## 3 Results and Analysis
### Test 1: LED Current Control in Boost Mode  
Figure 10 presents the behavior of the system when you have a real 12-volt lead acid battery (BW 1280 F1), which puts the system in boost mode according to the voltage of the LEDs.  
Figure 10a shows the current in the LEDs (\(i_{LED}\)) and the reference current (\(i_{Lref}\)). This figure shows that an event was performed in which \(i_{LEDref}\) is started at 1.3324 A (red color) for 0 to 20 ms, which corresponds to a luminous flux of 4900 lm generated by the set of LEDs, requiring a voltage in the LEDs of 17.61 V. Then, the \(i_{LEDref}\) is changed to 1.663 A and maintained for 20 ms to 40 ms, generating 6000 lm for the LED array, and requiring a total voltage of 18 V. Finally, \(i_{LEDref}\) is changed to 1.9936 A, and maintained from 40 ms to 60 ms, generating 7200 lm for the LEDs, and requiring a total voltage of 18.48 V. The simulation  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Battery** & **Battery Chemistry** & **Voltage (V)** & **Capacity (Ah)** & **Cost (USD)** & **Service Time at 5 A** \\ \hline BW 1280 F1 & Lead Acid & 12 & 8 & \$24.99 & 1.6 h \\ TOOL-486 LI-30 & Lithium Ion & 18 & 3 & \$38.69 & 0.6 h \\ UPS-BAT/VRLA-WTR & Lead Acid & 24 & 13 & \$695.54 & 2.4 h \\ CUSTOM-334 & Nickel Metal Hydride & 12 & 0.4 & \$25.58 & 288 s \\ \hline \hline \end{tabular}
\end{table}
Table 3: Overview of commercial batteries used in the system.  
shows that the \(i_{LED}\) signal correctly follows the reference signal \(i_{LEDref}\), showing that the ZAD control objective and the LED current control objective is met. It is also observed that there are no overimpulses, and the response is met with the defined settling time (3 ms). As the reference signal (\(i_{LEDref}\)) increases, the controlled signal (\(i_{LED}\)) has a greater amplitude in the ripple; however, this ripple has a maximum value of 4.22%.  
Figure 9(b) shows the voltage in the LEDs (black) and the voltage in the battery (blue). The simulation considers a real battery with BW 1280 F1 specifications, 12 volts, with a capacity of 8 Ah and charged to 100%. The figure shows that the voltage value of the LEDs corresponds to the characterization reported in Figure 5 multiplied by 3, given that there are 3 groups connected in parallel. Therefore, for the 12 Volt battery, the converter is always in boost mode, which shows that batteries with a voltage lower than that required by LEDs can be used.  
Figure 9(c) shows the duty cycle (\(d\)), which varies to ensure the current control of the LEDs according to the reference (\(i_{LEDref}\)). It is observed that the duty cycle is not saturated, which ensures that the ZAD controller can effectively act on the converter, imposing a fixed switching frequency. Finally, sudden changes in the duty cycle (20 ms and 40 ms) are due to the change in current reference (\(i_{LEDref}\)).  
Figure 9(d) shows the inductor current (\(i_{L}\)), which follows the reference current \(i_{Lref}\) generated by the current controller. This \(i_{L}\) current is controlled with the ZAD control technique, generating a current ripple of 7.83%. The results of Figure 9(a),\(d\) confirm the correct operation of the current/ZAD controller assembly, since both the inductor current and the LED current are stable and adjusted to the defined references.  
Finally, it should be noted that, over time, the temperature change in the LEDs will affect the effective luminous flux. Therefore, the current compensation will modify the  
Figure 10: Results of the LED current control in boost mode with a 12-volt battery.  
\(i_{LEDref}\) reference to ensure effective luminous flux. This temperature compensation is verified in Test 5.