## 3 Experimental Results  
The proposed control scheme is illustrated in Figure 3. The EXOSYSTEM block (defined in Equation (4) or (10)) generates the sinusoidal and constant signals that are fed to the REFERENCES block. This block generates the ideal steady state in Equations (55) and (57) for the boost circuit. Then, this steady state is compared with the real state of the boost circuit, obtaining the error signal vector shown in Equation (7). From the elements of this vector, the sliding function in Equation (20) is constructed as a linear combination and used in a super-twisting algorithm (Equations (21) and (22)). This control action is fed to the boost circuit and to the observer in Equation (59), along with the real state. The observer generates an estimate for the load resistance that is used for updating the ideal steady state for finally closing the loop. The proposed control scheme was implemented in a dSPACE 1104 board, represented by the gray shape; outside the board, a boost converter was connected using a Semikron module and controlled by the dSPACE board programmed with the control. Figure 3 represents only the control signals. The boost converter parameters used for the experimental results were \(L=0.098\)\(H\), \(C=10\) mF, \(R=200\)\(\Omega\), and \(E=8\) V (actually, this value was considered to be 10 V in the control algorithm in order to introduce a perturbation for all time). The design parameter \(c_{1}\) was fixed to a value of \(-200\), which corresponds to an eigenvalue \(\lambda_{1}=-412.2\). **Remark 4**. : _In order for Equation (26) not to reach zero, \(c_{1}\) should not be selected as_  
\[c_{1}=\frac{L(z_{1}+\pi_{1})}{C(z_{2}+\pi_{2})}=\frac{L(x_{1})}{C(x_{2})}. \tag{70}\]  
Since \(x_{1}>0\) and \(x_{2}>0\), it is clear that \(c_{1}\) should at least not be positive in order to avoid \(\delta(z,\omega)=0\). The input voltage source is made by a three-phase uncontrolled diode rectifier fed by a three-phase variable transformer (VARIAC). The input voltage can be adjusted by rotating the VARIAC knob. The resulting DC voltage is used to feed a Semikron power module. The Semikron power module is used to feed the boost converter. The controller is programmed in Simulink along with the PWM generator, and the output signals from Simulink are obtained with a dSPACE 1104 board. The board contains ADC converters to acquire the current through the inductor and the voltage across the capacitor. The used voltage and current sensors are the LEM HX 10-P and the LEM LV 25-P. Figure 4 shows a diagram of the experimental setup, and Figure 5 shows a photo of the prototype. Figure 3: Proposed control scheme block diagram. A first-order Butterworth low-pass filter having an edge frequency of 100 rad/s was used for filtering the inductor current in order to attenuate the measurement noise. The used sampling period was h = 60 ms. Initially, \(v\) was fixed at a value of 1 to operate the converter in an open-loop mode, where the output capacitor voltage was the same as the input voltage \(E\), calibrated at a value of 8 V (actually this value was considered to be 10 V in the control algorithm in order to introduce a perturbation for all time). Then, the converter was operated in closed-loop mode, allowing the observation of transient responses. The load resistance variations were introduced as steps. At time instants 50, 70, and 90 s, the resistance was reduced to approximately 50% of its nominal value; at time instants 60 and 80 s, the load resistance recovered to its nominal value. The capacitor voltage was forced to follow a signal with a sine waveform whose amplitude was equal to 5 V plus a DC (bias) voltage whose amplitude is 20 V. Several results were obtained with different frequency. Figure 6 shows the results for a frequency value of 1 rad/s, Figure 7 shows the results for a frequency of 5 rad/s, Figure 8 shows  
Figure 4: Experimental setup schematic diagram, including the proposed control scheme. Figure 5: Photograph of the prototype.