**6. Closed-Loop Numerical and Experimental Validations**

Firstly, numerical validations for the system operating in a closed-loop with the proposed controller are presented; this is done by using two CPL sweeps and the parameters established in Section 3. The first sweep consists of introducing 40 W steps in the CPL level, from 0 up to 200 W (PSIM), as shown in the upper plot of Figure 12. The proposed controller in Equation (25) is used to calculate the Boost converter input control *u*1, and the dynamic behavior is shown in the lower plots of such a figure. The second and third plots show the output voltage and output current dynamics, respectively; the controller adequately adapts voltage and current levels to achieve the CPL demand. Since power levels are achievable, the controller, besides stabilizing the converter, provides stable operating points for voltage and currents (inductor and output). In this test, the boost converter operates almost in DCM at all times because the duty cycle is calculated within zero and 0.85. For completeness purposes in the two last plots of Figure 12, the inductor current and the calculated duty cycle are shown. It is worth highlighting that using gains that do not accomplish conditions (26) and (27) or using regular proportional-integral controllers, unstable voltage, and current levels are obtained (not shown here). Regularly in such situations, the voltage suddenly increases, and the current falls, and the probability of devices' damage is very high.

A second CPL sweep of larger amplitudes is introduced to corroborate the controller's operation during the conduction mode changes. The associated dynamic behavior is presented in Figure 13. Note that in this case, up to 1 kW is demanded, and inductorcurrent peaks up to 200 A are reached. There are clear commutations from DCM to CCM and vice versa, in addition to significant changes in the inductor current. Despite the above, the CPL can be powered with acceptable voltage and current variations at the output. Although in the previous sweep, it was confirmed that fast changes to CCM were obtained, this test clearly proves that CCM is reached for long periods. In this severe scenario, the voltage gain limit of the converter is intentionally reached; oscillations are expected because the controller looks to increase the current to feed extremely high CPL levels.

**Figure 12.** CPL sweep in closed-loop operation. The duty cycle never reaches the upper limit (set to 0.95), and a DCM operation is achieved at almost all times.

**Figure 13.** CPL sweep in the closed-loop operation of the Boost converter. The duty cycle reaches the upper limit (set to 0.95), and it is not possible to compensate for the small oscillations in output voltage and current. This is an inherent characteristic of the Boost converter.

In the following, the results of the experimental tests in closed-loop are presented. The same Boost converter used for model validation in Section 3 is employed to perform the following experiments; however, the measurement of the output voltage and current must be performed to calculate the controller action (Equation (25)). The BK PRECISION-8510 electronic load is now programmed to consume constant power levels of 25, 50, 100, and 150 W. Figure 14 shows the four scenarios described; note that these signals are not averaged and are shown in different scales. At all the levels of CPL's power demand, it is possible to stabilize both the output voltage and the inductor current, and the CPL's power demand level is satisfied accordingly. It is worth mentioning that hard switching without any filters or snubbers is used; therefore, noise and a small transient staring at each MOSFET switch is expected. The used semiconductors are also generic (regular Si

and not SiC/GaN chemistry). Table 3 shows the efficiency at each level of power demand. The design of a high-efficiency production-level prototype is left for future research.

**Figure 14.** Output voltage (*v*), output current (*io*), and inductor current (*i*) for the Boost converter operating in closed-loop, with a CPL power demand of (**a**) 20, (**b**) 40, (**c**) 100, and (**d**) 135 W. 50 V/div is used for *v*, 1 A/div for *io*, and 5 A/div for *i* (the probe is configured for x/10). The output voltage and both currents are stabilized in the four scenarios despite the conduction mode type.

**Table 3.** Efficiency of the Boost converter operating in closed-loop.

