**3. Results and Discussion**

The orientation control system was implemented in the heliostat shown in Figure 18, whereas the printed circuit board (PCB) of the embedded system and the motor driver are shown in Figure 19. It is an azimuth–elevation mechanism heliostat, with a worm drive mechanism driven by a DC gear motor model ZYT6590-01 at each axis. The heliostat has a gap which allows directing the facets to the ground. The parameters of the heliostat and the DC motors are presented in Table 3.

**Figure 18.** Heliostat.

**Figure 19.** Printed circuit board of the embedded system (**a**) and the motor driver (**b**).


**Table 3.** Parameters of the heliostat and DC motors.

As mentioned already, the control algorithms were designed for the position control of a DC motor at no load. Afterwards, the control algorithms were implemented in the orientation control of the heliostat using the same controller parameters of the position control of the DC motor at no load.

Figure 20 shows the comparison of the consumption time of the PID controller (Figure 20a) and the FLC using the CoS (Figure 20b) and the CoG (Figure 20c) defuzzification methods, where the period of the signals represents the sampling time of the control algorithms. The results show that the FLC with the CoG defuzzification method does not accomplish with the design parameters because of its computational complexity.

The output response of the control algorithms for the position control of a DC motor at no load is shown in Figure 21 for the minimum change in the reference value of 0.087 degrees (1.533 mrad) and a reference value of 180 degrees (π rad). Both control algorithms accomplish with the design parameters for the position control of the DC motor at no load. However, Figure 21d shows that the FLC control signal decreases when the position of the DC motor is reaching the reference value.

**Figure 20.** Consumption time of the PID controller (**a**), and the fuzzy logic controller with the CoS (**b**) and the CoG (**c**) defuzzification methods.

**Figure 21.** Output response (**a**) and control signal (**c**) of the DC motor at no load at a minimum reference value. Output response (**b**) and control signal (**d**) of the DC motor at no load at a reference value of 180 degrees (π rad).

Finally, Figures 22 and 23 show the output response of the control algorithms for the orientation control for the DC motors at no load and the axes of the heliostat, respectively. The desired angles of the heliostat were calculated using the parameters of Table 4, whereas the error values are shown in Table 5.

**Figure 22.** Output response of the orientation control of the DC motors at no load for the azimuth axis (**a**) and the elevation axis (**b**).

**Figure 23.** Output response of the orientation control for the azimuth axis (**a**) and the elevation axis (**b**) of the heliostat. Desired reference error values of the orientation control of the heliostat for the fuzzy logic controller (**c**) and the PID controller (**d**). Final reference error values of the orientation control of the heliostat for the fuzzy logic controller (**e**) and the PID controller (**f**).


**Table 4.** Parameters of the orientation control test.

**Table 5.** Reference error values of the orientation control.


The experimental results show a similar Mean Squared Error (MSE) for the orientation control of the DC motors at no load and a similar output response between the orientation control of the heliostat and the final reference value for the FLC (Figure 23a) and the PID controller (Figure 23b), despite the load of the wind over the mechanical structure and the backlash in the axis mechanisms. However, for the orientation control of the heliostat, the FLC shows less dispersed error values (Figure 23c) and smaller final reference error values (Figure 23e) than the PID controller (Figure 23d,f).
