## 4 Conclusions  
The orientation control of a heliostat using an FLC was implemented on an embedded system based on a low-cost microcontroller. Also, the comparison against a traditional PID controller was performed. The advantage of the FLC is the fact that it is not necessary to know the mathematical model of the system, because it only uses the experience of an operator, which is easy to incorporate into the controller.  
The results show that both controllers exhibit a similar output response for the position control of a DC motor. However, the FLC has a better performance than the PID controller for the orientation control of the heliostat by using the same control parameters for the position control of the DC motor at no load. The FLC has higher flexibility since it is robust in front of changes in the dynamics of the process, whereas for a better output response of the PID controller, the control gains must be tuned for the mathematical models of the heliostat axes. The results also exhibit a smaller MSE of the FLC compared to the PID controller for the orientation control of the heliostat by using only a nine-rule rule base and a fuzzy set of three membership functions in each input and output signal in order to reduce the computational effort of the controller. Additionally, the center of the sums defuzzification method complies with the design parameter of 10 ms sample time, showing a faster response than the center of the gravity defuzzification method.  
In a central tower power plant that uses traditional PID controllers for the orientation control of the heliostats, the control gains of the controller of all the heliostats must be adjusted in order to  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Date & Friday, 13 September 2019 \\ Time & 13:00:00–14:00:00 \\ Latitude & 20.590636\({}^{\circ}\) N \\ Longitude & 100.413226\({}^{\circ}\) W \\ Monthly Mean Atmospheric Pressure & 819.795 mbar \\ Monthly Mean Temperature & 20.3 \({}^{\circ}\)C \\ Maximum Wind Speed & 8 m/s (28.8 km/h) \\ Target Height & 30.0 m \\ Heliostat Height & 2.85 m \\ East-West distance to the target & 15 m East \\ North-South distance to the target & 35 m North \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of the orientation control test.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Final Ref MSE** & **Desired Ref MSE** \\ \hline DC Motor at no load & PID Azimuth & 0.0\({}^{\circ}\) & 0.068610\({}^{\circ}\) \\  & PID Elevation & 0.0\({}^{\circ}\) & 0.026349\({}^{\circ}\) \\  & FLC Azimuth & 0.0\({}^{\circ}\) & 0.068610\({}^{\circ}\) \\  & FLC Elevation & 0.0\({}^{\circ}\) & 0.026349\({}^{\circ}\) \\ \hline  & PID Azimuth & 0.153941\({}^{\circ}\) & 0.168669\({}^{\circ}\) \\ Heliostat & PID Elevation & 0.051032\({}^{\circ}\) & 0.048347\({}^{\circ}\) \\  & FLC Azimuth & 0.131647\({}^{\circ}\) & 0.146435\({}^{\circ}\) \\  & FLC Elevation & 0.039328\({}^{\circ}\) & 0.047251\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Reference error values of the orientation control.  
avoid oscillations due to wrong controller parameters tuning. Therefore, the proposed control system can be applied in order to control an entire heliostat field by using the same controller parameters for all the heliostat. The system can also be adjusted to control other sun tracking systems, such as a photovoltaic, solar dish, or parabolic trough systems, which only need the solar tracker system.  
Conceptualization, E.S.-P. and M.T.-A.; Methodology, E.S.-P. and R.V.C.-S.; Project administration, M.T.-A.; Software, E.S.-P.; Validation, E.S.-P. and R.V.C.-S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors would like to thank Consejo Nacional de Ciencia y Tecnologia (CONACYT-Mexico) for supporting this research.  
The authors declare