## 4 Results and Discussion
### Comparison with Conventional DI-SMC Scheme  
The tracking performance of the simplified DI-SMC circuit of the PWM dc-ac buck converter was compared with the conventional counterpart scheme presented in [3]. The proposed \(u_{1}\) and conventional \(u_{2}\) DI-SMC equations are given in (21) and (22), respectively. \[\left\{ \begin{array}{l}u_{1}=\gamma\big{[}K_{p}(V_{r}-\beta\overline{v}_{O})+K _{i}\int(V_{r}-\beta\overline{v}_{O})dt+\beta\overline{v}_{O}\big{]}\\ V_{T}=\gamma\beta\overline{v}_{I}\end{array} \right. \tag{21}\]  
\[\left\{ \begin{array}{l}u_{2}=\gamma\big{[}K_{p}(V_{r}-\beta v_{O})+K_{i}\int( V_{r}-\beta v_{O})dt-K_{c}i_{C}+\beta v_{O}\big{]}\\ V_{T}=\gamma\beta v_{I}\end{array} \right. \tag{22}\]  
To gain a fair comparison between the two controllers, the parameters \(K_{p}\), \(K_{i}\), \(\gamma\), and \(\beta\) in (21) and (22) are set to 27.5, 13.8 \(\times\) 10\({}^{4}\), 0.4, and 0.3571, respectively. The gain, \(K_{c}\), in the conventional DI-SMC equation is set to 1. The two control schemes are designed for the same dynamic buck converter parameters, as given in Table 1. It should be noted that (22) contains capacitor current \(i_{C}\) and constant gain \(K_{C}\) as part of the equivalent control equation. This control term requires a capacitor current sensor and other relevant components to be integrated into the control circuit. In contrast, the simplified control equation in (21) does not include this term, which reduces the control scheme's complexity and implementation cost. To investigate the tracking performance of the two control methods, the response under load disturbances is depicted in Figure 6a. The enlarged view of the response in Figure 6b shows that the conventional control scheme exhibits a percentage undershoot of 5.1% when the load resistance changes from 350 \(\Omega\) to 20 \(\Omega\) at \(t\) = 4 ms. However, the output voltage, \(v_{O}\), converges to the reference voltage within 100 \(\upmu\)s, and a steady-state error of 1.5% is generated under such load disturbance. It can be noticed that the transient response and the tracking capability of the conventional DI-SMC scheme are degraded. The switching frequency of the proposed and conventional control schemes has been compared in Figure 7. The ramp voltage, proposed control voltage, gate-to-source voltage, and output voltage of the proposed control scheme are shown in Figure 7a,b, whereas the corresponding waveforms of the conventional control scheme are depicted in  
Figure 6: (**a**) The tracking performance of the proposed and conventional control schemes under load disturbance. (**b**) Enlarged view of the transient response when the load changes from 350 \(\Omega\) to 20 \(\Omega\) at \(t\) = 4 ms. Figure 7a,b show that the output voltage of the closed-loop dynamic power supply is 3 V and 23 V when the duty cycle \(d\) of the gate-to-source voltage, \(v_{GS}\), is 10% and 90%, respectively. It can also be observed that the switching frequency of the proposed control method is maintained constant at 1 MHz. In contrast, the conventional control method produces a pulse width modulated signal with variable and high switching frequency, as shown in Figure 7c,d. Although the output voltage of the conventional control scheme tracks the reference voltage with a small steady-state error, operating the power converter at variable and high switching frequencies is not acceptable since it creates issues with filter design and EMI requirements [3]. Table 2 summarizes the comparison between the two control methods. In the conventional control equation, the large \(K_{C}\) value amplifies the noise accompanied by the output capacitor current, which is related to the time derivative of the output voltage by \(C\frac{d\vec{v}_{C}}{dt}=i_{C}\), where \(v_{C}\approx v_{O}\). The amplified noise affects the controller action, degrades the  
Figure 7: The ramp voltage, control voltage, gate-to-source voltage, and output voltage of the (**a,b**) proposed and (**c,d**) conventional control schemes.