## 3 Experimental Results
the results for a frequency of 10 rad/s, and Figure 9 shows the results for a frequency of 15 rad/s. Figure 6: Real-time results at \(\alpha\) = 1 rad/s. (**a**) Capacitor voltage (solid) and capacitor voltage reference signal (dashed) [\(V\) vs. \(s\)]. (**b**) Inductor current (solid) and inductor current reference signal (dashed) [\(A\) vs. \(s\)]. (**c**) Estimated load resistance [\(\Omega\) vs. \(s\)]. (**d**) Zoomed-in view of the same variables in (**a**). (**e**) Zoomed-in view of the same variables in (**b**). Figure 7: Real-time results with \(\alpha\) = 5 rad/s. (**a**) Capacitor voltage (solid) and capacitor voltage reference signal (dashed) [\(V\) vs. \(s\)]. (**b**) Inductor current (solid) and inductor current reference signal (dashed) [\(A\) vs. \(s\)]. (**d**) Zoomed-in view of the same variables in (**a**). (**e**) Zoomed-in view of the same variables in (**b**). Figure 8: Real-time results with \(\alpha=10\) rad/s. (**a**) Capacitor voltage (solid) and capacitor voltage reference signal (dashed) [\(V\) vs. \(s\)]. (**b**) Inductor current (solid) and inductor current reference signal (dashed) [\(A\) vs. \(s\)]. (**c**) Estimated load resistance [\(\Omega\) vs. \(s\)]. (**d**) Zoomed-in view of the same variables in (**a**). (**e**) Zoomed-in view of the same variables in (**b**). Figure 9: Real-time results with \(\alpha=15\) rad/s. (**a**) Capacitor voltage (solid) and capacitor voltage reference signal (dashed) [\(V\) vs. \(s\)]. (**b**) Inductor current (solid) and inductor current reference signal (dashed) [\(A\) vs. \(s\)]. (**c**) Estimated load resistance [\(\Omega\) vs. \(s\)]. (**d**) Zoomed-in view of the same variables in (**a**). (**e**) Zoomed-in view of the same variables in (**b**). In general, a similar behavior can be appreciated in all cases, i. e., a good performance for the voltage across the capacitor where the exponentially transient response (without overshoot) was due to the natural sliding mode dynamics in all cases, although the inductor current tracking was not clear due to measurement noise. It is important to mention that, in all cases, there were minimal transient responses at the voltage across the capacitor when load resistance variations were introduced. On the contrary, the transient responses of the output capacitor voltages reported in [34; 35; 36], through simulation studies, were considerably larger. In order to better evaluate the control performance at all four frequencies, we considered the precision error Pe and the chattering effect Ch. The former is defined as the relative error of the output variable and is calculated as the difference between the average steady-state control output and the reference value, divided by the reference value:  
\[P_{e}=\frac{|S_{r}-V_{mc}|}{S_{r}}\times 100, \tag{71}\]  
where \(S_{r}\) is the imposed reference, and \(V_{mc}\) is the average of the output controlled variable in the steady state. The latter is characterized by the amplitude of the signal, and is given by the difference between the amplitude of the output variable and the average in the steady state of the reference signal:  
\[c_{1}=\frac{L(z_{1}+\pi_{1})}{C(z_{2}+\pi_{2})}=\frac{L(x_{1})}{C(x_{2})}. \tag{70}\]0  
where \(A_{mc}\) is the maximum amplitude of the deviations of the output signal with respect to its average value \(V_{mc}\). Table 1 summarizes the evaluation parameters for all four frequencies. One can observe that the proposed controller had approximately a zero precision error at all frequencies, but the chattering effect decreased as the frequency increased. One final observation can be drawn between the inductor current and the load resistance. The current increased as the load resistance decreased and vice versa. This was expected since \(\pi\)1(w) was updated with the resistance estimation.