**5. Simulation Results and Analysis**

In order to verify whether the proposed method has a faster convergence rate and loadresistance performance, for Buck converters with matched and unmatched disturbances, the proposed method was simulated and compared with the control methods in other works from the literature under the condition that the circuit parameters are the same. The results show that the proposed method can effectively suppress the influence of perturbation and ensure the stability of output voltage. It can improve the anti-interference performance of the whole system.

### *5.1. Simulation Model Construction*

The simulations are conducted in Simulink, using GPI observers to estimate the state and lumped disturbances of the system. Then, the estimated values of the observers are introduced into the controller for feedforward compensation, achieving fast and accurate tracking of the output voltage to the reference voltage. Select the input and output voltage, use the inductance current as feedback variables, and perform a high-order sliding-mode control algorithm to limit the calculated amplitude to prevent the switch from being in a continuous on or off state. Build a simulation model of a three-phase interleaved parallel bidirectional DC/DC converter in Simulink and write a sliding-mode control algorithm through the MATLAB function. The circuit uses ideal components, and the simulation diagram is shown in Figure 12.

**Figure 12.** Sliding-mode control simulation model.

#### *5.2. Set System Parameters*

The control objective of this simulation experiment is, under the same circuit system, sequentially use two methods to control, observe, and analyze the value of each state variable with time from the figure, compare the transient performance and resistance of the system under the control of the two methods' interference performance. In order to ensure the fairness of the comparison, the two methods should be simulated and compared under the same converter circuit system.

The effectiveness of the proposed control strategy is verified by the following simulation. The parameter values of the simulation experiment are shown in Table 3. To further illustrate the advantages, this paper compares the NDO-Integral SMC scheme with the GPIO-SMC scheme. A MATLAB simulation is used to compare the two methods:


**Table 3.** Parameters of simulation system.

In Method 2, the switching function of the system can be designed as follows:

$$\begin{cases} \mathbf{s} = \mathbf{k}\_1 \mathbf{x}\_1 + \mathbf{x}\_2 + \mathbf{d}\_1 + \mathbf{k}\_2 \int\_0^t \mathbf{x}\_1 \mathbf{d}t\\ \dot{\mathbf{s}} = \mathbf{k}\_1 (\mathbf{x}\_2 + \mathbf{d}\_1) + \dot{\mathbf{x}}\_2 + \dot{\mathbf{d}}\_1 + \mathbf{k}\_2 \mathbf{x}\_1 \end{cases} \tag{32}$$

Then, the switching signal is as follows:

$$\mathbf{u} = -\frac{\mathbf{L}\mathbf{C}}{\mathrm{V}\mathrm{in}0} \left[ \mathbf{k}\_{1} \left( \mathbf{x}\_{2} + \hat{\mathbf{d}}\_{1} \right) - \frac{\mathbf{x}\_{1} + \mathbf{v}\_{\mathrm{ref}}}{\mathrm{LC}} - \frac{\mathbf{x}\_{2}}{\mathrm{R}\mathrm{C}} + \hat{\mathbf{d}}\_{2} + \dot{\mathbf{d}}\_{1} + \dot{\mathbf{k}}\_{2}\mathbf{x}\_{1} + \eta\mathrm{sat}(\mathbf{s}) \right]\_{}^{\prime} \tag{33}$$

Since the observers used for load estimation provide composite controller reference values, it is necessary to first design their parameters to ensure that the observers can accurately estimate the power of the load. The size of gain *l*<sup>1</sup> and *l*<sup>2</sup> will affect the accuracy of the observer in tracking load power. In order to investigate the tracking effect of the *l*<sup>1</sup> size on the observer's load power, the parameters *k*1, *k*2, and *l*<sup>2</sup> are first fixed to 200, 1000, and 200, respectively, and the observer's observation effect is observed by setting different values. As shown in Figure 13a, when the CPL power jumps from 5 W to 10 W, the observer can quickly track the fluctuation of load power as the gain *l*<sup>1</sup> increases. The gain *l*<sup>1</sup> can be set to 1000.

**Figure 13.** Load estimation performance of l1 and l2 under different values: (**a**) load estimation response with different values of l1 and (**b**) load estimation response with different values of l2.

The same settings *k*<sup>1</sup> = 200 and *k*<sup>2</sup> = 1000, fix *l*<sup>1</sup> at 1000, and different values of *l*<sup>2</sup> will be set to observe the impact of their magnitude on the performance of load power fluctuation estimation. From Figure 13b, we can see that when *l*<sup>2</sup> < 2000, as *l*<sup>2</sup> increases, the observer's tracking effect on load power fluctuations remains almost unchanged. However, when *l*<sup>2</sup> < 2000, the observer was unable to accurately estimate the fluctuation of load power. To prevent the observer from being unable to track load-power fluctuations, the gain *l*<sup>2</sup> was set to 200.

Afterwards, it is necessary to adjust the relevant parameters of the composite controller. To obtain the impact of parameter changes on the DC bus voltage, first fix *k*<sup>1</sup> at 200 and observe the fluctuation of DC bus voltage by setting different values of *k*2, as shown in the Figure 14. From Figure 14a, it can be seen that, as *k*<sup>2</sup> increases, the time it takes for the bus voltage to recover to its steady-state value becomes shorter. However, when *k*<sup>2</sup> exceeds 1000, the time it takes for the bus voltage to recover to the stable value does not change, so *k*<sup>2</sup> will be set at 1000.

**Figure 14.** Load estimation performance of *k*<sup>1</sup> and *k*<sup>2</sup> under different values: (**a**) voltage tracking response with different values of *k*<sup>2</sup> and (**b**) voltage tracking response with different values of *k*1.

After obtaining *l*1, *l*2, and *k*2, analyze the impact of their values on the DC bus voltage by setting different *k*<sup>1</sup> values. From Figure 14b, it can be seen that as *k*<sup>1</sup> gradually increases, the fluctuation amplitude of the DC bus voltage increases. When *k*<sup>1</sup> = 1000, the DC bus voltage even exhibits oscillation, so *k*<sup>1</sup> can be set at 100.

#### *5.3. Analysis of Simulation Examples*

5.3.1. Keep the Constant Power Load and Change the Load Resistance

The load resistance experiences a sudden change during the simulation; that is, the resistance drops from 20 Ω to 10 Ω at 0.04 s and then rises to 20 Ω at 0.08 s.

For three-phase interleaved parallel converter systems with matched and unmatched disturbances, as shown in Figure 15a, both methods can make the output voltage rapidly approach the set reference value, and there is no steady-state error in the output voltage. However, it is clear from Figure 15a that the output voltage response time of Method 1 and Method 2 is about 0.005 s and 0.009 s, respectively, so Method 1 has a faster convergence speed. As shown in Figure 15b, although the overshoot of the inductance current in Method 1 is greater than that in Method 2, the rise time and adjustment time of Method 1 are about 0.002 s and 0.004 s respectively. Both are less than the rise time and adjustment time of Method 2. As shown in the controller output in Figure 15c, the response speed of controller output, u, in Method 1 is higher than that in Method 2, and the convergence time of the controller is shorter.

**Figure 15.** Comparison of output responses under load variation: (**a**) output voltage, (**b**) inductive current, (**c**) control input, and (**d**) load resistance.

Figure 16a,b capture the estimation effect of the GPI observer on the unmatched disturbance and the matched disturbance, respectively. From the comparison results in Table 4, it can be seen that at the moment 0.04 s, the resistance drops from 20 Ω to 10 Ω, and the estimated convergence time of the observer's sum is 0.014 s and 0.006 s, respectively. The resistance increases from 10 Ω to 20 Ω at 0.08 s, and the convergence time of the observer is 0.012 s and 0.007 s, respectively. It can be seen that when the load resistance changes abruptly, the GPI observer can quickly track the value of the disturbance and make an accurate estimation of and match the disturbance, thus further proving that the GPI observer has strong adaptability to the resistance load change in the system; that is, the observer has a fast response speed and good accuracy when estimating the system interference.


**Table 4.** Comparison of dynamic response of the proposed controller under changes in load resistance.

**Figure 16.** Estimate of the observer under load variation: (**a**) estimation of unmatched perturbations, d1; and (**b**) estimation of matching perturbations, d2.
