*4.2.3 Mode 3:* i*L\* =* i*<sup>L</sup>*

In this mode, the calculated inductor current is equal to the detected inductor current. This corresponds to a steady state, and because the input and output powers are ideally equal, the following relation holds:

$$\dot{\mathbf{u}}\_{\mathcal{L}}^{\*} = \dot{\mathbf{u}}\_{\mathcal{L}} \tag{13}$$

As a result, as the signal to be added to the output signal of the voltage compensator becomes zero, the duty ratio does not fluctuate.

These conditions are summarized in Eq. (14).

$$\begin{cases} \begin{aligned} \dot{\mathbf{i}}\_{\mathcal{L}} \,^\* &> \dot{\mathbf{i}}\_{\mathcal{L}} \\ \dot{\mathbf{i}}\_{\mathcal{L}} \,^\* &< \dot{\mathbf{i}}\_{\mathcal{L}} \end{aligned} & \text{if } P\_{\mathbf{o}} > P\_{\mathbf{i}} \\ \begin{aligned} \dot{\mathbf{i}}\_{\mathcal{L}} \,^\* &= \dot{\mathbf{i}}\_{\mathcal{L}} \end{aligned} & \text{if } P\_{\mathbf{o}} < P\_{\mathbf{i}} \\ \dot{\mathbf{i}}\_{\mathcal{L}} \,^\* &= \dot{\mathbf{i}}\_{\mathcal{L}} \quad \text{otherwise } (P\_{\mathbf{o}} = P\_{\mathbf{i}}) \end{aligned} \tag{14}$$

To sum up, the PBMC is a control method that always compares the input power and the output power and compensates for the difference if there is one. In the next sections, operation verification studies for the different control methods are reported.

### **5. Control design and simulation verification**

#### **5.1 Control design**

In this study, a comparative verification of the different control systems was performed using circuit simulations. **Table 1** shows the circuit constants of the

### *Power Balance Mode Control for Boost-Type DC-DC Converter DOI: http://dx.doi.org/10.5772/intechopen.82787*


#### **Table 1.**

inductor current *i*L\* increases according to the load. In contrast, the inductor current for detection increases. Therefore, until the input power becomes equal to the

*i*L

In this mode, the calculated inductor current *i*L\* is lower than the detected inductor current *i*L. An example would be the case in which a shift to a light load occurs. Because the output current suddenly extracts electric charge from the output capacitor, the calculated output *P*o\* power decreases. On the other hand, as the input voltage corresponds to a DC voltage source such as a battery, the voltage does not fluctuate significantly even when the load fluctuates. Therefore, the calculated inductor current *i*L\* decreases according to the load. In contrast, the inductor current for detection increases. Therefore, until the input power becomes equal to

*i*L

As a result, the signal to be added to the output signal of the voltage compensa-

In this mode, the calculated inductor current is equal to the detected inductor current. This corresponds to a steady state, and because the input and output

As a result, as the signal to be added to the output signal of the voltage compen-

<sup>∗</sup> > *i*<sup>L</sup> if *P*<sup>o</sup> > *P*<sup>i</sup>

<sup>∗</sup> < *i*<sup>L</sup> if *P*<sup>o</sup> < *P*<sup>i</sup>

<sup>∗</sup> <sup>¼</sup> *<sup>i</sup>*<sup>L</sup> otherwise ð Þ *<sup>P</sup>*<sup>o</sup> <sup>¼</sup> *<sup>P</sup>*<sup>i</sup>

To sum up, the PBMC is a control method that always compares the input power and the output power and compensates for the difference if there is one. In the next sections, operation verification studies for the different control methods are

In this study, a comparative verification of the different control systems was performed using circuit simulations. **Table 1** shows the circuit constants of the

*i*L

As a result, the signal to be added to the output signal of the voltage compensa-

<sup>∗</sup> > *i*<sup>L</sup> (11)

<sup>∗</sup> < *i*<sup>L</sup> (12)

<sup>∗</sup> <sup>¼</sup> *<sup>i</sup>*<sup>L</sup> (13)

(14)

output power, the relationship of Eq. (11) holds.

tor becomes positive and the duty ratio increases.

the output power, the relationship of Eq. (12) holds.

tor becomes negative and the duty ratio decreases.

powers are ideally equal, the following relation holds:

sator becomes zero, the duty ratio does not fluctuate. These conditions are summarized in Eq. (14).

> 8 ><

> >:

**5. Control design and simulation verification**

*i*L

*i*L

*i*L

*4.2.2 Mode 2:* i*L\* <* i*<sup>L</sup>*

*Control Theory in Engineering*

*4.2.3 Mode 3:* i*L\* =* i*<sup>L</sup>*

reported.

**258**

**5.1 Control design**

*Circuit parameters and specifications.*

single-phase boost-type DC-DC converter, which is the analysis circuit. The control systems were constructed using these circuit parameters.

To provide a reference for the responses of these control systems, the gain crossover frequencies of the loop transfer functions for the different control methods were designed to be equal. In addition, the voltage compensator for the PBMC used the same 2-pole-1-zero (type-2) compensator as the current mode control.
