## 5 Experimental Validation
### Experimental Validation of the Current Reference Tracking  
The performance of the proposed LQG-FF controller and the comparison techniques (classical LQG and PI) are shown in Figure 25, where the supercapacitor voltage is 9 V, and hence the HESS operates in boost mode. A step of current of 1 A is applied to the DC bus, and the converter current (magenta color trace) exhibits an adequate tracking of the reference current (yellow color trace). The PI controller shows the longest response delay in comparison with the LQG controller. In contrast, the LQG-FF controller has an improved dynamic performance over both LQG and PI; this is confirmed by the reduced overshoot in the battery current (white color trace) provided by the LQG-FF controller. This experiment also shows the stability of the proposed solution to oscillations and noise in the load current (\(i_{dc}\)), since the proposed controller transfer these oscillations to the converter current by means of the reference current. Therefore, this solution operates correctly with stable load currents, as observed in Figure 12, and with noisy and oscillating load currents, as observed in Figure 25.  
Figure 25: Dynamic performance of current control (**a**) PI, (**b**) LQG, and (**c**) LQG-FF with \(v_{sc}=9\) V and \(v_{dc}=12\) V (boost mode). Magenta: converter current (\(i_{sc}\)); yellow: reference current (\(i_{ref}\)); cyan: supercapacitor voltage (\(v_{sc}\)); green: bus current (\(i_{dc}\)); white: battery current (\(i_{b}\)). Figures 26 and 27 report the experimental results for supercapacitor voltages equal to 12 V (unitary gain) and 15 V (buck mode) of the HESS, respectively. Similar to the previous experiment, these results confirm the improved performance of the proposed LQG-FF controller in terms of tracking speed and precision. In addition, these experiments confirm that the battery is exposed to low-frequency transients, which is observed in the battery current (white traces). The RMSE values for the experiments are calculated using the data from the dynamic response generated by the three controllers under boost, buck, and unitary gain modes (from 7 V to 15 V). Table 3 summarizes these errors, where the lowest RMSE is provided by the proposed LQG-FF controller. In addition, the LQG controller shows better performance than the PI strategy. Similar to the simulations, these experiments show that the proposed LQG-FF solution provides only a fraction of the errors introduced by the classical approaches, which is confirmed in the last two columns of Table 3.  
Figure 26: Dynamic performance of current control (**a**) PI, (**b**) LQG, and (**c**) LQG-FF with \(v_{sc}=12\) V and \(v_{dc}=12\) V (unitary gain). Magenta: converter current (\(i_{sc}\)); yellow: reference current (\(i_{ref}\)); cyan: supercapacitor voltage (\(v_{sc}\)); green: bus current (\(i_{dc}\)); white: battery current (\(i_{b}\)). The performance of the HESS to longer dynamic profiles is validated using the experimental load current (green traces) reported in Figures 28-30. In these experiments, the proposed LQG-FF controller correctly regulates the Sepic output current in boost (\(v_{sc}=9\) V), buck (\(v_{sc}=15\) V), and unitary gain modes (\(v_{sc}=12\) V). In the bottom, the mean value of the supercapacitor voltage is shown in cyan color. In the experiments the battery starts working in stand-by mode (\(i_{dc}=0\) A), and later the DC bus current changes to 1 A, and hence the battery changes to discharging mode. At 6 s, the battery returns to stand-by mode; a similar profile is applied to set the battery in charging mode, which means the DC bus current changes to \(-1\) A and 6 s later it is increased to 0 A. In these experiments, the supercapacitor absorbs or delivers the high-frequency components of the DC bus current, thus reducing the dynamic demand to the battery. In addition, the stabilization time of the battery current is 1 s, which is in agreement with the simulations.