \( ec \).
- Defuzzification: The min-operation method is used for fuzzy inference, and the center of gravity method converts fuzzy outputs to crisp values for control actions.
| \( e \) | \( ec \) | ||||||
|---|---|---|---|---|---|---|---|
| NB | NM | NS | Z | PS | PM | PB | |
| NB | PB | PB | PM | PM | Z | Z | PS |
| NM | PB | PB | PM | PS | NS | Z | PS |
| NS | PM | PM | PM | PS | NS | NS | Z |
| Z | PM | PM | PM | Z | NM | NM | NS |
| PS | Z | Z | NS | NS | NB | NB | NM |
| PM | PS | Z | NS | NS | NB | NM | NM |
| PB | PS | PS | Z | NS | NM | NM | NS |
This controller is then implemented in the robot’s control system to regulate the motor outputs and maintain a deflection angle near zero, ensuring stable motion across solar panels. The use of PSO optimization significantly enhances the controller’s responsiveness to dynamic changes, such as variations in surface conditions or external forces on the solar panels.
Simulation Experiments and Results Analysis
To validate the proposed PSO-optimized fuzzy PID control method, simulation experiments were conducted using MATLAB/Simulink. The test subject was a ZTFBX-1705 portable solar panel cleaning robot, which features remote control, a mass of 36.5 kg, a speed range of 0–50 m/min, a cleaning width of 1100 mm, and a cleaning efficiency of 1500–2000 m²/h. This robot is ideal for solar panel maintenance due to its high adaptability and intelligence. The simulation environment included models of the robot’s motor and kinematics, with parameters set as follows: target speed of 30 m/min, desired deflection angle of 0 rad, resistance coefficients of 0.10 and 0.12 in the x and y directions, rotational resistance coefficient of 0.15, solar panel installation angle of 0.524 rad, spring natural length of 0.1 m, spring stiffness of 10,000 N/m, and moment of inertia of 1.7 kg·m². For PSO, the population size was 10, particle dimension was 2, learning factor was 2, and iterations were 50.
The first experiment evaluated the step response of the fuzzy PID controller before and after PSO optimization. As shown in the results, the optimized controller achieved faster convergence to the setpoint with minimal overshoot and no oscillations after stabilization, indicating improved stability for solar panel cleaning tasks. This enhancement is critical for maintaining consistent robot motion on large arrays of solar panels, where sudden changes can lead to deflection.
Next, the anti-deflection performance was tested under both undisturbed and disturbed conditions. In undisturbed scenarios (0–2.0 s), both the standard and optimized controllers kept the deflection angle close to 0 rad, but the optimized version exhibited smaller oscillations. When disturbances were introduced (2.0–4.5 s), such as simulated obstacles on the solar panels, the optimized controller quickly returned the deflection angle to 0 rad, whereas the standard controller showed larger deviations and slower recovery. This demonstrates the robustness of the PSO-optimized method in real-world environments where solar panels may have uneven surfaces or debris.
For comparison, the proposed method was tested against other common control strategies, such as fuzzy sliding mode control and fuzzy active disturbance rejection control. Under undisturbed conditions, all methods maintained the deflection angle near 0 rad. However, with disturbances, the fuzzy sliding mode and fuzzy active disturbance rejection controls resulted in significant deflection angles that failed to return to zero, while the PSO-optimized fuzzy PID control minimized deflection and ensured rapid recovery. This superiority is attributed to the dynamic parameter adjustment enabled by PSO, which adapts to the specific challenges of solar panel cleaning.
Finally, a prototype test was conducted by integrating the PSO-optimized fuzzy PID controller into the robot’s STM32F407IGT6 main control board. The system used a 24V20AH lithium battery and a tilt sensor with 0.01° precision to monitor deflection. Results showed that the controller reduced the overall deflection angle compared to uncontrolled operation, with quick recovery after encountering obstacles at 4.0–5.0 s and 7.0–8.0 s. This confirms the practical applicability of the method for solar panel cleaning robots. Additionally, cleaning efficiency was measured with an initial dust accumulation of 10 g/m² and a cleanliness threshold of 92% transmittance. The optimized controller achieved a cleaning efficiency of 94.22%, an 8.56% improvement over the uncontrolled baseline, highlighting its effectiveness in maintaining solar panel performance.
Conclusion and Future Work
In this study, a PSO-optimized fuzzy PID control method was developed to address the anti-deflection motion control of solar panel cleaning robots. By optimizing the quantization and scaling factors of the fuzzy PID controller, the approach enhanced stability and responsiveness, enabling the robot to maintain a deflection angle near 0 radians under various conditions. Simulation and prototype tests demonstrated that the method outperforms traditional controls, such as fuzzy sliding mode and fuzzy active disturbance rejection, in terms of deflection minimization and recovery speed. Moreover, it significantly improved cleaning efficiency to 94.22%, making it a valuable solution for maintaining solar panels in photovoltaic power stations. The integration of PSO allows for real-time adaptation to dynamic environments, which is crucial for large-scale solar panel arrays where consistency and reliability are paramount.
Despite these promising results, there are limitations to this work. For instance, the experiments were conducted on a limited section of solar panels, and the controller’s performance across diverse panel configurations and environmental conditions requires further validation. Future research will focus on expanding the testing scope to include various solar panel layouts and real-world scenarios, such as different tilt angles and weather conditions. Additionally, we plan to explore other optimization algorithms, like genetic algorithms or neural networks, to further enhance the controller’s capabilities. Improvements in sensor integration and machine learning could also enable predictive control for better handling of unexpected obstacles on solar panels. Ultimately, this research aims to contribute to the development of more efficient and autonomous cleaning systems for solar energy infrastructure, supporting the global transition to renewable energy.